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.

A Projected Inverse Dynamics Approach for Multi-Arm Cartesian Impedance Control

“…where the superscript i denotes the i th contact. Following the methods proposed in [22], multiplying both sides in (13)…”

Modeling and Control of Multi-Arm and Multi-Leg Robots: Compensating for Object Dynamics During Grasping

“…The PIDC approach can be employed for optimization of contact wrenches considering friction cones [22], [23]. We demonstrated optimization of contact wrenches for multi-arm robots in [21] without compensating for object dynamics.…”

“…PIDC was extended in [22] and [23] to the underactuated case. These approaches employ quadratic programming to project desired contact wrenches control torques onto the active joints.…”

“…In that specific situation the contacts are coplanar and the grasp matrix degenerates [27]. [22] and [23] solve the equality constraint imposed by underactuation (15) for controlling contact wrenches based on quadratic programming. We instead solve it analytically.…”

“…The PIDC approach was validated with a torque-controlled manipulator for wiping a board [20] and dual-arm manipulating an object [21]. [22], [23] extend the framework to the underactuated case employing constrained optimization to maintain the contact. We instead aim for an analytic solution to project the desired contact wrench control torques onto the active joints.…”