Summary 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. Copyright © 2014 John Wiley & Sons, Ltd.
In order to avoid obstacles, reference tracking schemes rely on a higher-level path planner. A simple point mass model in the high-level path planner is used in @cite_22 to limit the computational complexity. This can be problematic if the generated trajectories are infeasible with respect to the car's physical dynamics, which can lead to preventable collisions @cite_7 . The latter reference suggests to use a library of steady-state movements (trims) with parametrizable length, which are generated from a more complex dynamical model, and to connect them by maneuvers which allow the transition from one trim to another, similar to the idea of @cite_26 . This path planning has the advantage that it generates feasible reference trajectories for the low level tracking controller, and that drifting trims can be included to increase the agility of the car. However, the resulting optimization problem is a mixed-integer program that is too complex to be solved within the typical sampling times on embedded platforms. Consequently, the approach is not well suited for real-time autonomous racing.
@cite_26 @cite_22 @cite_7
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Summary 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. Copyright © 2014 John Wiley & Sons, Ltd. The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal control problem is typically computationally expensive and infeasible for real-time trajectory planning. This paper presents an iterative algorithm that divides the path generation task into two sequential subproblems that are significantly easier to solve. Given an initial path through the race track, the algorithm runs a forward-backward integration scheme to determine the minimum-time longitudinal speed profile, subject to tire friction constraints. With this fixed speed profile, the algorithm updates the vehicle's path by solving a convex optimization problem that minimizes the resulting path curvature while staying within track boundaries and obeying affine, time-varying vehicle dynamics constraints. This two-step process is repeated iteratively until the predicted lap time no longer improves. While providing no guarantees of convergence or a globally optimal solution, the approach performs very well when validated on the Thunderhill Raceway course in Willows, CA. The predicted lap time converges after four to five iterations, with each iteration over the full 4.5 km race course requiring only thirty seconds of computation time on a laptop computer. The resulting trajectory is experimentally driven at the race circuit with an autonomous Audi TTS test vehicle, and the resulting lap time and racing line is comparable to both a nonlinear gradient descent solution and a trajectory recorded from a professional racecar driver. The experimental results indicate that the proposed method is a viable option for online trajectory planning in the near future. Autonomous vehicles need to plan trajectories to a specified goal that avoid obstacles. Previous approaches that used a constrained optimization approach to solve for finite sequences of optimal control inputs have been highly effective. For robust execution, it is essential to take into account the inherent uncertainty in the problem, which arises due to uncertain localization, modeling errors, and disturbances. Prior work has handled the case of deterministically bounded uncertainty. We present here an alternative approach that uses a probabilistic representation of uncertainty, and plans the future probabilistic distribution of the vehicle state so that the probability of collision with obstacles is below a specified threshold. This approach has two main advantages; first, uncertainty is often modeled more naturally using a probabilistic representation (for example in the case of uncertain localization); second, by specifying the probability of successful execution, the desired level of conservatism in the plan can be specified in a meaningful manner. The key idea behind the approach is that the probabilistic obstacle avoidance problem can be expressed as a disjunctive linear program using linear chance constraints. The resulting disjunctive linear program has the same complexity as that corresponding to the deterministic path planning problem with no representation of uncertainty. Hence the resulting problem can be solved using existing, efficient techniques, such that planning with uncertainty requires minimal additional computation. Finally, we present an empirical validation of the new method with a number of aircraft obstacle avoidance scenarios. This paper presents a hierarchical control framework for the obstacle avoidance of autonomous and semi-autonomous ground vehicles. The high-level planner is based on motion primitives created from a four-wheel nonlinear dynamic model. Parameterized clothoids and drifting maneuvers are used to improve vehicle agility. The low-level tracks the planned trajectory with a nonlinear Model Predictive Controller. The first part of the paper describes the proposed control architecture and methodology. The second part presents simulative and experimental results with an autonomous and semi-autonomous ground vehicle traveling at high speed on an icy surface.