Adaptive NonlinearBoundary Control of a

Flexible Link RobotArm

Background :

Over the last ten years, the effects of linkflexibility in robot manipulator systems have received muchattention among robotics and controls researchers. The design offlexible link robot arms is primarily motivated by the need forlightweight robot systems. For example, due to theprohibitive cost of placing equipment into outer space, the use ofstandard rigid link robot manipulators is impractical; furthermore,the lack of gravity allows robot designers to constructspace-based robot manipulator systems which would beimpractical on earth. That is, space-based robot manipulators aremore likely to be characterized by long links manufactured fromlightweight metals or composites. Unfortunately, the use of long,lightweight links greatly complicates the corresponding positioncontrol problem since the links are subject to deflection and/orvibration.

Research Objective:

We consider the problem of designing a boundarycontroller for a flexible link robot arm with a payload mass at thelink's free-end. Specifically, we utilize a nonlinear, hybrid dynamic model (the model is hybridin the sense that it is comprised of a distributed parameter,dynamic field equation coupled to discrete, dynamic boundaryequations) to design an exact model knowledge control law whichasymptotically stabilizes the link displacement while driving theactuator hub's position to a desired setpoint.

We then illustrate how the control law can beredesigned as an adaptive controller which asymptotically achievesthe same control objective while compensating for parametricuncertainty. The control strategy is composed of a boundary controltorque applied to the actuator hub and a boundary control force atthe link's free-end. Experimental results are presented toillustrate the performance of the proposed control laws.

Experimental Validation

Description of the Experimental Setup:

The experimental setup consisted of a flexiblealuminum beam attached to the shaft of a NSK Corp., model RS-0810,torque controlled, 3-phase switched reluctance motor which was usedto apply the hub control torque.

A lightweight plastic assembly supporting twoair nozzles located at the endpoint of the beam was used to applythe boundary control force. The nozzles were aligned such that theoutlets were in diametrically opposite directions. Compressed airat 90 psi was supplied through the lightweight flexible air tubescontrolled by high-speed proportional air valves.

A Sensor Development, model 20005 shear forcesensor located at the beam's endpoint was utilized to measure asignal directly proportional to the free-end shear. The signal fromthe shear sensor's bridge circuit was amplified and filtered beforebeing read by an analog input channel on the data acquisitionboard. The measured relationship between input voltage and outputforce was then inverted to enable the application of the desiredboundary control force.

A modular line scan camera mounted on the motorshaft and a high luminescence LED mounted at the beam's endpointwere used to measure the beam's endpoint displacement. Formonitoring purposes only, a second LED was placed at the beam'smidpoint to measure the midpoint displacement. The camera is a 2048pixel, linear CCD camera with an 85 mm F1.4 Nikon lens. The camerahas a resolution of 0.014 cm/pixel when the light source is onemeter away while the capture board hardware provides sampling at arate of 0.588 msec.

Photographs of the Setup:


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