Optimal Control for Kinematic Bicycle Model with Continuous-time Safety Guarantees: A Sequential Second-order Cone Programming Approach

TL;DR

This paper introduces a sequential SOCP-based method for solving the optimal control problem of a kinematic bicycle model, ensuring continuous-time safety guarantees through differential flatness and relaxation techniques.

Contribution

It proposes a novel sequential SOCP approach leveraging differential flatness to guarantee continuous-time safety in optimal control of bicycle models.

Findings

Effective in ensuring continuous-time safety constraints

Outperforms state-of-the-art solvers in simulations

Provides a computationally efficient sub-optimal solution

Abstract

The optimal control problem for the kinematic bicycle model is considered where the trajectories are required to satisfy the safety constraints in the continuous-time sense. Based on the differential flatness property of the model, necessary and sufficient conditions in the flat space are provided to guarantee safety in the state space. The optimal control problem is relaxed to the problem of solving three second-order cone programs (SOCPs) sequentially, which find the safe path, the trajectory duration, and the speed profile, respectively. Solutions of the three SOCPs together provide a sub-optimal solution to the original optimal control problem. Simulation examples and comparisons with state-of-the-art optimal control solvers are presented to demonstrate the effectiveness of the proposed approach.