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An Embodied Multiagent Framework Based on Token Communications for Cooperative ISAC
Jiahe Guo, Jun Du, Chunxiao Jiang, Jintao Wang
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 95%
Last extracted: 10/9/2026, 7:15:13 AM
Summary
This paper proposes the State-Intent Token Communications (SI-TokCom) framework for cooperative Integrated Sensing and Communication (ISAC) networks using embodied Unmanned Aerial Vehicle (UAV) agents. To address the high signaling overhead and latency associated with exchanging full local states in dynamic environments, the framework utilizes discrete semantic tokens (S-Tokens for state, I-Tokens for intent) via pretrained codebooks. The system formulates a joint optimization problem to minimize propulsion energy while meeting communication and sensing rate constraints, solved using Multi-Agent Proximal Policy Optimization (MAPPO) combined with closed-form beamforming updates. Simulation results demonstrate that SI-TokCom achieves near-centralized performance (98.9% communication and 99.1% sensing rates) with significantly reduced communication payload compared to baselines.
Entities (8)
Relation Signals (7)
Jiahe Guo → affiliatedwith → Tsinghua University
confidence 99% · Jiahe Guo... are with the Department of Electronic Engineering, Tsinghua University
UAV → supports → ISAC
confidence 96% · unmanned aerial vehicle (UAV)-enabled integrated sensing and communication (ISAC)
SI-TokCom → uses → TokCom
confidence 95% · this paper investigates a cooperative ISAC network of embodied UAV agents and formulates a joint token communications (TokCom) and physical control problem
SI-TokCom → utilizes → S-Token
confidence 94% · separate shared state token (S-Token) and intent token (I-Token) codebooks to represent current operating states
SI-TokCom → utilizes → I-Token
confidence 94% · intent token (I-Token) codebooks to represent current operating states and intended behavior
SI-TokCom → optimizes → propulsion energy
confidence 93% · formulates a joint token communications (TokCom) and physical control problem to minimize total propulsion energy
SI-TokCom → employs → MAPPO
confidence 92% · design an online alternating optimization algorithm using MAPPO for token selection and composition
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Abstract
Abstract:The emerging low-altitude economy demands unmanned aerial vehicle (UAV)-enabled integrated sensing and communication (ISAC) for reliable connectivity and environmental awareness. In particular, embodied UAV agents offer a promising means of supporting autonomous operations through a closed loop linking perception, decision-making, and physical actions. However, each UAV has access only to local observations, and effective cooperation requires exchanging local states and intentions. Directly sharing such information can incur substantial signaling overhead and hinder timely coordination in dynamic environments. To deal with this problem, this paper investigates a cooperative ISAC network of embodied UAV agents and formulates a joint token communications (TokCom) and physical control problem to minimize total propulsion energy subject to communication and sensing rate requirements. Then, we propose a state--intent TokCom (SI-TokCom) framework driven by multi-agent embodied policy learning. Specifically, separate pretrained codebooks enable compact exchanges of local states and intentions, while UAV agents jointly learn to select and compose tokens and determine physical actions based on local observations and received tokens. Simulation results show that SI-TokCom achieves 98.9\% and 99.1\% of the centralized baseline's communication and sensing rates, respectively. Compared with the local baseline, it improves the corresponding rates by 5.0\% and 43.6\%, respectively, with essentially unchanged propulsion energy. These results highlight the potential of TokCom for communication-efficient cooperation among embodied UAV agents in ISAC systems.
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- Source: https://arxiv.org/abs/2610.11434v1
- Canonical: https://arxiv.org/abs/2610.11434v1
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An Embodied Multiagent Framework Based on Token Communications for Cooperative ISACThanks: Jiahe Guo, Jun Du, and Jintao Wang are with the Department of Electronic Engineering, Tsinghua University, Beijing 100084, China. Jun Du and Jintao Wang are also with the State Key Laboratory of Space Network and Communications, Tsinghua University, Beijing 100084, China (e-mail: guojiahe1020@163.com; jundu@tsinghua.edu.cn; wangjintao@tsinghua.edu.cn).Thanks: Chunxiao Jiang is with Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China, and also with the State Key Laboratory of Space Network and Communications, Tsinghua University, Beijing 100084, China (e-mail: jchx@tsinghua.edu.cn). Jiahe Guo Jun Du Affiliation: Chunxiao Jiang, , and Jintao Wang, Abstract The emerging low-altitude economy demands unmanned aerial vehicle (UAV)-enabled integrated sensing and communication (ISAC) for reliable connectivity and environmental awareness. In particular, embodied UAV agents offer a promising means of supporting autonomous operations through a closed loop linking perception, decision-making, and physical actions. However, each UAV has access only to local observations, and effective cooperation requires exchanging local states and intentions. Directly sharing such information can incur substantial signaling overhead and hinder timely coordination in dynamic environments. To deal with this problem, this paper investigates a cooperative ISAC network of embodied UAV agents and formulates a joint token communications (TokCom) and physical control problem to minimize total propulsion energy subject to communication and sensing rate requirements. Then, we propose a state–intent TokCom (SI-TokCom) framework driven by multi-agent embodied policy learning. Specifically, separate pretrained codebooks enable compact exchanges of local states and intentions, while UAV agents jointly learn to select and compose tokens and determine physical actions based on local observations and received tokens. Simulation results show that SI-TokCom achieves 98.9% and 99.1% of the centralized baseline’s communication and sensing rates, respectively. Compared with the local baseline, it improves the corresponding rates by 5.0% and 43.6%, respectively, with essentially unchanged propulsion energy. These results highlight the potential of TokCom for communication-efficient cooperation among embodied UAV agents in ISAC systems. Index Terms: Embodied intelligence, integrated sensing and communication, reinforcement learning, token communications. I Introduction Sixth-generation (6G) wireless networks are envisioned to support emerging applications that require both high-quality communication and accurate environmental sensing [1, 2]. With the rapid growth of wireless services, the demand for spectrum and hardware resources for communication and sensing is continuously increasing. Since radar sensing and wireless communication systems exhibit significant commonality in spectrum usage and radio frequency (RF) front-end architectures, integrating these two functionalities has become a promising approach to improve spectral and hardware efficiency. This trend has led to the emergence of integrated sensing and communication (ISAC) [3]. Meanwhile, the emerging low-altitude economy (LAE) is driving demand for embodied unmanned aerial vehicle (UAV) agents that integrate perception, autonomous decision-making, and action in a closed loop [4]. Embodied agents can enhance the operational flexibility of ISAC, motivating cooperative multi-UAV ISAC, where agents coordinate their mobility and resource allocation to serve geographically distributed users and targets [5]. However, conventional optimization methods for multi-UAV ISAC often involve high computational complexity and rely on detailed prior knowledge of the system. Specifically, joint mobility control and resource allocation require frequent exchanges of local states and intended actions [6], as UAV movement directly affects wireless channels, sensing geometry, and propulsion energy consumption [7, 8]. These exchanges can consume substantial communication resources and introduce transmission delays. Moreover, iterative optimization algorithms may incur additional computational latency [7]. The resulting delays can render shared information outdated and impair coordinated decision-making [9]. The challenge is therefore to achieve energy-efficient mobility control and resource allocation in real time under highly dynamic and stochastic conditions. Recent advances in artificial intelligence (AI) and the emergence of embodied agents offer new opportunities for lightweight coordination in multi-UAV ISAC systems through learning-based control and semantic communication (SemCom). Instead of transmitting raw observations or full-dimensional features, SemCom exchanges task-relevant information to reduce signaling overhead [10]. However, practical implementations may still rely on complex models with substantial computational and memory costs. Recently, token communications (TokCom) have emerged as a promising approach for conveying information through discrete semantic tokens associated with shared embeddings, allowing agents to exchange compact indices instead of full-dimensional representations [11, 12]. For cooperative UAV-enabled ISAC, such compact exchanges can reduce signaling overhead and transmission latency while providing decision-relevant information for coordinated mobility control and resource allocation [13]. TokCom can therefore serve as a communication enabler for embodied UAV agents, supporting timely cooperation within the perception-action loop [14, 15]. I-A Related Work I-A1 Cooperative ISAC Existing studies have investigated cooperative ISAC among multiple base stations (BSs) [16, 17] and extended this research to UAV-enabled networks. Iterative optimization approaches have been widely adopted for cooperative ISAC [18, 19]. In particular, the authors in [20] developed a centralized alternating optimization framework for UAV deployment and resource allocation. Xiu et al. [21] proposed an iterative optimization algorithm based on block coordinate descent (BCD) and successive convex approximation (SCA) for ISAC. Learning-based methods have also been explored for adaptive UAV coordination [22, 23]. Wang et al. [24] proposed hierarchical graph-based multi-agent reinforcement learning (MARL), combining global coordination at the BS with local decision-making by UAVs. A centralized soft actor–critic approach was developed for joint trajectory planning and resource allocation in [25], while MARL was employed for distributed sensing and communication coordination in [26]. Learning-based cooperation has further been extended to integrated sensing, communication, and computation [27], including attention-assisted multi-agent proximal policy optimization (MAPPO) for cooperative trajectory and resource control [28]. More recently, SemCom has been explored to reduce signaling overhead by conveying compact, task-relevant representations. Existing studies have investigated task-oriented information exchange in cooperative UAV networks [29], including multimodal semantic transmission for relay cooperation [30]. For UAV-assisted ISAC, Guo et al. [31] combined perception-enhanced multimodal semantic transmission with semantic-aware resource allocation. Nevertheless, existing approaches may still incur substantial overhead from state exchange, iterative computation, or the transmission of continuous semantic representations. Efficient information exchange among UAVs under limited energy budgets remains insufficiently explored. I-A2 TokCom Building on SemCom, TokCom uses tokens as common units for semantic representation, processing, and transmission [11]. An early framework [12] exploited foundation models and cross-modal context for efficient semantic transmission. For compact token learning, Wei et al. [32] adopted an information bottleneck approach to preserve essential multimodal information. A geometric method [33] selects informative tokens through cross-modal dependencies under latency constraints. The authors in [34] used a shared masked language model for joint token masking and detection, reducing redundant transmissions and enabling context-assisted recovery. Research has further extended TokCom to wireless transmission and network coordination. Hierarchical TokCom [35] exploits semantic similarity to improve transmission robustness, while Ada-TokenCom [36] jointly adapts token compression and transmission schemes to channel conditions. Qiao et al. [37] proposed token-domain multiple access with context-assisted token recovery for concurrent uplink transmissions. For distributed multimodal sensing, AirTF [38] exploits wireless signal superposition to fuse spatially aligned tokens. At the system level, Jiang et al. [39] introduced agentic TokCom to adapt communication workflows to task and resource requirements. These studies focus on token representation and transmission efficiency. However, using TokCom to support cooperation among embodied agents remains insufficiently explored in the literature. I-B Motivation and Contributions Despite these advances, efficient information exchange remains a practical challenge for cooperative UAV-enabled ISAC. Centralized coordination requires global state collection and control dissemination, incurring signaling overhead and delay. Although SemCom can reduce data volume, its representations and associated models still incur communication, computation, and memory costs. Recent advances in TokCom motivate its application to this setting, using compact tokens to represent UAV states and intended actions. However, the value of exchanged tokens depends on their influence on the recipients’ subsequent decisions, which are shaped by local observations and physical constraints. This coupling calls for jointly optimizing token selection and composition with mobility control and resource allocation under limited communication payload and energy budgets. To address these challenges, we propose a state–intent TokCom (SI-TokCom) framework that integrates offline semantic codebook pretraining with online token exchange and physical control. During execution, embodied UAV agents coordinate their decisions using local observations and received tokens, supported by analytical beamforming updates. The main contributions are summarized as follows. • We formulate a cooperative multi-UAV ISAC problem that couples token codebook design and selection with UAV trajectories, user association, bandwidth allocation, transmit power, and beamforming to minimize total propulsion energy under communication and sensing rate requirements. We derive the position Fisher information matrix (FIM) and the corresponding squared position error bound (SPEB) for cooperative target localization. The sequential decision process is modeled as a decentralized partially observable Markov decision process (Dec-POMDP). • We develop separate shared state token (S-Token) and intent token (I-Token) codebooks to represent current