Constraints Compliant Control: Constraints compatibility and the displaced configuration approach

Abstract

Abstract-Most of the literature reactive control laws have much difficulties to handle properly constraints such as joint limits, obstacles and saturations, including them as equalities in the Inverse Velocity Kinematics (IVK) problem. Actually, it seems relevant to handle them through inequalities, as the constraints are more numerous than the number of DOFs. However, the intuitive constraints expression can lead to incompatibilities between constraints, which necessarily induces constraints violations. This paper brings two distinct contributions. First, the usual constraints inequalities are modified to make them compatible permanently. Second, an intuitive and efficient constraint compliant control law is proposed.

Minimization of the rate of change in torques during motion and force control under discontinuous constraints

“…Indeed, with the decrease of δt, the error of h i increases dramatically. In [22] a constraint compliant control law is proposed to solve this problem, but it is only applied in the case of inverse kinematics. The approach in [23] increases the discretization time step δt in the constraint (not in the control time step) properly to diminish the error for dynamic control problem.…”

Synthesis of complex humanoid whole-body behavior: A focus on sequencing and tasks transitions

“…A second strategy consists in rewriting the constraints set in order to ensure compatibility and thus the existence of at least one solution. This second strategy was not implemented within the framework of this work but interested reader can refer to the recent work of Rubrecht et al ( [16]) who treat this problem at the velocity kinematics level.…”

Motion safety and constraints compatibility for multibody robots

“…The contribution of this paper is to propose a methodology to ensure safety at the control level. The control problem resolution is out of the scope of this paper: it is assumed that once the control problem is feasible, a control law algorithm such as the one proposed in Rubrecht et al (2010aRubrecht et al ( , 2010b, solves it appropriately (Constraints Compliant Control law). The present work focuses on the formulation of the control problem.…”

“…2. It has been locally treated by Decre et al (2009), but as shown in Rubrecht et al (2010b), the proposed method is tight and can be smoothened by imposing that the joint distance to the joint position limit at next time step should remain superior to the current joint distance needed to decelerate. As a result, a modified expression of F P is proposed (joint i)…”

“…Rubrecht et al 2010b). This condition implies that the vector of maximum deceleration velocityq dec (k + 1) which general term iṡ…”