Contact Stability Analysis of a One Degree-of-Freedom Robot

Bernard Brogliato (1) , P. Orhant (1)

1 LAG - Laboratoire d'automatique de Grenoble

The aim of this note is to examine the conditions of stability of a simple robotic task: we consider a one degree-of-freedom (dof) robot that collides with a spring-like environment with stiffness $k$, the goal being to stabilize the system in contact with the environment. We study conditions on the feedback gains that guarantee quadratic Lyapunov stability of the task with a well-conditioned solution to the Lyapunov equation. It is shown that when the environment's stiffness $k$ grows unbounded, those conditions yield unbounded values of the gains. Motivated by the stability analysis of the impact Poincaré map in the perfectly rigid case ($k = +∞$), we propose an analysis that is independent of $k$. It enables us to conclude on global asymptotic convergence of the system's state towards the equilibrium point. This work can also be seen as the study of stability of a contact (force control) phase, taking into account the unilateral feature of the constraint.

Mots clés: free and constrained motion; compliant and rigid environment; quadratic Lyapunov stability; contact stability; impact Poincaré map

Domaines: Mécanique des structures [physics.class-ph]

Bernard Brogliato, P. Orhant. Contact Stability Analysis of a One Degree-of-Freedom Robot. Dynamics and Control, 1998, 8 (1), pp.37-53. ⟨10.1023/A:1008226913003⟩. ⟨hal-02279953⟩