Systems & Control Letters 40 (2000) 31–35 www.elsevier.com/locate/sysconle Stability analysis of a rigid robot with output-based controller and time delay ( Amit Ailon a ; * , Michael I. Gil’ b a Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva 84105, Israel b Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel Received 18 April 1999; received in revised form 25 October 1999; accepted 4 December 1999 Abstract This study considers the problem of stabilizing a rigid robot with an output-based controller and time-delayed input functions applied to the robot joints. We establish sucient conditions for asymptotic stability of the system under consideration. These conditions are based on well-dened relationships between the magnitude of the controller gains and the time delay factor. c  2000 Elsevier Science B.V. All rights reserved. Keywords: Rigid robot; Time delay; Position measurements; Stability 1. Introduction A real-time controller computer can be thought of as consisting of three stages: acquiring data from sen- sors, processing data to generate control commands, and outputting the results to the actuators. Each of the three stages will take time to complete [10]. Further- more, in practice time delays may be encountered in various types of systems, especially in systems with hydraulic, pneumatic, or mechanical transmissions [9, Sections 4–8], which play major roles in the various actuators of industrial robots. Excluding some partic- ular cases of DC motors, the mathematical model of the augmented model including the robot and its actuators is highly involved and analytical tools to ( This research was supported in part by the Paul Ivanir Center for Robotics Research and Production Management, Ben Gurion University of the Negev, Beer Sheva, Israel. M. Gil’ was sup- ported by the Israel Ministry of Science and Technology Kamea Fellowship. * Corresponding author. Fax: +972-7-647-2949. E-mail address: amit@ee.bgu.ac.il (A. Ailon) treat the resulting nonlinear model are unknown in most cases. In [10] the eects of a time delay resulting from the computation of the control function on the sys- tem performances were considered. However, as far as the robot model is concerned, the control algorithm proposed in the last reference is based on the assump- tion that the system parameters are completely known and hence, by selecting a control torque= force vector that cancels the nonlinear terms, the resulting model reduces to a linear one. While control problems asso- ciated with time delay in the plant input in linear sys- tems have been the subject of previous papers, such as, for example, [12], the stability of the nonlinear model representing the dynamics of a rigid robot involving time delay in the torque input level, is still an open control problem in robotics. This situation stimulates our interest in study- ing the eects of a time delay appearing in the output-feedback loop on the stability of the model of a rigid robot with rotary joints. In particular, we establish here sucient conditions for stability of 0167-6911/00/$ - see front matter c  2000 Elsevier Science B.V. All rights reserved. PII:S0167-6911(99)00120-6