Global minimization of the robot base reaction force during 3-D maneuvers

This paper provides closed-form equations parameterizing the 2 smooth path that globally minimizes the Euclidean norm of a robot’s peak base reaction force while avoiding obstacles during three-dimensional maneuvers in a gravity-free environment. In addition, the paper describes a computationally efficient technique that leads to a path typically having a peak force within 5% of the optimal path. In both cases, the equations used to define the robot’s motion are formulated after mapping the initial robot configuration, final (or goal) Cartesian location, and obstacles into a new space termed the center of mass (CM) space. This space has the advantage of being a Cartesian-like space that allows direct application of many existing control techniques, such as resolved rate control. In the CM space, a series of path segments guide the robot around the obstacles. Solving a system of equations based on these segments for boundary condition dependent constants determines the path. Currently, closed-form equations are unavailable for the boundary dependent constants, preventing exact determination of the globally optimal path. This paper introduces a five-step procedure for locating the optimal path. The final step uses a sequential quadratic programming technique to locate boundary dependent constants. The equation formulations assume that the initial configuration of the robot is known and that the robot mass and obstacle positions are constant during the maneuver. The method developed has direct applicability to redundant and nonredundant robots. A detailed example, based on a nonredundant robot avoiding a single obstacle, illustrates the concepts presented.