Nonlinear Model-Based Control of a Parallel Robot Driven by Pneumatic Muscle Actuators

In this contribution, three nonlinear control strategies are presented for a two-degree-offreedom parallel robot that is actuated by two pairs of pneumatic muscle actuators as depicted in Fig. 1. Pneumatic muscles are innovative tensile actuators consisting of a fibrereinforced vulcanised rubber hose with appropriate connectors at both ends. The working principle is based on a rhombical fibre structure that leads to a muscle contraction in longitudinal direction when the pneumatic muscle is filled with compressed air. Pneumatic muscles are low cost actuators and offer several further advantages in comparison to classical pneumatic cylinders: significantly less weight, no stick-slip effects, insensitivity to dirty working environment, and a higher force-to-weight ratio. The achievable closed-loop performance using such actuators has already been investigated experimentally at a linear axis with a pair of antagonistically arranged pneumatic muscles (Aschemann & Hofer, 2004). Current research activities concentrate on the use of pneumatic muscles as actuators for parallel robots, which are known for providing high stiffness, and especially for the capability of performing fast and highly accurate motions of the end-effector. The planar parallel robot under consideration is characterised by a closed-chain kinematic structure formed by four moving links and the robot base, which offers two degrees of freedom, see Fig. 1. All joints are revolute joints, two of which the cranks are actuated by a pair of pneumatic muscles, respectively. The coordinated contractions of a pair of pneumatic muscles are transformed into a rotation of the according crank by means of a toothed belt and a pulley. The mass flow rate of compressed air is provided by a separate proportional valve for each pneumatic muscle. The paper is structured as follows: first, a mathematical model of the mechatronic system is derived, which results in a symbolic nonlinear state space description. Second, a cascaded control structure is proposed: the control design for the inner control loops involves a decentralised pressure control for each pneumatic muscle with high bandwidth, whereas the design of the outer control loop deals with decoupling control of the two crank angles and the two mean pressures of both pairs of pneumatic muscles. For the inner control loops nonlinear pressure controls are designed taking advantage of differential flatness. For the outer control loop three alternative approaches have been investigated: flatness-based control, backstepping, and sliding-mode control. Third, to account for nonlinear friction as