EXPERIMENTS ON THE END-POINT POSITION CONTROL OF A VERY FLEXIBLE ONE-LINK MANIPULATOR (FEEDBACK, NON-RIGID, ELASTIC, ROBOTS, LARGE SPACE STRUCTURES, VIBRATION)

An experiment has been constructed to demonstrate control strategies for the next generation of fast-moving and lightweight industrial robots as well as for future manipulators for space applications: it consists of a one link, one meter long, very flexible manipulator in which the position of one end (tip) is to be sensed and precisely positioned by torquing at the other end. The arm is moving and bends freely in the horizontal plane but is stiff in torsion and vertical bending. For such a situation, where the sensor used for feedback and the actuator are separated by a flexible structure (non colocation), the problem of achieving stability is severe.; After a description of the dynamic modelling of the arm and of the experimental apparatus, the application of classical and modern control design techniques to the design of a tip position controller is discussed. It is shown that good stability can be obtained with a closed-loop bandwidth that is effectively two times the frequency of the fundamental cantilevered mode of the arm (f(,c) = 0.5 Hz). The main advantages of tip-position versus joint-angle feedback are higher precision on tip positioning, faster recovery from external tip disturbance forces and the capability to achieve target tracking. The nonminimum phase transmission zeros of the open-loop transfer function from torque to tip-position output limit the ultimate bandwidth of the tip-position loop. An increase in the position bandwidth has to be traded-off versus a decrease in the stability margins of the tip-position loop. The nonminimum phase zeros have the same effect as an equivalent time delay equal to about 1/10 of the period of the fundamental cantilevered mode of the experimental arm. This equivalent delay includes a pure time delay that is interpreted as the time for a bending wave to travel the length of the beam.; Good closed-loop performance is strongly dependent on the addition of auxiliary colocated sensors (hub-rate and strain-gauge mounted close to the actuator) to the primary tip-position sensor. Excellent agreement has been obtained between experimental and simulated time responses.; A fixed-gain reduced-order compensator that is robust to changes in the arm payload has been successfully implemented.; A scheme for switching smoothly between control using an end-point position sensor and control using a colocated joint-angle sensor has been designed and demonstrated for large angle slew maneuvers of the manipulator.