Control Engineering Practice 9 (2001) 411}423 Fuzzy predictive algorithms applied to real-time force control  L.F. Baptista, J.M. Sousa, J.M.G. Sa H da Costa* Escola Na & utica Infante D. Henrique, Department of Marine Engineering, Av. Eng. Bonneville Franco, Lisbon, Portugal Technical University of Lisbon, Instituto Superior Te & cnico, Department of Mechanical Engineering/GCAR, Av. Rovisco Pais, 1049-001 Lisbon, Portugal Received 5 June 2000; accepted 11 August 2000 Abstract This paper proposes combining a classical impedance controller with a fuzzy predictive algorithm. This algorithm calculates the optimal virtual trajectory that is given to the impedance controller. This control strategy allows for the inclusion of a non-rigid environment, represented by a nonlinear model, in the control design in a straightforward way. Thus, improving the global force control performance. In order to reduce the oscillations of the optimized reference position, a fuzzy scaling machine is included in the force control strategy. The performance of the force control scheme is illustrated for an experimental two-degree-of-freedom robot. A real-time implementation of the fuzzy predictive algorithm revealed better performance in terms of force control than the classical force control algorithms.  2001 Elsevier Science Ltd. All rights reserved. Keywords: Force control; Fuzzy predictive algorithms; Impedance control; Real-time control 1. Introduction Nowadays, the development of new materials, the im- provement in the mechanical design of robot manipula- tors and faster microprocessors have highlighted the necessity of applying more sophisticated control algo- rithms in the new generation of industrial robots (Siciliano, 1998). The implementation and validation of advanced control algorithms requires a #exible structure in terms of hardware and software. This equipment is of crucial importance in studying and analyzing the con- troller's performance. However, one of the major di$cul- ties in testing new force/position control algorithms relies on the lack of available commercial open-robot control- lers. In fact, industrial robots are equipped with digital controllers having "xed control laws, generally of the PID type, with no possibility of modifying the control algorithms to improve their performance. Generally, ro- bot controllers are programmed with speci"c languages like VAL # with "xed programmed commands having  This work was partly supported by PRODEP Program 5.2, No. 3/94 and PRAXIS XXI under Contract 3/3.1/GEC/2707/95. * Corresponding author. Tel.: #351-21-8417-187; fax: #351-21- 8498-097. E-mail address: sadacosta@dem.ist.utl.pt (J.M.G. Sa H da Costa). internally de"ned path-planners, trajectory interpolators and "lters, among other functions (Baptista & Sa H da Costa, 2000). Moreover, in general, these controllers only deal with position and velocity control, which is insu$- cient when to obtain an accurate force/position tracking performance is necessary. Considering these di$culties, in the last few years several open control architectures for robotic applica- tions have been proposed. Generally, these solutions rely on digital signal processor techniques (Jaritz & Spong, 1996; Mandal & Payandeh, 1995) or on expensive VME hardware running under the VxWorks operating system (Kie!er & Yu, 1999). This fact has stimulated the devel- opment of a low cost, open PC-based management, supervision and control software kernel. The real-time software tool was developed taking into account require- ments such as low cost, #exibility and the possibility of incorporating new hardware and software (Costescu & Dawson, 1998). Traditionally, industrial robotic tasks are generally related to manipulation, which requires only controlling the position of the arm, but other tasks like assembly, pushing and polishing require interaction between the manipulator's end-e!ector and the environment. This fact leads to the necessity of controlling the force of interaction between the robot and the environment, and consequently the development of more sophisticated 0967-0661/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved. PII:S0967-0661(00)00119-2