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The problem of maneuvering a vehicle through a race course in minimum timerequires computation of both longitudinal (brake and throttle) and lateral(steering wheel) control inputs. Unfortunately, solving the resulting nonlinearoptimal control problem is typically computationally expensive and infeasiblefor real-time trajectory planning. This paper presents an iterative algorithmthat divides the path generation task into two sequential subproblems that aresignificantly easier to solve. Given an initial path through the race track,the algorithm runs a forward-backward integration scheme to determine theminimum-time longitudinal speed profile, subject to tire friction constraints.With this fixed speed profile, the algorithm updates the vehicle's path bysolving a convex optimization problem that minimizes the resulting pathcurvature while staying within track boundaries and obeying affine,time-varying vehicle dynamics constraints. This two-step process is repeatediteratively until the predicted lap time no longer improves. While providing noguarantees of convergence or a globally optimal solution, the approach performsvery well when validated on the Thunderhill Raceway course in Willows, CA. Thepredicted lap time converges after four to five iterations, with each iterationover the full 4.5 km race course requiring only thirty seconds of computationtime on a laptop computer. The resulting trajectory is experimentally driven atthe race circuit with an autonomous Audi TTS test vehicle, and the resultinglap time and racing line is comparable to both a nonlinear gradient descentsolution and a trajectory recorded from a professional racecar driver. Theexperimental results indicate that the proposed method is a viable option foronline trajectory planning in the near future.

A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories