Impedance Adaptation during a Contact Task 2 Impedance Control 2.1 Basic Principle

In this article we consider, from an experimental point of view, the use of an impedance controller for manipulator in a contact task. During an assembly task, impacts, dynamical perturbations due to contact geometry variations or environment behavior changes, uncertainties and noises induce dii-culties to keep the system stable. The choice of the desired impedance and the reference velocities is a critical problem. To deal with this, from an analysis of contact phenomena, closed loop performances and stability constraints, we propose a control scheme based on an adaptive impedance controller. Before and during the contact, the reference velocity of contacting part (provided by the oo-line part of the system) and the impedance of the driving mechanical system are continously adjusted by a supervisor using the techniques of the fuzzy logic. Basic considerations on impedance control are rst developed and critically analysed. The adaptation rules are then brieey developped and experimental results on bi-dimentional impacts are presented. In many applications of robot manipulators, the end-eeector has to be in contact with the environment. These applications require the control of the wrench exerted by the end-eeector. To cope with this problem , two basic methods have appeared recently : impedance control Hog85] and hybrid force/position control Rai81]. Both have been the subject of numerous implementations ((Kha86] Hog87] Del92]). The principle of hybrid F/P control is to decompose the directions of a task frame in constrained directions , which are force controlled and free directions, which are motion controlled. The diiculty with this method is that the interactions are supposed to be perfect (without energy loss). In practice, this assumption is seldom veriied. In addition, a pure force control in constrained directions induces stability problems, specially during the transitions to establish contact, where a simple switch can induce rebounds ((Mil90]). Impedance control theory takes account of the energy dissipated in the contact. The principle of this method is to program the end-eeector behavior such that the system remains stable when it contacts the environment. Very few works were developed on the choice of impedance to be programmed during an assembly task. Modelizing the environment behavior with an admittance, Colgate introduced the concept of coupled stability to nd the stability condition on end-eeector impedance ((Col88]). Introducing performance speciications (stiiness, bandwidth and closed-loop stability constraints) Kazerooni et al. studied the innuence of desired impedance terms Kaz86]. After a brief review on impedance control, and propositions …