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

Provides closed-form equations parameterizing the C² smooth path that globally minimizes the Euclidean norm of a robot´s peak base reaction force while avoiding obstacles during 3D maneuvers in a gravity-free environment. Also, describes a computationally efficient technique that leads to a path typically having a peak force within 5% of the optimal path. The equations used to define the robot´s motion are formulated after mapping the initial configuration, final (or goal) Cartesian location, and obstacles into a new space, the center of mass (CM) space. This is 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 procedure for locating the optimal path. Its final step uses sequential quadratic programming 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