Control of constrained robots subject to unilateral contacts and friction cone constraints

Abstract

The projection-based control of a rather general class of robots subject to linear and quadratic inequality constraints pertinent to unilateral contacts and friction cones is presented. The controller can also take into account other physical constraints levied by actuator saturation limits and/or existence of some unactuated joints, and can minimize actuation effort for redundant systems. Moreover, since the controller is not based on derivation of minimal-order dynamics model, it can easily handle contact switching. Therefore, a single controller can be used for different constraint conditions, which is very appealing for applications such as legged robots or grasping robots. The orthogonal decomposition of the generalized force vector yields the primary and secondary control inputs, which are used for motion control and interaction control, respectively. It is shown that the problem of minimizing actuation effort subject to the constraints due to the friction cones, unilateral contacts, and actuation limitations, can be transcripted into an optimization programming in terms of the secondary control variable. The latter optimization problem has a quadratic cost function accompanied by a set of quadratic and linear inequality constraints plus linear equality constraints that can be solved by barrier methods.