Online Motion Planning based on Nonlinear Model Predictive Control with Non-Euclidean Rotation Groups

TL;DR

This paper introduces an online motion planning method for robot navigation that explicitly accounts for non-Euclidean rotation groups using nonlinear model predictive control, improving accuracy in rotational state spaces.

Contribution

It presents a novel MPC-based approach that incorporates nonlinear operators for non-Euclidean rotations, with practical implementation and comparative analysis.

Findings

Effective in complex parking scenarios for kinematic bicycle models

Comparable performance and computation times for simpler robots

Available as open-source C++ software

Abstract

This paper proposes a novel online motion planning approach to robot navigation based on nonlinear model predictive control. Common approaches rely on pure Euclidean optimization parameters. In robot navigation, however, state spaces often include rotational components which span over non-Euclidean rotation groups. The proposed approach applies nonlinear increment and difference operators in the entire optimization scheme to explicitly consider these groups. Realizations include but are not limited to quadratic form and time-optimal objectives. A complex parking scenario for the kinematic bicycle model demonstrates the effectiveness and practical relevance of the approach. In case of simpler robots (e.g. differential drive), a comparative analysis in a hierarchical planning setting reveals comparable computation times and performance. The approach is available in a modular and highly configurable open-source C++ software framework.