operating states and intended behavior, respectively. Offline pretraining combines vector quantization (VQ), semantic reconstruction, expert-action consistency, and codeword-usage regularization to retain decision-relevant information. The codebooks and semantic decoders are subsequently frozen, preserving shared semantic mappings while token selection and composition adapt through online policy learning. • We design an online alternating optimization algorithm using MAPPO for token selection and composition followed by mixed discrete and continuous physical decisions, with closed-form beamforming updates. Counterfactual token masking assigns token-specific credit by evaluating changes in the team reward. Closed-form beamforming updates are derived by applying the Karush–Kuhn–Tucker (KKT) conditions to the subproblems reformulated via fractional programming (FP). This decomposition removes complex-valued beamforming matrices from the learned action space. • We perform numerical simulations to evaluate the performance of the proposed SI-TokCom framework. In the evaluated setting, SI-TokCom uses a coordination payload of 96 bits per UAV per time slot and achieves 98.9% and 99.1% of the centralized baseline’s communication and sensing rates, respectively. It also improves the communication and sensing rates by 5.0% and 43.6%, respectively, over the baseline with essentially unchanged propulsion energy. In addition, we evaluate the SPEB to characterize localization performance. Token ablations, trajectory examples, and codebook-usage comparisons further illustrate the learned coordination behavior. I-C Organization and Notation The remainder of this paper is organized as follows. Section I presents the system model and problem formulation. Section I develops the proposed SI-TokCom framework, including offline codebook pretraining and online alternating optimization. Section IV presents the simulation results, and Section V concludes the paper. Notation: (⋅)T(·)^T, (⋅)H(·)^H, and (⋅)−1(·)^-1 denote transpose, conjugate transpose, and inverse, respectively. |⋅||·| denotes the absolute value or modulus of a scalar. []i,j[A]_i,j denotes the (i,j)(i,j)th entry of matrix A. ⋆A denotes an optimal solution for the matrix variable A. ∥⋅∥2\|·\|_2 and ∥⋅∥F\|·\|_F denote the Euclidean and Frobenius norms, respectively. ⋅E\·\ denotes expectation. Im⋅Im\·\ denotes the imaginary part of a complex scalar or matrix. tr(⋅)tr(·) denotes the matrix trace, and diag(⋅)diag(·) constructs a diagonal matrix from its arguments. nI_n denotes the n×n× n identity matrix, and [x]+≜maxx,0[x]^+ \x,0\. sg[⋅]sg[·] denotes the stop-gradient operator. DKL(⋅∥⋅)D_ KL(·\|·) denotes the Kullback–Leibler (KL) divergence between two probability distributions. I System Model and Problem Formulation As illustrated in Fig. 1, we consider a cooperative multi-UAV ISAC system comprising K UAVs, NcN_c ground communication users (CUs), and NsN_s ground sensing targets (STs) over NTN_T time slots. The UAVs cooperatively provide data services to the CUs and perform detailed sensing of the STs based on coarse prior estimates of their positions [40]. Their index sets are denoted by ≜1,…,KK \1,…,K\, ≜1,…,NcC \1,…,N_c\, ≜1,…,NsS \1,…,N_s\, and ≜1,…,NTT \1,…,N_T\, respectively. Each UAV is equipped with an M-element transmit antenna array and a single receive antenna, while each CU has a single receive antenna. The position and velocity of UAV k in time slot t are denoted by k[t]≜[xk[t],yk[t],H]T∈ℝ3q_k[t] [x_k[t],y_k[t],H]^T ^3 and k[t]∈ℝ3v_k[t] ^3, respectively, with k[t+1]=k[t]+Tk[t]q_k[t+1]=q_k[t]+Tv_k[t], where t is the slot index and T is the duration of each slot. All UAVs fly at the same constant altitude H. The fixed ground positions of CU i and ST j are denoted by ic≜[xic,yic,0]Tp_i^c [x_i^c,y_i^c,0]^T and js≜[xjs,yjs,0]Tp_j^s [x_j^s,y_j^s,0]^T, respectively. Fig. 1: Cooperative multi-UAV ISAC system. The slot-level cooperative protocol is illustrated in Fig. 2. At the beginning of each time slot, the UAVs exchange compact semantic tokens over air-to-air links. Based on their local observations and received tokens, the UAVs determine their trajectory and resource allocation decisions in a distributed manner, and subsequently provide downlink communication services to the CUs while cooperatively sensing the STs. Fig. 2: Slot-level cooperative protocol for the multi-UAV ISAC system. I-A Channel Model Given the dominant line-of-sight (LoS) propagation in UAV-assisted networks, we adopt a far-field LoS channel model. The distances from UAV k to CU i and ST j in time slot t are denoted by dk,ic[t]=∥k[t]−ic∥2d_k,i^c[t]= _k[t]-p_i^c _2 and dk,js[t]=∥k[t]−js∥2d_k,j^s[t]= _k[t]-p_j^s _2, respectively. For the M-element uniform linear array, the steering vector toward angle θ is given by [41] (θ)=[1,eȷ2πdaλcosθ,…,eȷ2πdaλ(M−1)cosθ]T,a(θ)= [1,e 2π d_aλ θ,…,e 2π d_aλ(M-1) θ ]^T, (1) where dad_a and λ denote the antenna spacing and carrier wavelength, respectively. Accordingly, the channel from UAV k to CU i is modeled as k,ic[t]=β0(dk,ic[t])−αck,ic(θk,ic[t]),h_k,i^c[t]= _0 (d_k,i^c[t] )^- _ ca_k,i^c ( _k,i^c[t] ), (2) where β0 _0 is the reference channel power gain and αc _ c is the path-loss exponent. For monostatic sensing, the round-trip channel between UAV k and ST j is expressed as k,js[t]=ρk,js[t](k,js(θk,js[t]))H,g_k,j^s[t]= _k,j^s[t] (a_k,j^s ( _k,j^s[t] ) )^H, (3) where ρk,js[t]=βs(dk,js[t])−4 _k,j^s[t]= _ s (d_k,j^s[t] )^-4 denotes the monostatic sensing channel amplitude coefficient, and βs _ s is the effective sensing reflection gain. I-B Communication and Sensing Signal Model To characterize the association between UAVs and CUs, we define the binary variable αk,i[t]∈0,1 _k,i[t]∈\0,1\, where αk,i[t]=1 _k,i[t]=1 indicates that CU i is served by UAV k at time slot t, and αk,i[t]=0 _k,i[t]=0 otherwise. Each CU is associated with one UAV, satisfying ∑k∈αk,i[t]=1,∀i∈ _k _k,i[t]=1,∀ i . We adopt frequency-division multiple access for downlink transmission, where UAV k allocates an orthogonal subchannel with bandwidth bk,i[t]b_k,i[t] to each associated CU i. On the subchannel assigned to CU i, UAV k transmits one communication stream and NsN_s dedicated sensing streams. The corresponding stream vector is defined as k,i[t]=[sk,i[t],sk,i,s1[t],…,sk,i,sNs[t]]T∈ℂ(Ns+1)×1s_k,i[t]= [s_k,i[t],s_k,i,s_1[t],…,s_k,i,s_N_s[t] ]^T ^(N_s+1)× 1, where sk,i[t]s_k,i[t] denotes the information symbol intended for CU i, while sk,i,sj[t]s_k,i,s_j[t] denotes the dedicated sensing symbol transmitted by UAV k over subchannel i for ST j. All streams are assumed to be mutually independent complex Gaussian random variables with zero mean and unit variance, satisfying k,i[t]k,i[t]H=E\s_k,i[t]s_k,i[t]^H\=I. The corresponding transmit beamforming matrix is expressed as k,i[t]= _k,i[t]= [k,i[t]⏟for communication and sensing, [ w_k,i[t]_ subarraycfor communication and sensing subarray, (4) k,i,s1[t],…,k,i,sNs[t]⏟dedicated for sensing]∈ℂM×(Ns+1). w_k,i,s_1[t],…,w_k,i,s_N_s[t]_dedicated for sensing] ^M×(N_s+1). Thus, the received signal at CU i served by UAV k is yk,ic[t] y_k,i^c[t] =k,ic[t]Hk,i[t]sk,i[t] =h_k,i^c[t]^Hw_k,i[t]s_k,i[t] (5) +∑r=1Nsk,ic[t]Hk,i,sr[t]sk,i,sr[t]+nk,ic[t], + _r=1^N_sh_k,i^c[t]^Hw_k,i,s_r[t]s_k,i,s_r[t]+n_k,i^c[t], where nk,ic[t]∼(0,N0bk,i[t])n_k,i^c[t] (0,N_0b_k,i[t]) denotes the additive white Gaussian noise, and N0N_0 is its power spectral density. Accordingly, the achievable communication rate over the link between UAV k and CU i is expressed in terms of the signal-to-interference-plus-noise ratio (SINR) as Rk,ic[t]=bk,i[t]log2(1+SINRk,i[t]),R_k,i^c[t]=b_k,i[t] _2 (1+SINR_k,i[t] ), (6) where