Initial Experiments on the End-Point Control of a Flexible One-Link Robot

Abstract

It has been known for some time ( Gevarter 1970) that if a flexible structure is controlled by locating every sensor exactly at the actuator it will control, then stable operation is easy to achieve. Nearly all commercial robots are controlled in this way, for this reason. So are most flexible spacecraft. Conversely, when one attempts to control a flexible struc ture by applying control torques at one end that are based on a sensor at the other end, the problem of achieving stability is severe. Solving it is an essential step for better control in space: the space-shuttle arm is a cogent example. The next generation of industrial robots will also need such control capability, for they will need to be much lighter in weight ( to achieve quick response with modest energy), and they will need to achieve greater precision by employing end-point sensing. A set of experiments has been constructed to demonstrate control strategies for a single-link, very flexible manipulator, where the position of one end is to be sensed and precisely positioned by torquing at the other end. The objective of this first set of experiments is to uncover and solve problems related to the control of very flexible manipulators where sen sors are not colocated with the actuator. The experimental arrangement described here is also a test bed for new designs for flexible-structure controllers, designs that use insensitive, reduced-order control and adaptive control methods, for example. This paper describes the experimental arrangement, model identification, control design, and first experimental results. Some interesting results are the following. First, good stability can be achieved for such noncolocated systems, and reponse can be achieved that is effectively three times faster than the first natural cantilever period of the system: but a good model of the system dynamics and rather sophisticated control algorithms are essential to doing so. Even then, the system will always be conditionally stable. In addition to the tip sensor, a colocated rate sensor and nearly colocated strain gauges have been found to be very useful for achieving good closed-loop performance, that is, high gain and high band width. Second, there is an ultimate physical limit to achiev able response time, namely, the time required for a wave to travel the length of the member. Well-designed controllers can approach this limit. Third, the use of end-point sensing makes less critical the elaborate dynamic conditioning of position-command signals— "model-following " differentia tors, feed-forward, and the like—such as are typically needed in present-generation robots that use "dead reckoning" in lieu of end-point sensing. With end-point sensing, feedback alone ( suitably conditioned) is sufficient to whip the tip to the commanded position and hold it there precisely. Even more important, a shift in, for example, workpiece with respect to robot base, no longer produces an error.

Vibration Suppression of a Two-Link Flexible Manipulator

“…To improve the system response, energy consumption, and the overall mass components of robot manipulators, various types of flexible link manipulators have been modeled, designed, and implemented [1][2][3]. In [4], modeling and control of a single flexible-link robot arm was proposed and developed.…”

Embedded Sensors and Actuators for Lightweight Structures

“…Much effort has been invested in developing control methodologies that modify the joint torque profiles in a lightweight, high speed robot manipulator in order to suppress vibration in the flexible links and improve end-point positional accuracy [1][2][3][4][5][6][7]. Similar concerns arise regarding the interaction between structures and control methodologies for large space structures [8].…”

“…These techniques rely on a model of the flexural behavior of the link(s). Some of them operate in real-rime [1,2], while others are computed prior to motion and may depend on inverse dynamics [3][4][5][6]. The principal drawback to all of these is that while the vibration modes are properties of the flexible links, the attempted solutions rely on actuation at the joint motors.…”

“…This condition of non-collocation of the vibrational coordinates and the actuators' degrees-of-freedom has hampered the satisfactory identification of a real-time controller. Furthermore, techniques for sensing have also relied on location of sensors remote from the actual vibrational coordinates [1][2][3][4][5][6]8].…”

Estimation of the flexural states of a macro-micro manipulator using point-acceleration data

“…In [1], an optical sensor-comprising a light bulb, a focusing lens, and a photodetector-was used to determine the end-point displacement of a single-link flexible manipulator, which was then used in a state-feedback control loop. The data were then processed in a discrete filter to obtain the system states.…”