Joint-space Recipes for Manipulator Robots Performing Compliant Motion Tasks: Trajectory-optimization, Interpolation, and Control

This thesis reports research results on three different topics under the theme of the automatic execution of compliant motion tasks for robot manipulators: numerical trajectory optimization, smooth interpolation of orientation, and control algorithm design. The major purpose of this research is to present a comprehensive joint-space solution for robot’s hybrid motion/force control, which we believe is more general and robust than the conventional operational-space ones. Firstly, a two-step motion planning scheme for robots subject to motion constraints is proposed. The underlying mathematical foundation of our path optimization method is calculus of variations, for which an iterative algorithm is designed to calculate the intermediate points of the resulting curve without solving a corresponding Euler-Lagrange equation. In the following chapter, we move to the next topic of smooth interpolation of orientation, i.e., the Special Orthogonal Group SO3, which is a smooth submanifold embedded in R3×3. The novelty of our approach lies in its combination of rolling and wrapping with the existing pull back/push forward technique, which further yields several remarkable features appropriate for real-time applications. The dynamics and control aspects of the compliant motion task execution are studied lastly. We will raise a brand-new joint-space formulation of hybrid motion/force control, motivated from difficulties experienced in practical experimentations on a real robotic system. Issues such as contact geometry, closed-loop dynamics, and control algorithm will all be derived in the joint-space. We believe such a melioration xviii