- The paper introduces a viability theory method to compute trajectory planning that maintains feasibility within track constraints.
- It integrates a viability kernel with a low-level MPC, enabling robust, real-time decision-making for autonomous race cars.
- Experimental results show that conservative kernel approximations enhance safety and computational efficiency with minor lap time trade-offs.
Overview of the Paper: Real-Time Control for Autonomous Racing Based on Viability Theory
The research presented in the paper by Liniger and Lygeros contributes to the field of autonomous driving by focusing on real-time control for miniature race cars. The authors propose to approach the path planning problem through viability theory, efficiently determining racing trajectories that maximize progress while maintaining feasibility with respect to track constraints and obstacles. This viability-based methodology is integrated with a low-level Model Predictive Controller (MPC) to enable real-time autonomous racing.
Significant in their approach is the utilization of the viability kernel, which represents the set of states for which there exists a sequence of viable control actions that keep the system within its constraints over a given horizon. The authors introduce a novel method to compute an inner approximation of the viability kernel, incorporating game-theoretical principles to model discretization errors. By doing so, they significantly enhance the robustness of trajectory planning in the presence of static obstacles.
Numerical and Experimental Outcomes
The paper details comprehensive simulations and experiments conducted at the Automatic Control Laboratory of ETH Zurich. The authors observe that incorporating a more conservative approximation of the viability kernel yields safer driving behavior, albeit with a slight increase in lap time. This finding is supported by extensive numerical analyses showing significant reductions in computational load and improvements in recursive feasibility when using the viability kernel.
In terms of performance, several factors were examined, including the density of the grid used for kernel computation, the number of modes considered for stationary velocities (N_m), and the planning horizon length (N_S). The detailed results reveal that finer grid resolutions and more extensive planning horizons yield better performance, although often at an increased computational cost. Importantly, the computational benefits allow the approach to outperform non-viability constrained methods significantly.
Theoretical and Practical Implications
The paper contributes theoretically by proposing a robust scheme for computing viability kernels that account for space discretization errors through game theory. This advancement addresses a common challenge in grid-based methods, enhancing the method's practical applicability to real-time scenarios. From a practical standpoint, the approach supports real-time feasibility, a critical requirement for autonomous racing, where decisions must be executed at high speed with low latency.
The work also highlights the potential for application beyond miniature racing environments, suggesting that the methodology could be generalized to other autonomous driving tasks where safety and feasibility are paramount. Future research directions include exploring uncertainty within the dynamic model itself, perhaps integrating robust MPC formulations to accommodate discrepancies between the model and reality.
The application of viability theory to real-time autonomous control offers a robust, theoretically sound framework that enhances both the computational efficiency and safety of path planning for racing scenarios. The research paves the way for future innovations in autonomous vehicle control systems, promising more reliable and efficient real-time decision-making applications.