SINRk,i[t]=|k,ic[t]Hk,i[t]|2∑r=1Ns|k,ic[t]Hk,i,sr[t]|2+N0bk,i[t].SINR_k,i[t]= |h_k,i^c[t]^Hw_k,i[t] |^2 _r=1^N_s |h_k,i^c[t]^Hw_k,i,s_r[t] |^2+N_0b_k,i[t]. (7) The communication rate of CU i is Ric[t]=∑k=1Kαk,i[t]Rk,ic[t]R_i^c[t]= _k=1^K _k,i[t]R_k,i^c[t]. Meanwhile, both the communication and dedicated sensing streams are exploited for monostatic sensing. We assume that the echoes reflected by different STs have resolvable round-trip delays and can therefore be separated through delay-domain matched filtering. Hence, no inter-target interference remains after signal processing. For an active subchannel assigned to CU i, the processed echo associated with ST j at UAV k is given by yk,j,is[t]=k,js[t]k,i[t]k,i[t]+nk,j,is[t],y_k,j,i^s[t]=g_k,j^s[t]W_k,i[t]s_k,i[t]+n_k,j,i^s[t], (8) where nk,j,is[t]∼(0,N0bk,i[t])n_k,j,i^s[t] (0,N_0b_k,i[t]) denotes the sensing noise. Echoes from different STs can be separated in the delay domain owing to their resolvable propagation-delay differences, thereby suppressing inter-target interference [42]. Accordingly, the sensing signal-to-noise ratio (SNR) is given by γk,j,is[t]=αk,i[t]Gp‖ρk,js[t]k,js[t]Hk,i[t]‖22N0bk,i[t], _k,j,i^s[t]= _k,i[t]G_p \| _k,j^s[t]a_k,j^s[t]^HW_k,i[t] \|_2^2N_0b_k,i[t], (9) where GpG_p is the processing gain of the matched filter. Accordingly, the aggregate sensing rate contributed by subchannel i of UAV k is given by [43] Rk,is[t]=∑j=1Nsbk,i[t]log2(1+γk,j,is[t]).R_k,i^s[t]= _j=1^N_sb_k,i[t] _2 (1+ _k,j,i^s[t] ). (10) The contribution for ST j is denoted by Rk,j,is[t]=bk,i[t]log2(1+γk,j,is[t])R_k,j,i^s[t]=b_k,i[t] _2(1+ _k,j,i^s[t]), so that Rk,is[t]=∑j=1NsRk,j,is[t]R_k,i^s[t]= _j=1^N_sR_k,j,i^s[t]. The overall sensing rate is then expressed as Rs[t]=∑k=1K∑i=1Ncαk,i[t]Rk,is[t]R^s[t]= _k=1^K _i=1^N_c _k,i[t]R_k,i^s[t]. I-C TokCom for Inter-UAV Coordination To alleviate the partial observability of decentralized UAV control under a fixed communication budget, each UAV broadcasts a compact semantic message to the other UAVs. The message consists of two complementary token types: the S-Token, which summarizes the current local state, and the I-Token, which conveys the locally intended behavior. The set of token types is denoted by =S,IG=\S,I\. For each token type g∈g , all UAVs share an offline-pretrained semantic codebook ℰg=g,n∈ℝDgtokn=1Ngtok,E_g= \e_g,n ^D_g tok \_n=1^N_g tok, (11) where g,ne_g,n denotes the nnth embedding in ℰgE_g, while NgtokN_g tok and DgtokD_g tok denote the corresponding codebook size and embedding dimension, respectively. During online policy learning, the codebooks are frozen, and UAV k selects the token index in each slot according to mk,g,l[t]∼πθk,gtok(⋅∣k[t]),mk,g,l[t]∈1,…,Ngtok,m_k,g,l[t] _ _k,g tok (· _k[t] ), m_k,g,l[t]∈\1,…,N_g tok\, (12) where πθk,gtok _ _k,g tok denotes the token selection and composition policy of UAV k for type g, parameterized by θk,g _k,g, and k[t]o_k[t] is the local observation of UAV k at time slot t. The variable mk,g,l[t]m_k,g,l[t] denotes the token index selected for the llth message slot of type g. These selected indices form the type-g token sequence generated by UAV k, given by k,g[t]=[mk,g,1[t],…,mk,g,Lg[t]],g∈,m_k,g[t]= [m_k,g,1[t],…,m_k,g,L_g[t] ],g , (13) where LgL_g denotes the number of token slots for type g. The complete token message is formed by concatenating the S-Token and I-Token sequences as k[t]=[k,S[t],k,I[t]]m_k[t]= [m_k,S[t],m_k,I[t] ]. The slot count and the semantic role of each slot remain fixed throughout online training and execution, while different token combinations across these slots convey different message semantics. The semantic codebooks and decoders are pretrained offline and subsequently frozen to preserve a shared semantic basis. Token selection and composition are jointly optimized with the control policy, allowing context-dependent inter-UAV coordination to emerge through collaborative policy learning. I-D Problem Formulation UAV energy consumption mainly consists of the energy required for inter-UAV token transmission and mobility. Owing to the small token payload, the corresponding transmission energy is typically several orders of magnitude lower than the propulsion energy. Therefore, the token transmission energy is neglected, and only the UAV propulsion energy is considered. The propulsion power is modeled as a function of the UAV flight speed, given by Pkfly[t]=P0+12ρairACD‖k[t]‖23+Pi1+‖k[t]‖244v04,P_k fly[t]=P_0+ 12 _ airAC_D \|v_k[t] \|_2^3+P_i 1+ \|v_k[t] \|_2^44v_0^4, (14) where P0P_0 and PiP_i denote the blade-profile power and induced power, respectively, ρair _ air is the air density, A is the rotor-disc area, CDC_D is the drag coefficient, and v0v_0 is the mean rotor-induced velocity. Accordingly, the propulsion energy consumed by UAV k during time slot t is Ekfly[t]=Pkfly[t]TE_k fly[t]=P_k fly[t]T. The total propulsion energy consumed by all UAVs over the considered time horizon is therefore given by Efly=∑t=1NT∑k=1KEkfly[t]E fly= _t=1^N_T _k=1^KE_k fly[t]. We jointly optimize the UAV velocities =k[t]V=\v_k[t]\, UAV–CU associations =αk,i[t]A=\ _k,i[t]\, bandwidth allocation =bk,i[t]B=\b_k,i[t]\, link power allocation =pk,i[t]P=\p_k,i[t]\, and transmit beamforming matrices =k,i[t]W=\W_k,i[t]\. Let ≜mk,g,l[t]∣k∈,g∈,l=1,…,LgM \m_k,g,l[t] k ,g ,l=1,…,L_g\ denote the collection of token indices selected by all UAVs, and let ℰ≜ℰgg∈E \E_g\_g denote the collection of codebooks. The energy-minimization problem is formulated as 1 _1 minℰ,,,,,,∑t=1NT∑k=1KEkfly[t] E,M,V,A,B,P,Wmin _t=1^N_T _k=1^KE_k fly[t] (15a) s.t. .t. Ric[t]≥Rmin,ic,∀i,t, R_i^c[t]≥ R_ ,i^c,∀ i,t, (15b) Rs[t]≥Rmins,∀t, R^s[t]≥ R_ ^s,∀ t, (15c) ∑k=1Kαk,i[t]=1,αk,i[t]∈0,1,∀k,i,t, _k=1^K _k,i[t]=1, _k,i[t]∈\0,1\,∀ k,i,t, (15d) ∑i=1Ncbk,i[t]≤Bk,∀k,t, _i=1^N_cb_k,i[t]≤ B_k,∀ k,t, (15e) ∑i=1Ncpk,i[t]≤Pkmax,∀k,t, _i=1^N_cp_k,i[t]≤ P_k ,∀ k,t, (15f) ‖k,i[t]‖F2≤pk,i[t],∀k,i,t, \|W_k,i[t] \|_F^2≤ p_k,i[t],∀ k,i,t, (15g) ‖k[t]‖2≤Vkmax,∀k,t, \|v_k[t] \|_2≤ V_k ,∀ k,t, (15h) ‖k[t]−ℓ[t]‖2≥Dmin,∀k≠ℓ,t, \|q_k[t]-q_ [t] \|_2≥ D_ ,∀ k≠ ,t, (15i) where Rmin,icR_ ,i^c is the minimum required communication rate of CU i, and RminsR_ ^s is the minimum required aggregate sensing rate. BkB_k, PkmaxP_k , and VkmaxV_k specify the bandwidth, transmit power, and speed limits of UAV k, respectively, while DminD_ denotes the minimum inter-UAV separation. Constraints (15b) and (15c) impose the communication and sensing requirements, respectively. Constraint (15d) associates each CU with exactly one UAV in each time slot. Constraints (15e) and (15f) enforce the bandwidth and power budgets of each UAV, while (15g) bounds each link’s beamforming power by its allocated power. Finally, (15h) limits UAV speed, and (15i) maintains the prescribed inter-UAV separation. Problem 1P_1 involves discrete association and token decisions coupled with UAV mobility and resource allocation. Moreover, decentralized execution requires each UAV to coordinate its decisions using local observations and limited information exchange. I Multi-Agent Embodied Policy-Driven SI-TokCom Framework I-A Overview and Dec-POMDP Formulation To address the coupled optimization problem 1P_1, we propose an SI-TokCom framework driven by multi-agent embodied policy learning. Treating each UAV as an embodied agent, we formulate the sequential decision process as a Dec-POMDP ⟨,st,~kk∈,kk∈,rkk∈,γ⟩ ,s_t,\ o_k\_k ,\u_k\_k ,\r_k\_k ,γ , where st∈s_t is the global state at time slot t, ~k o_k, ku_k, and rkr_k denote the state, action, and reward of UAV k∈k , respectively, and γ is the discount factor. The detailed formulations are as follows. I-A1 State Space At time slot t, the state of UAV k can be expressed as ~k[t]=[k[t],k[t]] o_k[t]= [o_k[t],c_k[t] ], where k[t]c_k[t] is the aggregated semantic representation constructed from the received token messages, given by k[t]=Concatℓ∈∖k(S(ℓ,S[t]),I(ℓ,I[t])),c_k[t]= Concat_ \k\ (D_S (m_ ,S[t] ),D_I (m_ ,I[t] ) ), (16) where S(⋅)D_S(·) and I(⋅)D_I(·) denote the frozen semantic decoders. Moreover, k[t]o_k[t] can be expressed as k[t]=[kself[t],k,ic[t]i∈,k,js[t]j∈]∈k,o_k[t]= [o_k self[t], \o_k,i^c[t] \_i , \o_k,j^s[t] \_j ] _k, (17) where kself[t]=[k[t],k[t],Ekr[t],k[t−1],k[t−1],k[t−1]]o_k self[t]=[q_k[t],v_k[t],E_k r[t], α_k[t-1],b_k[t-1], _k[t-1]]. Here, Ekr[t]E_k r[t] denotes the remaining onboard energy of UAV k, k[t−1]≜[αk,i[t−1]]i∈ α_k[t-1] [ _k,i[t-1] ]_i , k[t−1]≜[bk,i[t−1]]i∈b_k[t-1] [b_k,i[t-1] ]_i , and k[t−1]≜[pk,i[t−1]]i∈p_k[t-1] [p_k,i[t-1] ]_i . Moreover, k,ic[t]=ic−k[t]o_k,i^c[t]=p_i^c-q_k[t] and k,js[t]=js−k[t]o_k,j^s[t]=p_j^s-q_k[t] characterize the relative positions of CU i and ST j, respectively, where ^js[t] p_j^s[t] denotes the estimated position of ST j. I-A2 Action Space The action of UAV k is defined as k[t]=mk,g,l[t]∀g,∀l,k[t],αk,i[t],bk,i[t],pk,i[t],k,i[t]i∈u_k[t]=\\m_k,g,l[t]\_∀ g,∀ l,v_k[t],\ _k,i[t],b_k,i[t],p_k,i[t],W_k,i[t]\_i \. The beamforming matrices are included in the joint action but updated via closed-form solutions, avoiding the difficulty of learning complex-valued outputs. I-A3 Surrogate Reward For policy learning, we adopt a penalty-relaxed surrogate of 1P_1 that penalizes communication and sensing rate shortfalls to encourage constraint satisfaction. The surrogate reward of UAV k is defined as rk[t]= r_k[t]= wc∑i=1NcRic[t]+wsRs[t]−wEEfly[t]−k[t] w_ c _i=1^N_cR_i^c[t]+w_ sR^s[t]-w_ EE fly[t]-P_k[t] (18) +η(ck[t]−1K∑ℓ=1Kcℓ[t]), +η (c_k[t]- 1K _ =1^Kc_ [t] ), where Efly[t]≜∑ℓ=1KEℓfly[t]E fly[t] _ =1^KE_ fly[t]. The penalty term k[t]P_k[t] is given by k[t]=wcPNc∑i=1Nc[1−Ric[t]Rmin,ic]++wsP[1−Rs[t]Rmins]++kphy[t]P_k[t]= w_ c PN_c _i=1^N_c [1- R_i^c[t]R_ ,i^c ]^++w_ s P [1- R^s[t]R_ ^s ]^++P_k phy[t], where kphy[t]P_k phy[t] penalizes the mobility, safety-distance, bandwidth, power, and energy constraint violations associated with UAV k. The term ck[t]c_k[t] measures its local communication and sensing contributions, flight energy, and service load. The local term improves credit assignment without changing the average team reward. Building on the above Dec-POMDP formulation, the proposed SI-TokCom framework comprises the following two stages, as shown in Fig. 3: • Offline codebook pretraining: The S-Token and I-Token codebooks, together with their semantic encoders and decoders, are pretrained using an expert dataset and frozen to preserve consistent semantic mappings. • Online joint optimization: To avoid directly learning complex-valued beamforming matrices, 1P_1 is decomposed into two variable blocks. For fixed W, the token-interactive policies optimize token selection and determine the physical actions V, A, B, and P. With these physical actions fixed, W is optimized via FP and KKT-based closed-form updates. The updated W is then fed back to the policy learning block for the next iteration. Fig. 3: Overview of the proposed framework with offline codebook pretraining and online joint optimization. I-B Offline S-Token and I-Token Codebook Pretraining As illustrated in Fig. 3, the S-Token and I-Token codebooks are pretrained using the expert dataset ED_ E. The dataset contains paired samples obtained by evaluating pretrained centralized and local policies from the same environment states. Half of the rollout episodes follow the centralized policy, and the other half follow the local policy. For each token type g∈g , the encoder produces a continuous representation k,g,l[t]z_k,g,l[t]. VQ maps this representation to its nearest codeword, whose index is given by mk,g,l[t]=argminn∈1,…,Ngtok‖k,g,l[t]−g,n‖22.m_k,g,l[t]= n∈\1,…,N_g tok\arg\,min \|z_k,g,l[t]-e_g,n \|_2^2. (19) The quantized representation is ¯k,g,l[t]=g,mk,g,l[t] z_k,g,l[t]=e_g,m_k,g,l[t]. The VQ loss is defined as ℒVQ=E[∑g∈∑l=1Lg _ VQ=E_D_ E [ _g _l=1^L_g ‖sg[k,g,l[t]]−¯k,g,l[t]‖22 \|sg [z_k,g,l[t] ]- z_k,g,l[t] \|_2^2 (20) + + βg‖k,g,l[t]−sg[¯k,g,l[t]]‖22], _g \|z_k,g,l[t]-sg [ z_k,g,l[t] ] \|_2^2 ], where βg _g is the commitment coefficient. Let ^k,g[t]=g(k,g[t]) χ_k,g[t]=D_g(m_k,g[t]) denote the decoded semantic representation and k,g[t] χ_k,g[t] denote the corresponding task-relevant target obtained from ED_ E. The semantic reconstruction loss is given by ℒsem=E[∑g∈‖^k,g[t]−k,g[t]‖22].L_ sem=E_D_ E [ _g \| χ_k,g[t]- χ_k,g[t] \|_2^2 ]. (21) To preserve decision-relevant information, an auxiliary predictor ℋψH_ψ with parameters ψ reconstructs the expert action from the decoded state and intent semantics. The action-consistency loss is defined as ℒact=E[ℓact(ℋψ([^k,ST[t],^k,IT[t]]T),k⋆[t])],L_ act=E_D_ E [ _ act (H_ψ ( [ χ_k,S^T[t], χ_k,I^T[t] ]^T ),a_k [t] ) ], (22) where k⋆[t]a_k [t] denotes the expert physical action provided in ED_ E, and ℓact(⋅) _ act(·) combines classification and regression losses for discrete and continuous control decisions, respectively. To prevent codebook collapse, the codeword-usage distribution is regularized as ℒuse=∑g∈DKL(¯g∥g),L_ use= _g D_ KL ( p_g \|u_g ), (23) where ¯g p_g is the empirical codeword-usage distribution and gu_g is the corresponding uniform distribution. The overall offline training loss is ℒCB=ℒsem+λactℒact+λVQℒVQ+λuseℒuse,L_ CB=L_ sem+ _ actL_ act+ _ VQL_ VQ+ _ useL_ use, (24) where λact _ act, λVQ _ VQ, and λuse _ use are weighting coefficients. This joint training encourages task-relevant semantics to emerge in the codebooks. After pretraining, the codebooks and semantic decoders are frozen to preserve the token-index-to-semantics mapping during online policy optimization. I-C Online Joint Optimization With the pretrained codebooks and semantic decoders fixed, the online stage alternates between two optimization blocks. The beamforming block updates W for given V, A, B, and P using closed-form updates. The policy block learns token selection and composition while jointly optimizing the mixed discrete and continuous physical decisions through MAPPO. I-C1 Beamforming Optimization Based on Closed-Form Updates Since the propulsion energy is independent of W, the beamforming subproblem maximizes a dynamically weighted sensing and communication utility: 2:maxk,i[t] _2: _W_k,i[t] ω1∑j=1NsRk,j,is[t]+ω2Rk,ic[t] _1 _j=1^N_sR_k,j,i^s[t]+ _2R_k,i^c[t] (25a) s.t. .t. ‖k,i[t]‖F2≤pk,i[t]. \|W_k,i[t] \|_F^2≤ p_k,i[t]. (25b) Here, the base weights ω1,ω2≥0 _1, _2≥ 0 satisfy ω1+ω2=1 _1+ _2=1 and control the relative priorities of sensing and communication, respectively. To address the non-convexity of 2P_2, we apply the Lagrangian dual transform and quadratic transform under the FP framework. The resulting beamforming update is characterized below. Theorem 1. For fixed weights and FP auxiliary variables, and pk,i[t]>0p_k,i[t]>0, an optimal solution to the resulting quadratic subproblem is k,i,r⋆=(r+λ⋆M)−1r,r=1,…,Ns+1,w_k,i,r = ( _r+λ I_M )^-1 _r, r=1,…,N_s+1, (26) where r _r and r _r are defined in (27) and (28), respectively, and λ⋆≥0λ ≥ 0 is the optimal Lagrange multiplier associated with the power constraint. Proof: See Appendix A for more details. □ r[t]=∑j=1Nsω1αk,i[t]bk,i[t]1+μjsGp(ρk,js)∗(ξj,rs)∗k,js+ω2bk,i[t]1+μc(ξc)∗k,ic,r=1,∑j=1Nsω1αk,i[t]bk,i[t]1+μjsGp(ρk,js)∗(ξj,rs)∗k,js,r=2,…,Ns+1. _r[t]= cases _j=1^N_s _1 _k,i[t]b_k,i[t] 1+ _j^s G_p ( _k,j^s )^* ( _j,r^s )^*a_k,j^s+ _2b_k,i[t] 1+μ^c (ξ^c )^*h_k,i^c,r=1,\\ _j=1^N_s _1 _k,i[t]b_k,i[t] 1+ _j^s G_p ( _k,j^s )^* ( _j,r^s )^*a_k,j^s,r=2,…,N_s+1 cases. (27) r[t]= _r[t]= ∑j=1Nsω1bk,i[t]‖js‖22αk,i[t]Gp|ρk,js|2k,js(k,js)H+ω2bk,i[t]|ξc|2k,ic(k,ic)H. _j=1^N_s _1b_k,i[t] \| ξ_j^s \|_2^2 _k,i[t]G_p | _k,j^s |^2a_k,j^s (a_k,j^s )^H+ _2b_k,i[t] |ξ^c |^2h_k,i^c (h_k,i^c )^H. (28) To account for communication and sensing quality-of-service (QoS) violations, the effective weights at outer iteration ℓ are updated as ω1eff,(ℓ)=ω1+ηsBF,(ℓ),ω2eff,(ℓ)=ω2+ηcBF,(ℓ), _1 eff,( )= _1+ _ s BF,( ), _2 eff,( )= _2+ _ c BF,( ), (29) where ηsBF,(ℓ+1)=minηs,maxBF,ηsBF,(ℓ)+τs[1−Rs,(ℓ)/Rmins]+ _ s BF,( +1)= \ _ s, BF, _ s BF,( )+ _ s[1-R^s,( )/R_ ^s]^+\ and ηcBF,(ℓ+1)=minηc,maxBF,ηcBF,(ℓ)+τc[1−mini∈Ric,(ℓ)/Rmin,ic]+ _ c BF,( +1)= \ _ c, BF, _ c BF,( )+ _ c[1- _i \R_i^c,( )/R_ ,i^c\]^+\. An unsatisfied QoS requirement therefore receives greater priority in the subsequent beamforming update. The outer iteration terminates when both requirements are satisfied or the maximum number of iterations is reached. The optimization based on closed-form updates is summarized in Algorithm 1. Algorithm 1 Beamforming Optimization Based on Closed-Form Updates 1: Input: Fixed V, A, B, and P; channel information 2: Initialize feasible W and ηsBF=ηcBF=0 _ s BF= _ c BF=0 3: for ℓ=0 =0 to Lout−1L_ out-1 do 4: Update ω1eff,(ℓ) _1 eff,( ) and ω2eff,(ℓ) _2 eff,( ) using (29) 5: for n=0n=0 to Lin−1L_ in-1 do 6: Update the FP auxiliary variables μ and ξ 7: Calculate r _r and r _r 8: Set λ⋆=0λ =0 if h(0)≤0h(0)≤ 0; otherwise, obtain λ⋆λ by bisection 9: Update k,i,r⋆w_k,i,r using (26) 10: if the inner FP-KKT iteration converges then 11: break 12: end if 13: end for 14: Calculate RsR^s and Rici∈\R_i^c\_i 15: if Rs≥RminsR^s≥ R_ ^s and Ric≥Rmin,icR_i^c≥ R_ ,i^c for all i∈i then 16: break 17: end if 18: Update ηsBF _ s BF and ηcBF _ c BF from the sensing and communication QoS violations, respectively. 19: end for 20: Output: Optimized beamforming matrices ⋆W I-C2 Token Selection and Policy Optimization The token-selection policy is optimized using proximal policy optimization (PPO). For the llth token slot of type g, the token-policy probability ratio is defined as ϱk,g,ltok[t]=πθk,gtok(mk,g,l[t]∣k[t])πθk,g,oldtok(mk,g,l[t]∣k[t]), _k,g,l tok[t]= _ _k,g tok (m_k,g,l[t] _k[t] ) _ _k,g, old tok (m_k,g,l[t] _k[t] ), (30) where θk,g _k,g denotes the current token-policy parameters of UAV k for type g, and θk,g,old _k,g, old denotes the parameters used to collect the rollout data. To assign credit to individual tokens, we augment the estimated UAV advantage with a counterfactual reward difference: A^k,g,ltok[t]=A^k[t]+λCF(r¯[t]−r¯(−k,g,l)[t]), A_k,g,l tok[t]= A_k[t]+ _ CF ( r[t]- r^(-k,g,l)[t] ), (31) where A^k[t] A_k[t] is the estimated advantage of UAV k, r¯[t]≜K−1∑ℓ=1Krℓ[t] r[t] K^-1 _ =1^Kr_ [t] is the average team reward, and λCF _ CF weights the counterfactual contribution. The reward r¯(−k,g,l)[t] r^(-k,g,l)[t] is evaluated by masking the selected token in the received messages, keeping the environment state and all other tokens unchanged, and recomputing the downstream physical actions and beamforming. The token-selection policy is trained by minimizing the per-slot clipped surrogate loss ℒtok()=−1K∑k=1Kt[∑g∈∑l=1Lgminϱk,g,ltok[t]A^k,g,ltok[t], _ tok( θ)=- 1K _k=1^KE_t [ _g _l=1^L_g \ _k,g,l tok[t] A_k,g,l tok[t], (32) clip(ϱk,g,ltok[t],1−ϵ,1+ϵ)A^k,g,ltok[t]]−λHℋtok, ( _k,g,l tok[t],1-ε,1+ε ) A_k,g,l tok[t] \ ]- _ HH_ tok, where θ collects the token-policy parameters θk,gk∈,g∈\ _k,g\_k ,g and the physical-policy parameters, tE_t denotes averaging over rollout samples, ϵε is the clipping parameter, ℋtokH_ tok is the token-policy entropy, and λH _ H is its regularization coefficient. The physical policy is trained by minimizing the standard clipped MAPPO loss [44]. The centralized critic Vϕ,k(st)V_ φ,k(s_t), parameterized by ϕ φ, estimates the expected discounted return of UAV k from the global state st∈s_t . It is trained by minimizing ℒcritic(ϕ)=12K∑k=1Kt[(Vϕ,k(st)−V^k[t])2],L_ critic( φ)= 12K _k=1^KE_t [ (V_ φ,k(s_t)- V_k[t] )^2 ], (33) where V^k[t] V_k[t] denotes the return target computed from the rollout data. The centralized critic is used only during training. The advantage estimates and return targets are computed using generalized advantage estimation (GAE). The overall online training procedure is summarized in Algorithm 2. Algorithm 2 Online Training of the SI-TokCom Framework 1: Input: Pretrained codebooks and semantic decoders ℰg,gg∈\E_g,D_g\_g 2: Freeze ℰg,g\E_g,D_g\; initialize policy parameters θ and critic parameters ϕ φ 3: for each training episode do 4: Reset the environment and obtain s1s_1 and k[1]\o_k[1]\; set old← θ_ old← θ 5: for t=1t=1 to NTN_T do 6: Each UAV selects mk,g,l[t]m_k,g,l[t] 7: Exchange k[t]\m_k[t]\ and construct ~k[t]\ o_k[t]\ using the frozen decoders 8: Each UAV selects k[t]v_k[t], αk,i[t] _k,i[t], bk,i[t]b_k,i[t], and pk,i[t]p_k,i[t] based on ~k[t] o_k[t] 9: Update k,i[t]W_k,i[t] using Algorithm 1 10: Execute the joint action [t]u[t]; observe rk[t]\r_k[t]\, st+1s_t+1, and k[t+1]\o_k[t+1]\ 11: Evaluate the masked-token rewards r¯(−k,g,l)[t] r^(-k,g,l)[t] under the same pre-action state 12: Store the rollout data and policy probabilities 13: end for 14: Compute A^k[t] A_k[t] and V^k[t] V_k[t] using GAE 15: Compute A^k,g,ltok[t] A_k,g,l tok[t] using (31) 16: for each PPO epoch do 17: Update θ using (32) and the physical-policy MAPPO objective 18: Update ϕ φ by minimizing (33) 19: end for 20: end for 21: Output: Trained token-selection and physical-policy parameters θ IV Simulation Results We evaluate the proposed SI-TokCom framework in a cooperative multi-UAV ISAC system operating in a 600×600m2600× 600~m^2 region with K=4K=4 UAVs, Nc=8N_c=8 CUs, and Ns=3N_s=3 STs. The initial horizontal UAV positions are (150,150)(150,150), (450,150)(450,150), (450,450)(450,450), and (150,450)(150,450) m. The CUs and STs are sampled within [30,570]×[30,570]m2[30,570]×[30,570]~m^2, with each ST initially observable by at least one UAV. The simulations are conducted using the Monte Carlo method. The main parameters are summarized in Table I. TABLE I: Main Simulation Parameters Parameter Value Parameter Value K,Nc,NsK,\,N_c,\,N_s 4, 8, 34,\,8,\,3 wc,ws,wEw_ c,\,w_ s,\,w_ E 0.6, 0.4, 0.80.6,\,0.4,\,0.8 H 80m80~m ω1,ω2 _1,\, _2 0.4, 0.60.4,\,0.6 NT,TN_T,\,T 12, 1s12,\,1~s Lin,LoutL_ in,\,L_ out 20, 820,\,8 VkmaxV_k 15m/s15~m/s FP–KKT tolerance 10−310^-3 DminD_ 20m20~m NStok,NItokN_S tok,\,N_I tok 64, 6464,\,64 M 44 DStok,DItokD_S tok,\,D_I tok 16, 1616,\,16 Carrier frequency 2.4GHz2.4~GHz LS,LIL_S,\,L_I 3, 133,\,13 λ,daλ,\,d_a 0.125m,λ/20.125~m,\,λ/2 Intent horizon 22 slots Bk,∑k=1KBkB_k,\, _k=1^KB_k (1.25, 5)MHz(1.25,\,5)~MHz γ,ϵγ,\,ε 0.95, 0.20.95,\,0.2 PkmaxP_k 1W1~W GAE parameter 0.950.95 N0N_0 10−17W/Hz10^-17~W/Hz Critic learning rate 5×10−45× 10^-4 β0,αc _0,\, _ c 10−3, 210^-3,\,2 Mini-batches per update 22 βs,Gp _ s,\,G_p 10−5, 110^-5,\,1 Offline epochs / batch size 100/ 32100\,/\,32 Rmin,icR_ ,i^c [1.84,2.76]U[1.84,2.76] Mbit/sMbit/s Codebook exponential moving average coefficient 0.990.99 RminsR_ ^s 20kbit/s20~kbit/s Training episodes / parallel envs. 1000/ 41000\,/\,4 We evaluate the following schemes with different information inputs and inter-UAV communication mechanisms. 1) SI-TokCom (TokenCom): The proposed scheme combines local observations with exchanged S-Tokens and I-Tokens. 2) Local: Each UAV selects its physical actions solely from its local observation. 3) Centralized: The policies use global system information, including the states of all UAVs and ground nodes. 