IMPACT PHENOMENA IN THE FRACTIONAL-ORDER POSITION/FORCE ROBOT CONTROL N. M. Fonseca Ferreira, J. A. Tenreiro Machado, J. Boaventura Cunha Keywords: Robot, position/force control, impact control. 1. Introduction In this early eighties (Raibert and Craig 1981) introduced the concept of force control based on the hybrid algorithm. Since then, several researchers (O. Khatib 1987) developed these ideas and proposed new algorithms such as the impedance controller. Problems with position/force control are further investigated in required (Hogan, 1985) while more recent studies of this algorithm can be found in ( Siciliano, 1999). There are two basic methods for force control, namely the hybrid position/force and the impedance schemes. The first algorithm (Raibert and Craig 1981) separates the task into two orthogonal subspaces corresponding to the force and the position subspaces. Once established the subspace decomposition two independent controllers are designed. Alternatively, with the second algorithm (Hogan, 1985), by a proper choice of the arm impedance, the interaction forces can be accommodated to obtain an adequate response. This paper studies the position/force control of robot manipulators, required in processes that involve contact between the gripper and the environment, using fractional-order (FO) algorithms. The application of the theory of fractional calculus is still in a research stage, but the recent progress in this area reveals promising aspects for future developments (Oustaloup, 1995, Pondlubny, 1999, Ferreira and Machado, 2003). In this line of thought the article is organized as follows. Sections two and three introduce the hybrid controller (HC) and the position/force cascade controller (CC) and the fundamentals of the FO algorithms, respectively. Section four analyses several experiments for the performance evaluation of two strategies, considering the robot impacts, for different working surfaces. Finally, section five outlines the main conclusions. Figure 1 – The 2R robot and the constraint surface. Dept. of Electrical Engineering Institute of Coimbra, Rua Pedro Nunes - Quinta da Nora 3031-601 Coimbra Codex, Portugal, email: nunomig@isec.pt Dept. of Electrical Engineering, Institute of Engineering of Porto, Rua Dr Ant. Bernardino de Almeida 4200-072 Porto Codex, Portugal,email: jtm@dee.isep.ipp.pt Dept. of Electrical Engineering, University of Trás dos Montes e Alto Douro, Ap 1013, 5000-911 Vila Real, Portugal, email: jboavent@utad.pt Abstract: This paper presents the implementation of fractional-order algorithms both for hybrid and cascade position/force control of robotic manipulators. The system performance and robustness is analyzed in the time domain. The effects of the robot end effect impactor with the environment are also investigated. Copyright © 2004 IFAC c ˆ θ θ c l 2 l 1 q 1 q 2 J 2m J 1m J 2g J 1g x y x c y c {x i ,y i } Trajectory