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

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.