Dynamic Nonprehensile Manipulation with Remote Contacts

When an object is manipulated, contacts between the object and the robot, and between the object and the environment, serve two purposes: they transmit forces to the object, and impose motion constraints on the object. Even if the robot can precisely control its configuration, it is slave to the interactions at the contacts for the control of the object. Contact interactions are governed by friction laws which are non-Newtonian, and hence hard to control. We define any contact between the object being manipulated (the manipuland) and the environment as a remote contact, as the robot can influence the contact interaction only indirectly by applying a force on the manipuland. This makes remote contacts much harder to control than contacts involving the robot and the manipuland. Remote contacts occur frequently in assembly and in part fixturing. They occur when we manipulate objects too large or heavy to lift, when we push on them or topple them, and in mobile manipulation, where a robot uses its wheels to move the manipuland. In both these cases, the environment provides a helping hand; the remote contacts assist in load-bearing and in stabilizing the manipuland. In this thesis, we propose to study three manipulation problems involving remote contacts that have not been addressed by the community. The trajectory generation problem addresses the synthesis of robot controls that move the manipuland from a start to a desired goal, in the presence of remote contacts. We propose to solve this problem by task/shape decomposition, where we are interested in controlling task variables (here the manipuland) and allow shape variables (here the robot) to follow compliantly along. This allows us to break down the problem into a smaller subproblem that is easier to control. The trajectory following problem addresses the robust tracing of the desired trajectory in spite of errors in actuation, sensing and model parameters like friction. We propose to use a hybrid position/force controller together with ideas from the theory of switching systems to control the motion of the manipuland, and intrinsic tactile sensing for contact position and contact force feedback. The design problem addresses the description of the set of shapes that can be manipulated by a given robot, and the set of feasible trajectories for a given robot and manipuland. We hope to shed light on this problem by studying the underlying structure in the dynamic equations of motion.