  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.
