#### Transcript Gravity Compensation and Compliance Based Force Control for

Gravity Compensation and Compliance Based Force Control for Auxiliarily Easiness in Manipulating Robot Arm Student ID ： MA020213 Student ： 莊沛語 Teacher ：謝銘原 Outline Abstract Introduction GRAVITY COMPENSATOR A. System structure B. Denavit - hartenberg’ form D. Auxiliary torque compensator IMPEDANCE CONTROL FORCE COUNTERBALANCE CONTROL CONCLUSIONS REFERENCES Abstract The objective of this paper is to present the gravity compensation and compliance based force control for auxiliarily easiness in manipulating robot arm. Haptical application of the safety-priority robot arm technique which interacts with people must reduce the ear ratio and design necessary algorithm which can provide auxiliarily easiness in moving the robot arm especially during the teach and learning mode. In this study, discuss the effects of two aspects and propose a control algorithm to improve efficiency of carrying heavy item. Firstly, the gear ratio of motor is bounded so that robot can be more flexibly compliant while user take grip on it. To solve this problem of gravity compensation, we propose a method that based on the concept of vector projection to calculate a general solution which can construct a gravity model of multi-DOF robot arm. Furthermore, we define a virtual mode that is proposed to compensate the deficiency of inertia’s physical phenomenon. Secondly, propose an approach which call it force counterbalance control (FCC) that not only balances external load variation in addition to robot weight itself, but also keeps the property of dexterous easiness in manipulating the multi DOF robot arm. The FCC algorithm can be applied on several applications such as carrying heavy item or being auxiliarily easinese in manipulating robot arm. Introduction Robot arm is widely used in different fields of application, from industrial automation to domestic service. In past time, traditional robot arm have been focused on stiff transmission, rapid movement and high accuracy. Recently, researchers begin to put more emphasis on the robot arm’s safety and reliability . The actuators are often used to drive the hardware of the robots. actuator control is one of the most important issues, and actuators are always used by motor, hydraulic, Pneumatic and so on. In the part of control, a lot of control methods are proposed by robotics researchers, like Impedance Control , Admittance Control (position based control), Force Control, Stiffness Control, force/position Control and even Hybrid control. The control algorithms that are mentioned above always suffer in some physical disturbance, such as gravity, Coriolis force and friction force. The gravity compensator is an indispensable issue; some researchers use special control algorithm that takes into account the maximum admissible payload to reduce the disturbance of gravity , or use the concept of energy , or use Lyapunov control theorem to compensate . The gravity compensator is based on dynamics. Vector projection is fully utilized to accurately compute the torque value that each joint have to be compensated. Thus the gravity compensator can be real time compensated in any position. If the gravity compensator is correct, the robot manipulator can stop in any position after it is moved to any position. Beside of adding gravity compensator, we also add a new method, auxiliary torque compensation, to compensate the deficiency that is caused by gear ratio. Contributed by the compensation, the robot manipulator can be moved freely and lightly. GRAVITY COMPENSATOR A. System structure In structure of the control system which is based on 6DOF arm, use PCI base motion control card that provide the powerful real time calculating capability to program the self design control algorithm . Fig. 1. Control Structure The motion control card provides 1ms servo interrupt time for the routine of the control, and sends out the control command to the servo driver through the D/A converter. The servo driver is configured to the mode which receives the torque command. The test platform of arm is actuated by servo motor with 50 ratio harmonic drives which is in between the arm and servo motor. So, use torque mode to drive motor, and gave robot manipulator some force compensator. TABLE I Fig. 2 .6 DOF Robot arm model TABLE II All of the physical model parameters of the system show in the Table , and the Fig. show the each link and each axis of robot manipulator, such as Link1, link2, kink3, axis1, axis2, axis3, axis4, axis5, axis6. B. Denavit- hartenberg’ form The robot arm is designed with 6-DOF to reach attempted point in 3D space. In order to understand the dynamic state of the robot, every joint space relationship must be established from base to end effector. Fig. 3. (a) 6 DOF Robot arm model. Relationship between every link coordinate systems of the 6- DOF arm using the Denavit - Hartenberg convention. The values of the kinematic parameters are listed in Table , where d1, d3 and d5 are the link lengths of base to shoulder, shoulder to elbow and elbow to wrist respectively. TABLE III And then they correspond to the position in the link coordinate diagram of The D-H convention allows the construction of the forward kinematics function by composing the coordinate transformations into one homogeneous transformation matrix: (1) (b) 4 axis Coordinate systems of the robot. (2) C. Gravity compensator The general control block diagram is . All of robot manipulator controls always suffer in external disturbance such as gravityG(q) , damping and even CoriolisforceC(q, q ) that are caused by angular velocity and linear velocity. , the damping can be reduced by low gear ratio and the Coriolis force is too small to be eliminated in this system. Fig. 4. Control block diagram Because the gripper is too light to ignore, just consider axis1 to axis 4. The coordinate transformation shows in Fig. Then, the dynamics is used to compute the compensator of gravity. Gravity has relationship with each joint, so we base on the concept of following with Fig. 1. Base coordinate bases on X0, Y0 and Z0. 