A Computationally Efficient and Human Implementable Minimum-lap-time Control Policy for Energy-limited Race Cars

TL;DR

This paper introduces a real-time, optimal energy management control policy for race cars that is simple enough for human drivers to implement, significantly reducing computation time while maintaining global optimality.

Contribution

The paper develops an analytically derived, bang-bang control policy for energy-limited race cars, enabling fast, human-implementable solutions with provable optimality.

Findings

Computes globally optimal control strategies in milliseconds

Reduces computational complexity compared to numerical methods

Provides a human-friendly control cue for race car energy management

Abstract

This paper presents a provably optimal, real-time capable energy management policy for race cars that provides simple human-driver-implementable control cues. Specifically, we first formulate the energy-constrained minimum-lap-time control problem via Pontryagin's Minimum Principle (PMP) and derive the optimal policy and costate dynamics using Karush-Kuhn-Tucker (KKT) optimality conditions. We show that the optimal control policy follows a bang-bang structure that is easily implementable by a human driver, eliminating the need for potentially dangerous active throttle pedal overwrites or distracting signals. Moreover, the analytical formulation of the optimal system dynamics allows us to recast the problem as a sequence of boundary-value problems, which can be efficiently solved using root-finding methods. Our results show that our proposed approach can compute the same globally optimal control strategies of existing numerical methods based on direct optimal control, whilst drastically reducing computation time from the order of seconds to milliseconds.