Design and Control of Precise Robots with Active and Passive Kinematic Pairs
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20-04-2010, 03:27 PM


This work features the design and a control scheme for an active multi-degree of freedom kinematic pair piezoelectric robot. We introduce the piezoelectric active kinematic pair where the joints between the links are made from piezoactive material. The objective is to design an energy efficient underactuated precision micromanipulator with a fault-tolerant design where not all joints require actuators. Typical configuration of this type of piezoelectric robot is that it consists of several identical joints, i.e. kinematic pairs of the 3rd class. Each pair has 3 degrees-of-freedom (DOF) consisting of passive spheres (unactuated joints) made from ferromagnetic material, and one active link (actuated joint) in the base or the gripper of the robot fabricated using a piezoceramic transducer (e.g. in a form of cylinder polarized in radial direction). Controlling the forces in the contact area of the kinematic pairs, leads to the motion of one link relative to the other. To control the friction in the contact zone of the kinematic pairs, resonant oscillations of a piezoceramic cylinder or disk are generated, i.e., symmetrical oscillations (e.g. lower radial or axial forms of the cylinder) are used. Effectively, the piezoceramic material also functions as a braking mechanism to control the degree of freedom of the manipulator.

In such type of hyper-redundant manipulator or snake-like robot, the exact position of the gripper (6 DOF) is important; and therefore the relative position of the intermediate links in the robot joint space has to be determined. Using the direct piezoeffect of the piezoelectric transducers and sectioning the electrodes, it is possible to determine the relative position of the links in each kinematic pair and the distribution of the forces in the contact area between passive and active links. This eliminates the need for any additional sensory instrumentation in every joint and therefore simplifies the final design of the manipulator.

For tracking and positioning applications using the piezoelectric robot, we utilize the coupling dynamics that exist between the active kinematic pairs to control the angles of the unactuated joints indirectly. A two-phase control sequence describes the positioning of the manipulator in the robot workspace. During the first phase, holding brakes are applied (by decoupling the electrical excitations to these joints) to all unactuated joints except to the joint to be controlled. An electrical excitation signal is applied to the piezoceramic material to generate high-frequency resonant mechanical oscillations in the contact zone of this joint. As a result, the friction force in this joint is sharply reduced and is therefore indirectly controlled by the motion of the actuated joint via the coupling characteristics of the manipulator dynamics. It is assumed that when the holding brake on this unactuated joint is released, it can move freely under the coupling forces generated by the motion of the actuated joint. The basic controllability of such a system using linearized dynamics has already been investigated. By controlling the magnitude and polarity of the torque in the actuated joint, precise positioning of the unactuated joints is accomplished using feedback control law to guarantee asymptotic convergence to desired positions in the robot joint space. The unactuated joint is locked into position as soon as it reaches the desired set point. Next, the piezoceramic material in the adjacent unactuated joint is excited, controlled, and locked, and the sequential control process repeats for all remaining unactuated joints. During the second control phase, while all unactuated joints are locked in their respective positions in robot joint space, the actuated joint is controlled without affecting the state of the other joints. This n-step sequence completes the manipulator positioning operation for an n-link robot.

To demonstrate the feasibility of this control scheme, a robust control strategy using the sliding mode control was developed for a 3-link manipulator that has one actuated and two unactuated joints. Simulation results show that both set point and time-varying trajectory tracking by the robot manipulator is attainable to a fairly high precision. In modeling the dynamics of the manipulator, it was assumed that when the holding brake in the unactuated joint is released, i.e. by subjecting the piezoceramic material in the joint to high frequency resonant oscillations, the friction in this joint becomes negligible. From a control point of view, this modeling imprecision among others can have adverse effects on the operation of the manipulator during real-time operation. However, the sliding mode control strategy that utilizes variable structure system theory ensures proper operation of the actuator and piezoelectric braking mechanisms in the presence of system uncertainties and modeling imprecision's. Simulations were performed on this micromanipulator using a modeling uncertainty of up to . Preliminary results indicate superior performance of this controller in controlling the actuated and unactuated joints of the manipulator in the presence of bounded disturbances.
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