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

This paper provides closed-form equations parameterizing the C-2 smooth pat h that globally minimizes the Euclidean norm of a robot's peak base reactio n force while avoiding obstacles during three dimensional maneuvers in a gr avity-free environment. In addition, the paper describes a computationally efficient technique that leads to a path typically having a peak force with in 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 Car tesian-like space that allows direct application of many existing control t echniques, such as resolved rate control. In the CM space, a series of path segments guide the robot around the obstacles. Solving a system of equatio ns based on these segments for boundary condition dependent constants deter mines the path. Currently, closed-form equations are unavailable for the bo undary 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 techni que to locate boundary dependent constants. The equation formulations assum e that the initial configuration of the robot is known and that the robot m ass and obstacle positions are constant during the maneuver. The method dev eloped has direct applicability to redundant and nonredundant robots. A det ailed example, based on a nonredundant robot avoiding a single obstacle, il lustrates the concepts presented.