Optimization-Based Autonomous Racing of 1:43 Scale RC Cars (1711.07300v1)

Abstract: This paper describes autonomous racing of RC race cars based on mathematical optimization. Using a dynamical model of the vehicle, control inputs are computed by receding horizon based controllers, where the objective is to maximize progress on the track subject to the requirement of staying on the track and avoiding opponents. Two different control formulations are presented. The first controller employs a two-level structure, consisting of a path planner and a nonlinear model predictive controller (NMPC) for tracking. The second controller combines both tasks in one nonlinear optimization problem (NLP) following the ideas of contouring control. Linear time varying models obtained by linearization are used to build local approximations of the control NLPs in the form of convex quadratic programs (QPs) at each sampling time. The resulting QPs have a typical MPC structure and can be solved in the range of milliseconds by recent structure exploiting solvers, which is key to the real-time feasibility of the overall control scheme. Obstacle avoidance is incorporated by means of a high-level corridor planner based on dynamic programming, which generates convex constraints for the controllers according to the current position of opponents and the track layout. The control performance is investigated experimentally using 1:43 scale RC race cars, driven at speeds of more than 3 m/s and in operating regions with saturated rear tire forces (drifting). The algorithms run at 50 Hz sampling rate on embedded computing platforms, demonstrating the real-time feasibility and high performance of optimization-based approaches for autonomous racing.

• The paper introduces two control schemes, HRHC and MPCC, to achieve autonomous racing near vehicle stability limits.
• The HRHC method combines high-level path planning with NMPC tracking to effectively handle non-linear dynamics and real-time constraints.
• The MPCC approach integrates trajectory planning and contour tracking, resulting in faster lap times and enhanced maneuver adaptability.

Overview of Optimization-Based Autonomous Racing for 1:43 Scale RC Cars

The paper authored by Liniger, Domahidi, and Morari presents a sophisticated approach to autonomous racing using radio-controlled (RC) cars at a reduced scale of 1:43. The research focuses on developing and implementing optimization-based control strategies that enable these small-scale vehicles to perform autonomously on a pre-defined racing track while avoiding obstacles and optimizing speed and position. The work is primarily concerned with the dynamics and control of autonomous vehicles near their stability limits, a challenging scenario given the non-linear operating conditions and limited computational resources typical of embedded systems.

Central to the presented work are two innovative control methodologies: a hierarchical receding horizon controller (HRHC) and a model predictive contouring control (MPCC). Both approaches seek to maximize track progress while ensuring the vehicle remains within track boundaries and avoids collisions.

Hierarchical Receding Horizon Control (HRHC)

The HRHC employs a two-tier strategy combining a high-level path planner and a nonlinear model predictive control (NMPC) tracking system. The path planner operates using a library of stationary vehicle velocities. By selecting and integrating these velocities, the planner generates trajectories that maximize progress given the constraints of road geometry and vehicle physical constraints. The NMPC then works to track the prescribed path, adjusting for deviations using a dynamic linearization approach. Soft constraints ensure the feasibility of solutions, accommodating real-time variations and providing robustness against dynamic changes on the track. This approach is computationally efficient due to the decoupling of trajectory planning and tracking, but it inherently introduces a limitation in adapting urgent maneuvers within its short prediction horizon.

Model Predictive Contouring Control (MPCC)

The MPCC framework adopts a more integrated approach by merging trajectory planning and tracking into a single nonlinear optimization problem. It leverages contouring control concepts to follow the track centerline, optimizing progress while penalizing deviations from the desired path. Unlike HRHC, the MPCC maintains a flexible prediction horizon that can accommodate complex track layouts and maneuvers by dynamically adjusting velocity and path curvature within the optimization problem. Solving the resulting nonlinear programming (NLP) problem in real-time is achieved by local linearization, allowing for iterative refinement and optimization within stringent computational limits.

Experimental Setup and Results

The authors implemented their algorithms on an embedded system comprised of modest computational resources, a necessary condition given the rapid data acquisition and processing capabilities required for real-time control. The autonomous vehicles employed have an impressive ability to operate at speeds exceeding 3 m/s, with the control loop executing decisions at 50 Hz. The experimental results demonstrated in a controlled track environment confirm the potential of the proposed control schemes. The HRHC and MPCC both successfully navigate the track and avoid static obstacles, although the HRHC occasionally exhibits limitations in complex maneuver scenarios due to its conservative path planning strategy. In contrast, the MPCC achieves faster lap times through its more aggressive and adaptive control style.

Implications and Future Directions

The paper's contributions lie in demonstrating effective methods for achieving high-speed autonomous racing with polynomial-time complex trajectory planning. It underscores the feasibility of using optimization-based strategies in embedded systems for real-time applications. However, there is room for enhancing obstacle prediction capabilities to extend application to dynamic and interactive racing environments, including head-to-head races with other AI-controlled or human-driven vehicles.

Future research might also explore improvements in sensor integration and algorithms to predict and adapt to dynamic obstacles. There is a potential to use advanced machine learning techniques for trajectory prediction, enhancing both the robustness and adaptability of these control systems. Integrating such methodologies could significantly advance the field of autonomous racing and provide valuable insights applicable to full-scale autonomous vehicles in more general traffic environments.