Optimization‐based autonomous racing of 1:43 scale RC cars

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. I. INTRODUCTIONAutonomous car racing is a challenging task for automatic control systems due to the need for handling the vehicle close to its stability limits and in highly nonlinear operating regimes. In addition, dynamically changing racing situations require advanced path planning mechanisms with obstacle avoidance executed in real-time. Fast dynamics constrain the sampling time to be in the range of a few tens of milliseconds at most, which severely limits the admissible computational complexity of the algorithms. This situation is even more challenging if the autonomous algorithms shall be executed on simple, low-power embedded computing platforms.In this paper, we investigate optimization-based control strategies for the task of racing an autonomous vehicle around a given track. We focus on methods that can be implemented to run in real-time on embedded control platforms, and present experimental results using 1:43 scale Kyosho dnano RC race cars that achieve top speeds of more than 3 m/s, which corresponds to an upscaled speed of about 465 km/h. For high performance, the proposed controllers operate the car at its friction limits, far beyond the linear region of what is typically used in other autonomous driving systems. This challenging task is generally mastered only by expert drivers with lots of training. In contrast, our approach requires merely a map of the track a...

Planning and Decision-Making for Autonomous Vehicles

“…(e.g., 34,35), whose main advantage is the probabilistic exploration of large state spaces, albeit at a high computational cost. The third is constrained optimization and receding-horizon control (e.g., 19,36), which have been applied mostly to path following but now can also compute collision-free trajectories to avoid other traffic participants, as shown by Schwarting et al (28), who formulated a nonlinear model predictive controller and employed it to safely navigate an intelligent vehicle. This has been possible thanks to recent advances in solvers for nonlinear constrained optimization.…”

Safe Nonlinear Trajectory Generation for Parallel Autonomy With a Dynamic Vehicle Model

“…To guide the planner along the road, we build upon Model Predictive Contouring Control (MPCC) [27], [28], [29], which approximates path progress inside a corridor, the road in our application. By tracking the center of the lane and remaining within the limits of the road our planner can be employed for both Parallel Autonomy, where we minimize the deviation from human input, and for fully autonomous vehicles.…”

“…In this section we build on the MPCC method of [27], [28], [29] and apply it to our problem setting. The control framework combines path generation and path tracking into one problem.…”

“…avoid another vehicle. We constrain the difference between the ego vehicle's heading φ k and the path's heading φ P (θ k ) (29) to maintain validity of a less conservative w(∆φ k ) as an upper bound on lateral projection of the ego-vehicle's occupancy B(z k ). …”

Predictive Guidance Control for Autonomous Kites with Input Delay * *This research was supported by the Swiss National Science Foundation (Synergia) No. 141836 and the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 642682.

“…In Diehl et al (2005) a real-time iteration scheme is considered, where an MPC problem with nonlinear kite dynamics is solved by iteratively linearising around past solutions. In this work, we consider a path following method, similar to the approach in Liniger et al (2015), where the dynamics are linearised around the reference path. We design a model predictive guidance controller that minimises the deviation from a reference path while satisfying constraints imposed by the limitations of the lower-level tracking controller that are subject to model uncertainty and input delay.…”