2. Gravity always points to X0 of base coordinate. 3. The torque that one joint sustains is the moment projection that relatives this joint. In Fig. 6, F means a force vector in 3D space, r means nearest distance vector of 3D space and e means the unit projection vector, so the equation of the moment in 3D space is got form Fig. (3) • The moment size that projects along unit vector computed with and by inner product in (4) can be (4) (5) Where means projection vector of torque. Base on the concept of (4) and (5), expand the single axis to multi-DOF axes and compute the torque of each axis that gravity causes. F is equivalent to each link weighting, R is equivalent to the center of each link and e is equivalent to the unit vector of motor of each joint. F, r and e of every joint can be computed form Fig.5 (b) and (6), (7). (6) (7) (8) (9) (10) By (8), (9), (10), each joint torque that have to be compensated by motor can be obtained with Fig.7. Fig. 7. The physical features of every axis. D. Auxiliary torque compensator In the condition of senseless, the gear ratio make the robot manipulator is manipulated difficultly on haptical control. Therefore, the methods that are angular momentum and angular impulse principle and parabolic curve are proposed to deal with this damper question. Therefore, bring up a method of parabolic curve to solve above problem, and the parabolic curve is shown in Fig.8. Fig. 8. The parabolic curve that be looked on as auxiliary force In a word, the dexterous gravity compensator is obtained by gravity compensator, parabola function and angular momentum and angular impulse principle shown in Fig.9. Fig. 9. The parabolic curve that be looked on as auxiliary force IMPEDANCE CONTROL In order to measure the torque that is caused by external weight, we use the closed loop system of impedance control. The definition of impedance control is the relationship between position and torque, and the concept of impedance control is introduced by Hogan and is considered as a classical control in robotics. The closed loop of impedance control is shown in Fig.10. Fig. 10. Impedance control. FORCE COUNTERBALANCE CONTROL A lot of workmen always have to carry heavy object; it may cause movement injury mindlessly because they have to make a power to move heavy item. Therefore, the method that combines the gravity compensator, auxiliary torque compensator and impedance control is proposed to solve this question. The force counterbalance control algorithm can increase force to arise heavy item, and user can also freely move the manipulator that loads heavy item to some place where user wants. The general block diagram of force counterbalance control is shown in Fig.11. Fig. 11. Force balance control. First, impedance control is utilized to construct spring model. we take the axis torques that above we can feel the movement of the robot manipulator that holds the heavy object is light and handy. The flow diagram is shown in Fig.12. Fig. 12. Weight estimate algorithm. EXPERIMENT RESULT (a) (c) (b) (d) (A) (f) (e) Fig. 13. Force counterbalance control experiment. (a) Moving robot manipulator freely and lightly by Auxiliary torque compensator. (b) Halting robot manipulator by gravity compensator. (c) Adding a 2.5Kgw heavy object. (d) Computing the weight of object and robot self by FCC. (e) Moving the robot and object freely and lightly after adding FCC. (f) Halting the robot and CONCLUSIONS In this paper, dexterous gravity compensator and FCC are proposed. Many advantages of the algorithm are listed as follows: 1. Because of the dexterous gravity compensator, robot arm has good performance in compliance. 2. The force counterbalance control (FCC) is helpful for arm to load weight payload and help people to move objects. REFERENCES [1] Physical Human –Robot Interaction: Dependability and Safety http://www.phriends.eu/ [2] A. Albu-Schaffer, C. Ott, U. Frese and G. Hirzinger, “Cartesian Impedance Control of Redundant Robots: Recent Results with the DLRLight- Weight-Arms”, IEEE International Conference of Robotics and Automation, 2003 [3] B. Heinrichs, N. Sepehri and A.B. Thornton-Trump “PositionBased Impedance Control of an Industrial Hydraulic Manipulator”, IEEE nternational Conference on Robotics and Automation Minneapolis, Minnesota , April 1996 [4] A. Kugi, C. Ott, A. Albu-Schaffer, and G. Hirzinger, “On the Passivity- Based Impedance Control of Flexible Joint Robots”, IEEE Transactions on Robotics April 2008, Volume: 24 Issue: 2, pp. 416 – 429. [5] A. De Luca, S. Panzieri, “A simple iterative scheme for learning gravity compensation in robot arms”, Proc. of the 36th ANIPLA Annual Conf. 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Hogan, "Impedance Control: An Approach to Manipulation: Part I-- Thoery," Journal of Llynamic Systems, Measurement, and Control, Yo1 IO?, pp. 1-7, Mar 1985 Thanks for your patience