Energy-Optimal Trajectories for Overactuated Robots

We present a method for computing energy optimal trajectories for an overactuated wheeled robot under quasistatic conditions, enabling it to climb over discontinuous terrain. The trajectories can be arbitrarily close to optimal with respect to energy, depending on available computing resources. We apply our approach to control the Goes-Over-All-Terrain (GOAT) vehicle. The GOAT has four active wheels connected by four separate lever arms to the robot’s body, giving it signi£cant mechanical ability. Our approach is to de£ne a continuous space of possible robot con£gurations as well as discrete actions that carry the robot through the space. When initial and goal states are speci£ed, a classical A.I. planning algorithm can be applied to £nd a sequence of actions to reach the goal con£guration. A thorough analysis of the stability of the robot is done along with a comparison of time-optimal and energy-optimal trajectories. We also compute the minimum required coef£cient of friction along the path. The approach is demonstrated in a two-dimensional simulation, applied to several challenging terrain problems.