4) State Only: This ablation supplements local observations with S-Tokens only. 5) Intent Only: This ablation supplements local observations with I-Tokens only. 6) SemanticCom: This baseline exchanges continuous semantic representations among UAVs to support cooperative control. Fig. 4: Average reward convergence of different schemes. Fig. 4 compares the average per-slot training reward of different schemes versus the number of episodes. SI-TokCom improves rapidly during the initial stage and attains a higher late-stage reward than Local, SemanticCom, and the two single-token variants, approaching that of Centralized. These results suggest that joint state and intent exchange helps alleviate partial observability and improve decentralized coordination. At the same message budget, SI-TokCom benefits from decision-oriented state and intent prototypes that better support cooperation than SemanticCom’s representations focused on state and action reconstruction. Moreover, compared with continuous messages, discrete tokens enable grouping of information with similar action-value structures during codebook training. Such grouping may help narrow the performance gap between policies under partial and full observability. TABLE I: Late-Stage Performance Comparison Scheme Comm. rate ↑ (Mbit/s) Sensing rate ↑ (kbit/s) Energy ↓ (J) Comm. QoS ↑ (%) Sensing QoS ↑ (%) Coord. payload (bit) Centralized 7.227.22 65.0465.04 42.1842.18 99.4599.45 93.4893.48 — TokenCom 7.147.14 64.4464.44 42.1142.11 98.7398.73 93.8993.89 9696 Local 6.806.80 44.8844.88 42.1142.11 99.3999.39 78.9178.91 00 Intent Only 7.067.06 58.6058.60 42.1642.16 98.8398.83 90.9190.91 7878 State Only 6.936.93 64.9364.93 42.2342.23 97.9697.96 92.4692.46 1818 SemanticCom 7.037.03 60.2160.21 43.1743.17 98.7698.76 90.2690.26 9696 QoS columns report satisfaction rates. Coordination payload is measured in bits per UAV per time slot, excluding packet headers and channel coding. The coordination overhead of Centralized is not modeled. Table I summarizes the average performance of different schemes after convergence. Communication rate is averaged over CUs, while sensing rate and propulsion energy are system totals; these metrics are averaged over time slots within each episode and across environments. With a coordination payload of 96 bits per UAV per time slot, SI-TokCom achieves 98.9% and 99.1% of the communication and sensing rates of Centralized, respectively. Compared with Local, it increases the communication and sensing rates by 5.0% and 43.6%, respectively, with comparable energy consumption. At the same payload, SI-TokCom achieves a 7.0% higher sensing rate and 2.5% lower energy consumption than SemanticCom. Although State Only attains a slightly higher average sensing rate, SI-TokCom achieves the highest sensing QoS satisfaction rate (93.89%), exceeding State Only and Intent Only. This indicates that a higher average sensing rate does not necessarily imply better satisfaction of sensing requirements. Fig. 5: Average SPEB over all STs during training for different schemes. Fig. 5 shows the SPEB averaged over all STs during training. The SPEB is computed as the trace of the Cramér–Rao bound (CRB) matrix for planar position, as derived in Appendix B. In the later stages of training, SI-TokCom achieves an SPEB comparable to Centralized and SemanticCom and generally lower than Local and the two single-token variants. These results support the benefit of joint state and intent exchange for cooperative sensing, with the lower SPEB suggesting the potential for more accurate localization. (a) K=4K=4, Ns=3N_s=3, Nc=8N_c=8 (b) K=6K=6, Ns=4N_s=4, Nc=10N_c=10 (c) K=3K=3, Ns=2N_s=2, Nc=6N_c=6 Fig. 6: UAV trajectories generated by TokenCom under different network sizes and randomly generated CU and ST layouts. Fig. 6 illustrates the UAV trajectories generated by SI-TokCom in three test scenarios with different numbers of UAVs, STs, and CUs. The ground-node locations are randomly generated and differ from those used during training. The trajectory variations provide qualitative evidence of adaptability across the evaluated layouts and network sizes. This adaptability may benefit from the complementary roles of state and intent tokens: state tokens convey local conditions, while intent tokens help UAVs anticipate their peers’ planned actions. Together, these cues may support coordinated mobility as service locations and the number of UAVs change. Fig. 7 compares the tradeoff between the communication and sensing rates for SI-TokCom, Local, Centralized, State Only, Intent Only, and SemanticCom during online testing. Varying ω1 _1 and ω2 _2 adjusts the relative priorities of the two services and produces different operating points. Higher communication rates are generally accompanied by lower sensing rates. At comparable communication rates, SI-TokCom generally achieves higher sensing rates than Local, State Only, Intent Only, and SemanticCom, while Centralized provides the best overall tradeoff. These comparisons support the benefit of joint state and intent exchange in balancing communication and sensing performance. Fig. 7: Tradeoff between the communication and sensing rates. Fig. 8(a) and (b) show the S-Token and I-Token usage frequencies in scenario A, respectively, providing the reference distributions for comparison. Scenario A has higher communication and lower sensing requirements, ground nodes near the initial UAV positions, and high initial battery levels. Scenario B has lower communication and higher sensing requirements, ground nodes clustered in the southwestern region, and low initial battery levels. Fig. 8(c) and (d) present the corresponding frequency differences, computed as scenario B minus scenario A. Positive and negative values indicate increased and decreased usage in scenario B, respectively. These nonuniform shifts reveal scenario-dependent token preferences, providing qualitative evidence of adaptive codebook reuse under changing service requirements, node layouts, and energy conditions. (a) S-Token usage in scenario A (b) I-Token usage in scenario A (c) S-Token usage difference (d) I-Token usage difference Fig. 8: Token usage statistics: (a), (b) usage frequencies in scenario A; (c), (d) usage-frequency differences between scenarios B and A (scenario B minus scenario A). Frequencies are expressed as percentages and differences as percentage points. Fig. 9 compares the terminal SPEB in a sensing-only task with Ns=1N_s=1 and Nc=0N_c=0, where each UAV dedicates all its bandwidth and transmit beams to sensing. The sensing SNR therefore becomes γk,js[t]=Gp‖ρk,js[t]k,js[t]Hk[t]‖22/N0Bk _k,j^s[t]=G_p\| _k,j^s[t]a_k,j^s[t]^HW_k[t]\|_2^2/N_0B_k, where k[t]=[k,s1[t],…,k,sNs[t]]W_k[t]=[w_k,s_1[t],…,w_k,s_N_s[t]] denotes the sensing beamforming matrix of UAV k. Fig. 9(a) shows the spatial SPEB distribution, Fig. 9(b) presents the central slices at x=300mx=300~m and y=300my=300~m, and Fig. 9(c) reports the empirical cumulative distribution function (CDF) over all sampled ST locations. The location-dependent peaks in (b) highlight the influence of sensing geometry on localization performance. SI-TokCom generally achieves lower SPEB than Local and can outperform Centralized along both slices. Its generally higher CDF further indicates that a larger fraction of sampled locations satisfies a given SPEB threshold, suggesting that the gains extend beyond the selected slices. These gains may stem from scenario-relevant token selection and explicit intent exchange, which help anticipate other UAVs’ actions and improve sensing coordination. Although Centralized has access to global information, SI-TokCom’s intent prediction may offer a more pronounced advantage in this simpler scenario. (a) Spatial SPEB distribution (b) Central SPEB slices (c) Empirical CDF of SPEB Fig. 9: Terminal SPEB at t=12t=12 in a sensing-only test