Constraints Compliant Control: constraints compatibility and the displaced configuration approach

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.