Optimal base positioning for complex mobile manipulation tasks

This paper presents a novel control architecture for kinematic control of the base and the arm of a vehicle-manipulator system during complex mobile manipulation tasks. Particularly, we address kinematic control of robots operating in the presence of constraints such as plane or entry hole constraints imposed on a point on the manipulator arm and an additional focal point constraint imposed on the base. The focal point constraint guarantees that any camera mounted on the base points in the desired direction. We present a formulation that allows us to represent both types of constraints in the same way by introducing a new set of velocity variables. The main advantage of the proposed approach is that we are able to control the end-effector motion in the normal way using conventional operational space control schemes, and by re-writing the Jacobian matrix we also guarantee that the constraints are satisfied. The most challenging problem with this type of constraints is the extremely complex structure that arises when the constraints are mapped from the operational space to joint space. We solve this by first finding a new set of velocity variables for a point on the robot in the vicinity of the obstacle, and on these new variables we impose a structure which guarantees that the robot does not violate the constraints. We then find a mapping denoted the Constrained Jacobian Matrix from the joint variables to these new velocity variables and use this mapping to find a trajectory in joint space for which the constraints are not violated. We present for the first time the Constrained Jacobian Matrix which imposes kinematic constraints on the base and the chain of the vehicle-manipulator system using the same formalism in both cases.