Control Engineering Practice 14 (2006) 1423–1433 Impact stabilizing controller for hydraulic actuators with friction: Theory and experiments P. Sekhavat, N. Sepehri à , Q. Wu Fluid Power Research Laboratory, Department of Mechanical and Industrial Engineering, The University of Manitoba, Winnipeg, Man., Canada R3T 5V6 Received 4 February 2004; accepted 24 October 2005 Available online 9 December 2005 Abstract Stabilizing manipulators during the transition from free to constraint motion is an important issue in contact task control design. This paper documents the development, theoretical analysis and experimental evaluation of a Lyapunov-based control scheme to regulate the impacts of a hydraulic actuator that comes in contact with a nonmoving environment. Upon sensing a nonzero force, the controller positions the actuator at the location where the force was first sensed, exerting minimal force on the environment. The scheme does not require continuous measurement of force or velocity during the short period of impacts, making it very useful for practical cases. Furthermore, no knowledge of the impact dynamics, friction effects, servovalve dynamics, or hydraulic parameters is required for control action. Stability of the control scheme is verified via analytical analyses. Due to the discontinuous friction model and the discontinuous nature of the proposed control law, the control system is nonsmooth. The existence, continuation and uniqueness of Filippov’s solution to the system are, therefore, investigated. The extension of LaSalle’s invariance principle to nonsmooth systems is next employed to prove that all the solution trajectories converge to the equilibria. The controller is finally tested experimentally to verify its practicality and effectiveness in collisions with hard and soft environments and with various approach velocities. r 2005 Elsevier Ltd. All rights reserved. Keywords: Impact control; Hydraulic actuators; Stability 1. Introduction Due to their high durability, high power-to-weight ratios and rapid responses, electrohydraulic manipulators play an important role in inspection, maintenance and repair purposes conducted in marine missions, oil and gas surveys, telerobotic operations, as well as military applica- tions. An essential issue in such applications is proper interaction between the manipulator and the environment. The manipulator should be able to follow a free space trajectory and make a stable contact with the environment while the energy of impacts is dissipated and the desired contact force is achieved. The transition between the free- space to constrained-motion may involve undesirable impact forces that drive an otherwise stable control system into instability. Stabilizing the end-effector during the transitional motion can be approached from two view- points (Brogliato, 1999): (i) study conditions that guarantee no rebound after the first contact; (ii) study conditions that ensure Lyapunov-based stability of the system at the expense of relaxing the bounceless condition. When the environment stiffness grows unbounded, bounceless con- dition becomes impossible to obtain using finite force control with nonzero contact velocity (Brogliato, 1999). Therefore, a unified realistic stability analysis that applies to both compliant and rigid models would seek the second viewpoint. One of the main approaches employed for stable contact task control is impedance control (Bilodeau & Papadopoulos, 1998; Ha, Nguyen, Rye, & Durrant-Whyte, 2000; Heinrichs, Sepehri, & Thornton-Trump, 1997). The advantage of the method is providing a unified control structure for all various modes of operation with no need for switching between control laws. On the other hand, there are a number of drawbacks rendering the algorithm vulnerable in realistic applications (Marth, Tarn, & Bejczy, 1994; Vukobratovic, 1997). For example, force tracking ARTICLE IN PRESS www.elsevier.com/locate/conengprac 0967-0661/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.conengprac.2005.10.007 à Corresponding author. Tel.: +1 204 474 6834; fax: +1 204 275 7507. E-mail address: nariman@cc.umanitoba.ca (N. Sepehri).