Trajectory modification considering dynamic constraints of autonomous robots

The classic "elastic band" deforms a path generated by a global planner with respect to the shortest path length while avoiding contact with obstacles. It does not take any dynamic constraints of the underlying robot into account directly. This contribution introduces a new approach called "timed elastic band" which explicitly considers temporal aspects of the motion in terms of dynamic constraints such as limited robot velocities and accelerations. The "timed elastic band" problem is formulated in a weighted multi-objective optimization framework. Most objectives are local as they depend on a few neighboring intermediate configurations. This results in a sparse system matrix for which efficient large-scale constrained least squares optimization methods exist. Results from simulations and experiments with a real robot demonstrate that the approach is robust and computationally efficient to generate optimal robot trajectories in real time. The "timed elastic band" converts an initial path composed of a sequence of way points into a trajectory with explicit dependence on time which enables the control of the robot in real time. Due to its modular formulation the approach is easily extended to incorporate additional objectives and constraints.