Live-constraint-based control for contact transitions

Many manipulation tasks involve transition from unconstrained to constrained motion marked by the contact with a constrained surface. This phenomenon divides the task into more than one phase, each of which requires a different control strategy. Switching from one control strategy to another leads to control discontinuities. The paper seeks to design a controller that avoids such discontinuities. The principle is based on the analysis of impulsive constraints. It is argued that, in theory, such a discontinuity can be avoided by modeling the cause of the force discontinuity of the end-effector as the velocity discontinuity of the constraint surface as opposed to the discontinuity of the Lagrange multiplier. This velocity discontinuity can then be dealt with by a continuous control strategy. A controller is designed based on this principle. Input-output linearization is performed to linearize and decouple the system. Simulation and experimental results are presented to demonstrate the effectiveness of this new approach