Hybrid Position/Force Control: A Correct Formulation

Abstract

This article will show conclusively that "kinematic instability" is not inherent to the hybrid position/force control scheme of robot manipulators but is a result of an incomplete and inap propriate formulation. The inverse of the manipulator Jacobian matrix is identified as causing the kinematic instability of the hybrid position/force control scheme. Linear algebra is used to explain clearly the implications of mapping between vec tor spaces and to reveal why the inverse of the manipulator Jacobian matrix should not be used in hybrid position/force control. A generalized architecture for hybrid position/force control is presented that can influence both joint positions and torques. This generalized formulation also includes the control of redundant manipulators. Some sufficient conditions for kine matic stability are proposed to determine when a system may become unstable without requiring a complete system analysis. A stable hybrid position/force control scheme is given and is demonstrated using an example that was previously shown to be unstable.

Control of Vibrational State of a Robot Interacting with a Rough Free-formed Surface

“…Особенностью рас� смотренной в этих работах системы управ� ления является то, что для ее работы не требуется заранее задавать профиль по� верхности, как это, например, делается в [11,12]. Профиль может быть произволь� ным, но достаточно гладким, чтобы исклю� чить заклинивание.…”

Automated Guiding Task of a Flexible Micropart Using a Two-Sensing-Finger Microgripper

“…The position control along the rail and the lateral contact force have to be separated. Thus, the use of hybrid control [31], [32] combined with an internal position control [17] is chosen. This control structure is named external hybrid force/position control and was first proposed in [33].…”

Hybrid position/force control of a flexible parallel manipulator

“…It is shown in [21] that the original hybrid control scheme does not satisfy the first set of conditions, which implies that kinematic instability can occur in the original control scheme. It is shown in [22,21] that the kinematic instability problem arises in manipulators with revolute joints due to the inappropriate formulation of selected joint space variables in the position control loop. More specifically, using the inverse of the Jacobian matrix to map the selected position error to the selected joint error causes this phenomena.…”

“…(19) is not a valid formulation and propose a solution to resolve the problem. A modified hybrid control scheme proposed in [21] is used in this study as depicted in Fig. 5, showing that the extra terms corresponding to the null space of J are added to the minimum norm solutions in both loops.…”