From path to trajectory deformation

Path deformation is a technique that was introduced to generate robot motion wherein a path, that has been computed beforehand, is continuously deformed on-line in response to unforeseen obstacles. This paper introduces the first trajectory deformation scheme as an effort to improve path deformation. The main idea is that by incorporating the time dimension and hence information on the obstacles' future behaviour, quite a number of situations where path deformation would fail can be handled. The trajectory deformation scheme presented operates in two steps, ie, a collision avoidance step and a connectivity maintenance step, hence its name 2-step-trajectory-deformer (2-STD). In the collision avoidance step, repulsive forces generated by the obstacles deform the trajectory so that it remains collision-free. The purpose of the connectivity maintenance step is to ensure that the deformed trajectory remains feasible, ie, that it satisfies the robot's kinematic and/or dynamic constraints. Moreover, unlike path deformation wherein spatial deformation only takes place, 2-STD features both spatial and temporal deformation. It has been tested successfully on a planar robot with double integrator dynamics moving in dynamic environments.