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

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

Flight Controller Design and Testing for Tailless Aircraft with Thrust Vectoring

A digital fly-by-wire control system is designed and results from flight testing are presented for a radio controlled electric ducted fan model of the Euro fighter Typhoon. The controller is gain scheduled on dynamic pressure and throttle setting and allows the pilot to command pitch, roll, and yaw rates directly. The controller also attempts to hold altitude, heading, and pitch angle when the pilot centers the sticks. An ArduPilot microcomputer incorporating accelerometers, gyroscopes, magnetometers, GPS, and an airspeed sensor is installed to measure the state of the aircraft and calculate control signals using feedback. The results of wind tunnel testing of the aircraft in both conventional and tailless con gurations are also presented. These tests informed the creation of a model of the aircraft's dynamics that is used in the design of the controller. Linear quadratic optimal control design is used to design a controller for individual operating points. Interpolation is then used to determined gain values at arbitrary flight conditions. This controller is implemented in new code running on the ArduPilot computer and used in a series of flight tests. Lastly, the pilot's impressions of the aircraft's handling are presented