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 t1 , the ego vehicle (magenta) trails Opponent 1 (gray) and evaluates the spatial gap for an outside overtake. (b) At t2 , the ego vehicle successfully clears the first opponent at the curve apex. (c) At t3 , it approaches Opponent 2 (teal) while continuously projecting spatiotemporal occupancy corridors. (d) At t4 , 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
Rot/c[%]
ΣT[s]
a˙ˉ[m/s3]
δ˙ˉ[rad/s]
SMP
M-PSpliner
71.4
35.75
39.60
0.76
Ours
81.3
17.32
22.70
0.72
DSL
M-PSpliner
45.5
24.12
62.80
1.05
Ours
93.8
16.33
32.20
0.62
TSO
M-PSpliner
42.9
88.00
57.10
0.64
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).
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/.
Zhouheng Li, Fangguo Zhao, Mattia Piccinini +6
Zhejiang University, Hangzhou, China. · Technical University of Munich, Garching, Germany. · Nanyang Technological University, Singapore.
Autonomous racing overtaking requires balancing competitive performance with safety under nonlinear vehicle dynamics and real-time constraints. Model Predictive Control (MPC) combined with Control Barrier Functions (CBFs) provides a principled mechanism for certifying forward invariance of a safe set. However, commonly used fixed-decay discrete-time CBF formulations can become overly conservative in interactive racing scenarios, limiting overtaking performance and requiring manual tuning across track conditions. This paper proposes a hierarchical overtaking framework that explicitly separates maneuver-level decision making from safety-certified trajectory control, reducing conservatism while preserving safety. A high-level Mixed-Integer Quadratic Program (MIQP) resolves the combinatorial passing-side selection problem by selecting a feasible overtaking topology, while a nonlinear Frenet-frame MPC enforces vehicle dynamics and safety through embedded discrete-time CBF constraints. This decomposition isolates the combinatorial complexity of maneuver selection from the continuous trajectory optimization. To further mitigate the sensitivity of fixed-decay barrier constraints, a reinforcement learning policy adapts the discrete-time CBF decay parameter online, enabling context-dependent modulation of safety margins without directly controlling vehicle inputs. Simulation and scaled-hardware experiments show that no single fixed decay parameter achieves uniformly strong performance across tracks, whereas the adaptive strategy attains the highest aggregate success rate and consistently strong safety--performance trade-offs without per-track tuning, improving robustness to environment variation while maintaining safety constraint satisfaction in nominal operation.
Hassan Jardali, Kai Yin, Lantao Liu
Luddy School of Informatics, Computing, and Engineering, Indiana University · Machine Learning Science, Expedia Group, Austin, TX 78758 USA
This paper addresses defensive blocking in autonomous racing, where a vehicle must prevent a faster opponent from overtaking while operating near its dynamic limits. Different from lap-time minimization, we formulate defense as a spatial occupancy regulation problem via a hierarchical reinforcement-learning guided model predictive control framework. A Soft Actor-Critic strategic layer operates in the Frenet domain to generate geometry-aware defensive references, which are embedded into the nonlinear model predictive control formulation as spatial regularization under friction constraints. Evaluated on the Thunderhill West circuit in simulation, the framework increases average overtake time from 8.8 s to 14.6 s while significantly reducing opponent progress. Meanwhile, it allows the vehicle to utilize 83.4% of available tire force. The framework achieves a 33.3 ms mean solve time (13.9 ms std), supporting real-time high-speed adversarial interaction.
Yufei Xi, Yijie Liao, Tulga Ersal
Department of Mechanical Engineering, College of Engineering, University of Michigan, Ann Arbor, MI, USA. · Department of Electrical Engineering and Computer Science, College of Engineering, University of Michigan, Ann Arbor, MI, USA. · School of Computing, National University of Singapore, Singapore.