Dynamic modelling of a three-axis pneumatic robot

Abstract

To serve any useful function, the model of a system must reflect the salient features of that system and reproduce, to within an acceptable degree of accuracy, the performance which is observed when it is in operation. When the system is a robot, active in three dimensions, the modelling is comparatively complex and the determination of the values to be attributed to the mechanical parameters and to the coefficients which quantify the interactive torques is far from trivial. As a prelude to the design of a controller which is effective throughout the operating envelope of the robot, the paper describes an investigation into the feasibility of simplifying the modelling procedure without incurring a penalty by way of a significant deterioration in performance prediction. If sufficiently accurate, this tentative model will form the basis of a probabilistic model of reduced complexity which will contain the uncertainty of motion which is exhibited by the robot in operation. Essentially, the estimation of the model parameters follows a two-stage process. On the assumption that the Lagrangian expressions defining a simplified mechanical configuration will describe adequately the actual motion of the robot, a preliminary estimation is made by use of a recursive least-squares technique which provides directly the coefficients of the continuous-time model. This is followed by a sequence of trials carried out on both the preliminary model and on the real system, and so arranged as to emphasise the contribution of each coefficient in turn. By comparison of their responses, the model coefficients are then tuned to achieve an acceptable matching. In addition to inherent cross-coupling, the industrial robot on which the investigation was conducted has nonlinearities introduced by way of pneumatic actuators with complex flow-rate characteristics and which operate in a bang-bang manner. The investigation has shown that the procedure is quite feasible and that the quality of response prediction which was achieved is impressive.