with Ns=1N_s=1 and Nc=0N_c=0: (a) spatial distribution over the ST position grid; (b) central slices at x=300mx=300~m (upper) and y=300my=300~m (lower); and (c) empirical CDF over all sampled ST locations. V Conclusion This paper developed SI-TokCom, an embodied multi-agent framework for cooperative multi-UAV ISAC. We formulated a joint TokCom and physical control problem to minimize propulsion energy subject to communication and sensing requirements. The proposed alternating optimization algorithm combined MAPPO-based joint learning of token selection, composition, and physical control with closed-form beamforming updates. Simulation results showed that SI-TokCom achieved 98.9% and 99.1% of the communication and sensing rates of Centralized, respectively, with a coordination payload of 96 bits per UAV per slot. Compared with Local, SI-TokCom improved these rates by 5.0% and 43.6%, respectively, with comparable propulsion energy. Changes in token usage across the evaluated scenarios further indicated that fixed semantic codebooks could support adaptive coordination. These findings suggest that jointly learning compact messages and physical decisions can enable effective decentralized cooperation in multi-UAV ISAC. Appendix A Derivation of the Closed-Form Beamforming Update First, we rewrite the objective function in (25a) based on the Lagrangian dual transform and quadratic transform under the FP framework [45], which can be expressed as G~(k,i[t]) G (W_k,i[t] ) =∑r=1Ns+1(2RerH[t]k,i,r[t]CLOSE = _r=1^N_s+1 (2Re \ _r^H[t]w_k,i,r[t] \ (34) OPEN−k,i,rH[t]r[t]k,i,r[t])+B[t], -w_k,i,r^H[t] _r[t]w_k,i,r[t] )+B[t], where r[t] _r[t], r[t] _r[t], and B[t]B[t] are defined in (27), (28), and (35), respectively. The Lagrangian dual transform introduces the auxiliary variables μjs _j^s and μcμ^c, whose optimal updates are given by μjs⋆=αk,i[t]Gp‖ρk,js(k,js)Hk,i[t]‖22N0bk,i[t], _j^s = _k,i[t]G_p \| _k,j^s(a_k,j^s)^HW_k,i[t] \|_2^2N_0b_k,i[t], (36) μc⋆=|(k,ic)Hk,i|2∑r=1Ns|(k,ic)Hk,i,r|2+N0bk,i[t].μ^c = |(h_k,i^c)^Hw_k,i |^2 _r=1^N_s |(h_k,i^c)^Hw_k,i,r |^2+N_0b_k,i[t]. (37) The quadratic transform further decouples the remaining ratios by introducing js ξ_j^s and ξcξ^c, whose optimal updates are given by js⋆=αk,i[t]1+μjsGpρk,js(k,js)Hk,iαk,i[t]Gp‖ρk,js(k,js)Hk,i‖22+N0bk,i[t], ξ_j^s = _k,i[t] 1+ _j^s G_p _k,j^s(a_k,j^s)^HW_k,i _k,i[t]G_p \| _k,j^s(a_k,j^s)^HW_k,i \|_2^2+N_0b_k,i[t], (38) ξc⋆=1+μc(k,ic)Hk,i,1∑r=1Ns+1|(k,ic)Hk,i,r|2+N0bk,i[t],ξ^c = 1+μ^c(h_k,i^c)^Hw_k,i,1 _r=1^N_s+1 |(h_k,i^c)^Hw_k,i,r |^2+N_0b_k,i[t], (39) where js=[ξj,1s,…,ξj,Ns+1s] ξ_j^s=[ _j,1^s,…, _j,N_s+1^s] is a row vector. For fixed auxiliary variables, r⪰ _r 0, and the resulting beamforming subproblem is convex. By omitting the constant term B, the Lagrangian associated with the power constraint is expressed as ℒ(k,i,λ)= (W_k,i,λ )= ∑r=1Ns+1(k,i,rHrk,i,r−2RerHk,i,r) _r=1^N_s+1 (w_k,i,r^H _rw_k,i,r-2Re \ _r^Hw_k,i,r \ ) (40) +λ(∑r=1Ns+1‖k,i,r‖22−pk,i[t]), +λ ( _r=1^N_s+1 \|w_k,i,r \|_2^2-p_k,i[t] ), where λ≥0λ≥ 0 is the dual variable associated with the power constraint. For pk,i[t]>0p_k,i[t]>0, Slater’s condition holds, so the KKT conditions are necessary and sufficient. Stationarity requires ∂ℒ∂k,i,r∗=(r+λM)k,i,r−r=, _k,i,r^*= ( _r+ _M )w_k,i,r- _r=0, (41) which yields (26). The optimal multiplier follows from complementary slackness: λ⋆(∑r=1Ns+1‖k,i,r⋆‖22−pk,i[t])=0.λ ( _r=1^N_s+1\|w_k,i,r \|_2^2-p_k,i[t] )=0. (42) For λ>0λ>0, define h(λ)=∑r=1Ns+1‖(r+λM)−1r‖22−pk,i[t],h(λ)= _r=1^N_s+1 \| ( _r+ _M )^-1 _r \|_2^2-p_k,i[t], (43) with h(0)=∑r=1Ns+1‖r†r‖22−pk,i[t]h(0)= _r=1^N_s+1\| _r _r\|_2^2-p_k,i[t]. If h(0)≤0h(0)≤ 0, then λ⋆=0λ =0. Otherwise, the power constraint is active, and λ⋆>0λ >0 satisfies h(λ⋆)=0h(λ )=0. Differentiating (43) gives h′(λ)=−2∑r=1Ns+1rH(r+λM)−3r≤0.h (λ)=-2 _r=1^N_s+1 _r^H ( _r+ _M )^-3 _r≤ 0. (44) The inequality is strict when h(0)>0h(0)>0. Since limλ→∞h(λ)=−pk,i[t]<0 _λ→∞h(λ)=-p_k,i[t]<0, the positive root is unique and can be efficiently obtained via bisection. This completes the proof of Theorem 1. Appendix B Derivation of the CRB for Planar Position The distance measurements obtained by the K UAVs at time slot t are collected as ~js[t]=js[t]+js[t]∼(js[t],js[t]), d_j^s[t]=d_j^s[t]+e_j^s[t] (d_j^s[t],C_j^s[t] ), (45) where js[t]=[d1,js[t],…,dK,js[t]]Td_j^s[t]=[d_1,j^s[t],…,d_K,j^s[t]]^T and js[t]=diag((σ1,jd[t])2,…,(σK,jd[t])2)C_j^s[t]=diag ( ( _1,j^d[t] )^2,…, ( _K,j^d[t] )^2 ). The individual ranging error is modeled as ek,js[t]∼(0,(σk,jd[t])2),e_k,j^s[t] (0, ( _k,j^d[t] )^2 ), (46) where (σk,jd[t])2=ζs/γk,js[t] ( _k,j^d[t] )^2= _s/ _k,j^s[t] and ζs _s denotes the ranging-error coefficient. By aggregating the sensing information carried by the allocated subchannels, the bandwidth-weighted sensing SNR is defined as γk,js[t]=∑i=1Ncαk,i[t]γk,j,is[t](bk,i[t]/b0)3 _k,j^s[t]= _i=1^N_c _k,i[t] _k,j,i^s[t] (b_k,i[t]/b_0 )^3, where b0b_0 is the reference bandwidth used for normalization. Based on the above Gaussian ranging model, the FIM jd[t]J_j^d[t] for the distance parameters is given by (47), where χk,js[t]≜∑i=1Ncαk,i[t]bk,i[t]2b03‖(k,js[t])Hk,i[t]‖22 _k,j^s[t] _i=1^N_c _k,i[t]b_k,i[t]^2b_0^3 \|(a_k,j^s[t])^HW_k,i[t] \|_2^2 and =diag(0,1,…,M−1)D=diag(0,1,…,M-1). B[t]= B[t]= ω1bk,i[t]∑j=1Nslog(1+μjs)+ω2bk,i[t]log(1+μc)−ω1bk,i[t]μjs−ω2bk,i[t]μc _1b_k,i[t] _j=1^N_s (1+ _j^s )+ _2b_k,i[t] (1+μ^c )- _1b_k,i[t] _j^s- _2b_k,i[t]μ^c (35) −ω2bk,i[t]|ξc|2N0bk,i[t]−ω1bk,i[t]|ξjs|2N0bk,i[t]. - _2b_k,i[t] |ξ^c |^2N_0b_k,i[t]- _1b_k,i[t] | _j^s |^2N_0b_k,i[t]. [jd[t]]p,q=[∂js[t]∂dp,js[t]]T(js[t])−1[∂js[t]∂dq,js[t]]+12tr[(js[t])−1∂js[t]∂dp,js[t](js[t])−1∂js[t]∂dq,js[t]] [J_j^d[t] ]_p,q= [ _j^s[t]∂ d_p,j^s[t] ]^T (C_j^s[t] )^-1 [ _j^s[t]∂ d_q,j^s[t] ]+ 12tr [ (C_j^s[t] )^-1 _j^s[t]∂ d_p,j^s[t] (C_j^s[t] )^-1 _j^s[t]∂ d_q,j^s[t] ] (47) =GpβsζsN0χk,js[t](dk,js[t])4+12(−4πdaHλχk,js[t](dk,js)2∑i=1Ncαk,i[t]bk,i[t]2b03Im((k,js[t])Hk,i[t])∗(k,js[t])Hk,i[t]+4dk,js[t])2, = G_p _ s _sN_0 _k,j^s[t] (d_k,j^s[t] )^4+ 12 (- 4π d_aHλ _k,j^s[t] (d_k,j^s )^2 _i=1^N_c _k,i[t]b_k,i[t]^2b_0^3\!Im \ ((a_k,j^s[t])^HW_k,i[t] )^*(a_k,j^s[t])^HDW_k,i[t] \+ 4d_k,j^s[t] )^2, p=q=k,k=1,…,K. p=q=k,k=1,…,K. Accordingly, the FIM for the planar target position is obtained through the Jacobian transformation as jp[t]=j[t]jd[t]jT[t],J_j^p[t]=Q_j[t]J_j^d[t]Q_j^T[t], (48) where j[t]=[1,j[t],…,K,j[t]]Q_j[t]=[q_1,j[t],…,q_K,j[t]] is the Jacobian matrix, whose kkth column is k,j[t]=[∂dk,js[t]∂xjs∂dk,js[t]∂yjs]=1dk,js[t][Δxk,j[t]Δyk,j[t]],q_k,j[t]= bmatrix ∂ d_k,j^s[t]∂ x_j^s\\ ∂ d_k,j^s[t]∂ y_j^s bmatrix= 1d_k,j^s[t] bmatrix x_k,j[t]\\ y_k,j[t] bmatrix, (49) where Δxk,j[t]=xjs−xk[t] x_k,j[t]=x_j^s-x_k[t] and Δyk,j[t]=yjs−yk[t] y_k,j[t]=y_j^s-y_k[t]. Substituting (49) into (48) yields jp[t]=∑k=1KJj,kd[t]k,j[t]k,jT[t]=[Θja[t]Θjc[t]Θjc[t]Θjb[t]], _j^p[t]= _k=1^KJ_j,k^d[t]q_k,j[t]q_k,j^T[t]= bmatrix _j^a[t]& _j^c[t]\\ _j^c[t]& _j^b[t] bmatrix, (50) where Θja[t] _j^a[t], Θjb[t] _j^b[t], and Θjc[t] _j^c[t] are given by Θja[t]=∑k=1K(Δxk,j[t]dk,js[t])2[jd[t]]k,k, _j^a[t]= _k=1^K ( x_k,j[t]d_k,j^s[t] )^2 [J_j^d[t] ]_k,k, (51) Θjb[t]=∑k=1K(Δyk,j[t]dk,js[t])2[jd[t]]k,k, _j^b[t]= _k=1^K ( y_k,j[t]d_k,j^s[t] )^2 [J_j^d[t] ]_k,k, (52) Θjc[t]=∑k=1KΔxk,j[t]Δyk,j[t](dk,js[t])2[jd[t]]k,k, _j^c[t]= _k=1^K x_k,j[t] y_k,j[t] (d_k,j^s[t] )^2 [J_j^d[t] ]_k,k, (53) where [jd[t]]k,k [J_j^d[t] ]_k,k is given by (47) with p=q=kp=q=k. Substituting (50) into the definition of the planar position CRB yields CRBj[t] _j[t] =(jp[t])−1 = (J_j^p[t] )^-1 (54) =1Θja[t]Θjb[t]−(Θjc[t])2[Θjb[t]−Θjc[t]−Θjc[t]Θja[t]]. = 1 _j^a[t] _j^b[t]- ( _j^c[t] )^2 bmatrix _j^b[t]&- _j^c[t]\\ - _j^c[t]& _j^a[t] bmatrix. 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