Vibration Control of Flexible Arm for Robot Experiment on JEM

Transcription

1 Vibration Control of Flexible Arm for Robot Experiment on JEM Daichi Hirano*, Hiroki Nakanishi*, Kazuya Yoshida*, Mitsushige Oda**, Taihei Ueno**, Takeshi Kuratomi*** *Department of Aerospace Engineering, Tohoku University, Japan **Space Robotics Research Group, JAXA, Japan ***WEL RESEARCH Co., Ltd, Japan Abstract In this paper, the dynamics and control of a novel mobile robot on the International Space Station (ISS) are discussed. The Japan Aerospace Exploration Agency (JAXA) is developing a robotic system which has an extendable arm and several tethers to support Extravehicular Activity (EVA) performed by astronauts. The robotic arm is build from a light material and can be extended longer. The vibration due to flexibility of the robot s long light arm makes its operation inefficient. The dynamic model of the robot and its control strategy are investigated in order to suppress these vibrations. The efficiency of the control is verified with numerical simulation. locomotion robot has been proposed. This robot has an extendable arm and several tethers, and move by controlling the length of tethers attached on the different points with the extendable arm as shown in Figure 1. The extendable arm and tethers can deploy and retract over 10 m and therefore make the robot possible to move in broader range. The risk that the robot floats and collides is lower because the robot is fixed by several tethers. The robot carrying a camera and dual arm can perform various tasks such as the inspection of a space structure and the transportation of materials. The advantage of this robotic system is to move and work at wider range safely. 1 Introduction Space development has been expanded in recent years. Results of scientific experiment on ISS and the performance of Hubble Space Telescope have contributed to social development. Human space exploration in future mission is expected to play an important role in revealing the origin of life and the universe. However, these space activities depend on the tasks by astronauts, such as inspecting of the outer surface of ISS or the repairing of Hubble Space Telescope. The development of the robots to support these tasks carried out by astronauts is expected. Robotic arms used in ISS such as Space Station Remote Manipulator System (SSRMS) and Japanese Experiment Module Remote Manipulator System (JEMRMS) are designed to transport instruments and payloads around the ISS in order to support EVA[1]. However, a working range of these robotic arms is limited in an area the tip of the robotic arm reaches. Free flying vehicle which developed for performing inspection on ISS such as AERCam[2] is possible to move to any with several thrusters. However, the danger of collision with the surface of ISS is pointed out. The robotic system move and work at wider range safely has not been established. As a system solves these issues, a tether based Figure 1. Tether based locomotion robot JAXA robotics research group has developed a tether based locomotion robot which has an extendable arm to move around the outer surface of ISS and transport the materials to build a space structure, such as space solar power system (SSPS), in future space mission. As part of the development of this robot, JAXA is going to launch a robotic experiment on ISS s Japanese Experiment Module (JEM) called Robot Experiment on JEM (REXJ) in 2012[3]. This experiment is intended to demonstrate the locomotion capability with the tethers and the performance of the extendable arm and a hand to attach a hook to the handrail as shown in Figure 2. The extendable arm used in REXJ is flexible since the arm is build from a light material and deployed longer. The vibration due to the flexibility of the arm makes its operation inefficient. This paper describes the extendable arm used in REXJ. The dynamic model of the robot and the control strategy to suppress the vibration of the arm are discussed. i-sairas 2010 August 29-September 1, 2010, Sapporo, Japan 820

2 Figure 2. REXJ mission JAXA 2 Extendable arm system The extendable robotic arm used in REXJ utilizes a system called Storable Tubular Extendible Member (STEM) which could be used to deploy the solar cell sheet of the Hubble Space Telescope and similar antennae of other satellites. The STEM Robotic Arm (SRA) for REXJ is lightweight and can be extended to more than 1.3 m. Figure 3 shows the mechanism of the SRA, including a sprocket and several motors to deploy and retract the arm made from carbon-fiber reinforced plastics (CFRP). The arm deploys by pushing out the CFRP rolled up on the reel. The size of the SRA is 300 mm 160 mm 100 mm. REXJ robot also has a robotic hand and wrist system attached to the tip of the SRA. The wrist has 2-DOF, pitch and roll, and the maximum torques of the wrist are both 1.4 Nm. The total amount of hand and wrist system is about 2.7 kg. The SRA is flexible because it is build from light material and deployed more than 1.3 m. The reaction force of these systems could cause a vibration of the SRA. Therefore, the identification of the dynamics of the SRA and the verification of control to suppress the vibration of the SRA is required for the safe and efficient operation of the REXJ robot. 2.1 Identification of the dynamic model The experiment to identify the dynamic model of the SRA was conducted to measure the displacement of the tip of the arm during the free vibration. The SRA was extended vertically and the tip of the SRA has initial displacement in a horizontal direction by the external force as shown in Figure 4. After the force was released, the SRA vibrated freely and the vibration attenuated with time. The displacement of the tip was measured by a laser range finder. The experiment was conducted five times at different lengths of the SRA (0.336 m, 0.7 m, m, 1.3 m). Figure 5 shows the change of the displacement of the tip during the free vibration when the length of the SRA was 1.3 m. The results of these experiments indicate that the SRA has mainly first-order vibration mode and can be modeled as one joint manipulator based on the main body of the REXJ robot as shown in Figure 6. Figure 4. Experimental setup Figure 3. STEM Structure for REXJ JAXA Figure 5. Free vibration of the SRA 821

