  Even though mobile robots have been around for decades, trajectory
optimization and continuous time collision avoidance remain subject of active
research. Existing methods trade off between path quality, computational
complexity, and kinodynamic feasibility. This work approaches the problem using
a nonlinear model predictive control (NMPC) framework, that is based on a novel
convex inner approximation of the collision avoidance constraint. The proposed
Convex Inner ApprOximation (CIAO) method finds kinodynamically feasible and
continuous time collision free trajectories, in few iterations, typically one.
For a feasible initialization, the approach is guaranteed to find a feasible
solution, i.e. it preserves feasibility. Our experimental evaluation shows that
CIAO outperforms state of the art baselines in terms of planning efficiency and
path quality. Experiments on a robot with 12 states show that it also scales to
high-dimensional systems. Furthermore real-world experiments demonstrate its
capability of unifying trajectory optimization and tracking for safe motion
planning in dynamic environments.
