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Trajectory-planning for Race Cars with LTL Specifications


H. Fuchs

Master Thesis, SS16 (10494)

This paper describes a method for race car trajectory planning involving different task specifications. The tasks include safety, progress, collision avoidance and recurring goals defined by a linear temporal logic (LTL) formula in the context of minimising travel time. The problem is motivated by requirements for autonomous driving in a racing environment to minimize lap times while avoiding obstacles and part of an ongoing experimental research project using 1:43 scale RC race cars.
Model predictive control (MPC) is used with the objective to minimise travel time by maximizing progress, based on a bicycle model representing the car with non-linear tyre forces on a piecewise affine approximation of the race track to find the optimal trajectory. The combination of a non-linear system dynamics and non-convex constraints from the race track under LTL specifications gives rise to a non-linear optimisation problem subject to mixed-integer constraints (MINLP). It is solved by applying a sequential quadratic programming (SQP) that is part of a real-time iteration algorithm at a sampling rate of 50 Hz in a simulation environment.
The developed mixed-integer quadratic program (MIQP) formulation can be used to compute a good approximation of an optimal trajectory. The control input at each step is computed on a 2.5 GHz dual-core CPU within less than a second, for a prediction horizon of 40 steps, and within tens of minutes for a horizon of 150 steps due to the large number of continuous and binary variables of this method in combination with the use of a generic MIQP solver. Example applications are provided that demonstrate different use-cases of this control strategy for autonomous racing with the purpose of model and performance checking of different tasks under LTL specifications.

Supervisors: Damian Frick, Alexander Liniger, Manfred Morari


Type of Publication:

(12)Diploma/Master Thesis

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2016:IFA_5515
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