Mid-air motion planning of robot using heat flow method with state constraints

We address in this paper the problem of planning motion of free floating robot with state constraints. Due to the conservation of angular and linear momentum during the in-air motion, the problem is two-fold: one needs to design, in addition to the in-air motion, the initial impulse that imparts the robot with the appropriate momentum to perform a desired motion. The existence of state constraints such as joint limit makes the planning problem even more challenging. We propose in this paper a new method to address this problem. The method is a homotopy method which deforms an arbitrary path connecting the desired initial and final states to a feasible trajectory between these states, that is a trajectory that meets the system's dynamics and constraints. From this trajectory, the method extracts both the controls and initial momentum needed to perform the motion. The deformation of path is leaded by geometric heat flow which is defined by a Riemannian metric that encodes the system dynamics and state constraints. We illustrate the method by designing somersault motions for a diver robot.