Designing a Receding Horizon Planner for an Autonomous Formula Student Racecar - Kerry He, 2021

Monash Motorsport Final Year Thesis collection

The Final Year Thesis is a technical engineering assignment undertaken by students of Monash University. Monash Motorsport team members often choose to conduct this assignment in conjunction with the team. 

These theses have been the cornerstone for much of the team’s success. The purpose of the team releasing the Monash Motorsport Final Year Thesis Collection is to share knowledge and foster progress in the Formula Student and Formula-SAE community.

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Summary

In autonomous driving, the motion planning subsystem is required to determine a feasible state and control trajectory to navigate the vehicle to perform a specific task. This thesis presents an implementation of a receding horizon planner (RHP) to perform motion planning for Monash Motorsport’s autonomous racecar to compete in the Formula Student Driverless competition. Multiple modelling and discretisation methods were explored to determine the best performing RHP formulation. An extensive comparison of each formulation was conducted by prototyping each RHP in MATLAB, and performing simulated experiments in a simplified environment. The best performing RHP was then translated into C++ and validated in a full real time hardware-in-the-loop simulation. Overall, a linear time-varying RHP formulation utilising a dynamic bicycle model is proposed, where the vehicle dynamics and path constraints are linearised at each time step, allowing the RHP to be formulated and solved as a quadratic program. An optimal racing line is precomputed offline by solving for a periodic time-optimal trajectory along the entire track, which the RHP then tracks in real time. Through simulated experiments, the proposed RHP is shown to be robust to noise, time delay and modelling error, and successfully outperforms Monash Motorsport’s previous motion planning and control implementations. The RHP is demonstrated to safely achieve speeds of up to 25 m/s while running in real time at 50 Hz in these simulated experiments.

Introduction

Formula Student Driverless (FSD) is a university engineering design competition which started in 2017 and is run by Formula Student . The competition tasks student teams with designing, building, and programming a Formula-style race car which can autonomously navigate through known and unknown tracks as quickly as possible. Monash Motorsport (MMS) is Monash University’s Formula Student team which began development of a driverless car in 2018. In 2019, the team converted their existing rear-wheel drive electric car into a driverless car named M19-D. On M19-D, cameras and light detection and ranging (LiDAR) sensors are used to detect cones around the track. M19-D is currently using an early implementation of a receding horizon planner (RHP) as its motion planner. Due to being an early implementation, the main goal for the planner was to be able to successfully finish missions, with lap time performance only being a secondary subgoal. Therefore, the RHP was implemented using a relatively simplistic formulation, and an optimal control library, ACADO Toolkit [1], was used as a high-level interface to solve the RHP problem. This thesis aims to improve upon the previous RHP implementation for use on M19-D, and ultimately improve the lap times that can be achieved by the autonomous systems.

Conclusion

This thesis presents a motion planning implementation for an autonomous Formula Student racecar to compete in the FSD competition. The proposed motion planner first computes an optimal racing line for the entire track horizon offline, then tracks this reference trajectory in real time using an LTV-RHP. The proposed RHP specifications were justified against alternative modelling and discretisation methods, before evaluating its performance in a full simulation. By transcribing the optimal control problem to an optimisation problem, additional flexibility over the design of the RHP was achieved. Multiple discretisation methods were explored to perform this transcription, where the successive linearisation scheme was ultimately chosen for being significantly computationally lighter, while still performing adequately compared to the heavier but more accurate nonlinear discretisation schemes. The fast computation times not only aids in reducing the total dead time that needs to be compensated for, but also allows the LTV-RHP to run at a higher frequency to achieve superior tracking behaviour. New modelling techniques were also explored given this additional flexibility. Significant performance improvements were achieved by utilising a dynamic bicycle model, which allowed the LTV-RHP to operate the vehicle closer to the limits of the vehicle dynamics, while the light successive linearisation discretisation scheme allowed the more complex vehicle model to be feasibly solved in real time. Curvilinear coordinates which required a parametric piecewise spline to describe the track path was implemented, which allowed for superior control of the car and consideration of the track boundaries. Modelling the transient response of the actuators also compensated for a significant portion of the time delay, thus reducing the amount of dead time the less stable forward-prediction compensation method needed to consider. Overall, the proposed RHP was validated and compared against existing planners in a hardware-in-the-loop simulation environment. The RHP is successfully shown to significantly outperform MMS’s previous motion planning implementations, and consistently achieve faster lap times in a variety of different tracks