Kinematics for combined quasi-static force and motion control in multi-limbed robots

This paper considers how a multi-limbed robot can carry out manipulation tasks involving simultaneous and compatible end-effector velocity and force goals, while also maintaining quasi-static stance stability. The formulation marries a local optimization process with an assumption of a compliant model of the environment. For purposes of illustration, we first develop the formulation for a single fixed based manipulator arm. Some of the basic kinematic variables we previously introduced for multi-limbed robot mechanism analysis in [1] are extended to accomodate this new formulation. Using these extensions, we provide a novel definition for static equilibrium of multi-limbed robot with actuator limits, and provide general conditions that guarantee the ability to apply arbitrary end-effector forces. Using these extended definitions, we present the local optimization problem and its solution for combined manipulation and stance. We also develop, using the theory of strong alternatives, a new definition and a computable test for quasi-static stance feasibility in the presence of manipulation forces. Simulations illustrate the concepts and method.