Robust Spatiotemporal Motion Planning for Multi-Agent Autonomous Racing via Topological Gap Identification and Accelerated MPC

Mingyi Zhang; Cheng Hu; Yiqin Wang; Haotong Qin; Hongye Su; Lei Xie

cs.ROMar 10, 2026

Robust Spatiotemporal Motion Planning for Multi-Agent Autonomous Racing via Topological Gap Identification and Accelerated MPC

Authors: Mingyi Zhang, Cheng Hu, Yiqin Wang, Haotong Qin, Hongye Su, Lei Xie

Organizations: Department of Control Science and Engineering, Zhejiang University. · Center for Project-Based Learning, D-ITET, ETH Zurich.

Abstract

High-speed multi-agent autonomous racing demands robust spatiotemporal planning and precise control under strict computational limits. Current methods often oversimplify interactions or abandon strict kinematic constraints. We resolve this by proposing a Topological Gap Identification and Accelerated MPC framework. By predicting opponent behaviors via SGPs, our method constructs dynamic occupancy corridors to robustly select optimal overtaking gaps. We ensure strict kinematic feasibility using a Linear Time-Varying MPC powered by a customized Pseudo-Transient Continuation (PTC) solver for high-frequency execution. Experimental results on the F1TENTH platform show that our method significantly outperforms state-of-the-art baselines: it reduces total maneuver time by 51.6% in sequential scenarios, consistently maintains an overtaking success rate exceeding 81% in dense bottlenecks, and lowers average computational latency by 20.3%, pushing the boundaries of safe and high-speed autonomous racing.

Figures & tables

Algorithm	Multi-Opp.	Kine. Feas.	Robust Solver	Topo. Gap
Frenet	Yes	No	No	No
FTG	Yes	No	No	No
M-PSpliner	Yes	No	No	No
FSDP	No	Yes	No	No
Proposed (ours)	Yes	Yes	Yes	Yes

TABLE I : Comparison of overtaking strategies. Multi-Opp. :Multiple opponent handling; Kine. Feas. :Strict kinematic restriction; Robust Solver :High-frequency accelerated solver; Topo. Gap :Dynamic gap identification. Ours uniquely satisfies all requirements.

Fig. 2 : Qualitative visualization of the multi-opponent behavior prediction via parallel SGPs. The models accurately infer the continuous lateral deviation and velocity profiles, generating variance-inflated spatial bounds to support the downstream dynamic corridor construction.

Fig. 3 : Illustration of the topology-aware gap selection and adaptive trajectory generation. The ego vehicle (blue) navigates a continuous safe corridor (green) to cleanly bypass the opponents’ Spatiotemporal Occupancy Corridors (SOCs, red hatched areas) utilizing a three-phase geometric path.

Fig. 4 : Overtaking maneuvers demonstrated in the F1TENTH RViz simulation environment across scenarios (b), (c), and (d). By utilizing the proposed TopoGap planner, the ego vehicle efficiently identifies navigable gaps (indicated by long rectangles) among the opponents’ SOCs(denoted by short rectangles) and generates an optimal, smooth trajectory to safely execute the overtakes.

Fig. 5 : Qualitative overview of the proposed Topo-Gap framework executing a multi-opponent overtaking maneuver under the SMP scenario. (a) At $t_{1}$ , the ego vehicle (magenta) trails Opponent 1 (gray) and evaluates the spatial gap for an outside overtake. (b) At $t_{2}$ , the ego vehicle successfully clears the first opponent at the curve apex. (c) At $t_{3}$ , it approaches Opponent 2 (teal) while continuously projecting spatiotemporal occupancy corridors. (d) At $t_{4}$ , a safe and smooth inside overtake is completed. The generated trajectories strictly maintain kinematic feasibility without decision oscillation during the highly dynamic multi-agent interactions.

Scen.	Planner	$\mathcal{R}_{\mathrm{ot/c}}[\%]$	$\Sigma\mathcal{T}[\mathrm{s}]$	$\bar{\dot{a}}[\mathrm{m/s^{3}}]$	$\bar{\dot{\delta}}[\mathrm{rad/s}]$
SMP	M-PSpliner	71.4	35.75	39.60	0.76
SMP	Ours	81.3	17.32	22.70	0.72
DSL	M-PSpliner	45.5	24.12	62.80	1.05
DSL	Ours	93.8	16.33	32.20	0.62
TSO	M-PSpliner	42.9	88.00	57.10	0.64
TSO	Ours	81.8	8.30	40.74	0.55

TABLE II : Quantitative Overtaking Performance Across Multi-Opponent Scenarios

Fig. 6 : GP latency comparison: Topo-Gap achieves significant speedups over M-PSpliner in model training (left) and prediction (right).

Solver	Mean ( $\mu_{t}$ )	Std ( $\sigma_{t}$ )	99th Pct. ∗	Max
FSDP MPC Solver	24.44	14.46	75.96	95.52
Our MPC Solver	19.48	10.90	53.90	67.18

TABLE III : MPC Solve Time Benchmark (ms)

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Autonomous Racing Safe Motion Planning Motion Planning Multi-Agent Planning Sampling-Based Motion Planning

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Autonomous multi-vehicle racing requires real-time planning of diverse competitive behaviors in intense interactions. Existing planners often struggle to balance strategic diversity and computational efficiency. To address this challenge, we propose Sampling-based Game-Theoretic Planning (SGTP), a real-time framework that combines game-theoretic reasoning with GPU-accelerated sampling of control sequences and dynamics rollouts. Sampled trajectories are ranked using a game-aware cost to capture competitive interactions and generate diverse racing behaviors. Our planner then performs feasibility selection by explicitly enforcing track-boundary and dynamic collision-avoidance constraints, ensuring safe and reliable transitions between racing strategies. Extensive simulations on challenging tracks show that SGTP achieves a 95.24% win rate and a 99.35% task-completion ratio in highly interactive races, with a mean computational time of 0.095 s over multiple iterative solving steps. We also demonstrate the successful application of SGTP in large-scale scenarios with up to 10 agents. We release our code and provide an open-source benchmark of multi-agent autonomous racing algorithms to facilitate future research. Project page: https://sgtp-racing.github.io/.

Abstract

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