3 Figure 6. Approximate model of the SRA The angle and the rotation moment at the base of the SRA can be written as follows. (1) (2) : angle at the base of the SRA : displacement of the tip : length of the SRA : rotation moment at the base : external force at the tip Figure 7. Force of the tip at different displacements The appropriate parameters at different lengths of the SRA are shown in Figure 8. Parameters a and b can be represented by the following equations through liner approximation. (5) The motion equation of the arm is represented as follows. (3) : moment of inertia about the base of the SRA : damping coefficient : stiffness coefficient 2.2 Stiffness of the arm The experiment to identify the stiffness coefficient was conducted to measure the relative position of the tip of the arm displaced by the external force though the tether. The experimental setup is similar to Figure 4. The external force was changed by a different weight, which is attached to the tip of the tether. The experiment was conducted three times at different loads and different lengths of the SRA (0.336 m, 0.7 m, m, 1.3 m). Figure 7 shows the force of the tip at different displacements of the tip when the length of the SRA was 1.3 m. Assuming that stiffness coefficient can be represented as shown in equation (4) and choosing the appropriate parameters a and b, the approximate curve can be written as shown in Figure 7. These appropriate parameters were calculated from the experimental data at different lengths of the SRA. (4) Figure 8. Liner approximations of the parameters 2.3 Damping coefficient The damping coefficient of the SRA was identified by comparing the wave shape of the experimental vibration results and the results of the numerical simulation calculated by the motion equation of the approximate model of the SRA represented in equation (3). The stiffness coefficient used in the motion equation was obtained by equation (4) and equation (5). The appropriate damping coefficient was identified as the value, which minimizes the difference between the experimental result and the simulated result. The appropriate parameter D at different length of the SRA is shown in Figure 9. The parameter D can be represented as following equations via liner approximation. (6) 822

4 simulator also assumes that the main robot body is stationary, fixed strongly with several tethers. The gravity force is not considered since this simulation focuses on the motion in micro gravity environment. Figure 11 shows the dynamic model used in this simulation. Figure 9. Liner approximation of the parameter D Figure 10 shows the comparison between the experimental result and the simulated result with the approximate dynamic model and the identified parameters of the SRA in the case that the length of the SRA is 1.3 m. This result indicated that the approximate dynamic model and identified parameters are valid. Figure 11. Dynamic model used the simulation The torque on the joint2 is given as follows from equation (7). (8) : torque on the joint2 : angle on the joint2 The torques on joints without joint2 can be controlled. The acceleration of the tip of the SRA is observed by the acceleration sensor and can use the feedback control. The angle of the joint 4 is limited between 0 and 90 degrees as shown in lower part of Figure 11. The maximum torque is also limited to 1.4 Nm. Figure 10. Vibrations of the experimental result and simulated result Using the identified parameters, the torque on the root of the SRA is represented by the following equation. 3 Dynamic simulator (7) Using the approximate model and the identified parameters, the numerical simulation was performed to demonstrate how the vibration of the arm with the hand on the top can be suppressed through a vibration control method implemented in MATLAB. This simulation was performed by SpaceDyn which is a toolbox for the numerical analysis and simulation of the kinematics and dynamics of articulated multibody systems [4]. This 4 Vibration suppression control The control method used in this research to minimize the deflection of the arm with the reaction force of the wrist based on the vibration suppression control for flexible structure mounted system. 4.1 Dynamics analysis of a flexible based manipulator In this subsection, vibration suppression control method is introduced. The equation of motion of the manipulator on the flexible base is generally written in the following equation. (9) 823

5 : number of the joints for manipulator : inertia matrix of the flexible base : coupling inertia matrix between the base and the arm : inertia matrix of the manipulator : position vector of the base : vector for the joint angle of the manipulator : stiffness of the base : non-linear velocity dependent term of the base : non-linear velocity dependent term of the manipulator : force and moment exerted on the centroid of the base : torque on the joints of the manipulator : Jacobian matrix for the base : Jacobian matrix for the manipulator : force and moment exerted on the end-point of the manipulator Assuming that the external force and moment exerted on the end-point of the manipulator and the non-liner velocity dependent terms are zero, upper part of the equation (9) can be written as follows. (10) Controlling an acceleration of the manipulator as a following feedback of the linear and angular velocity of the base, (11) Equation (10) can be rewritten as an equation of motion of a damping vibration system[5]. (12) : gain matrix : pseudo inverse of the coupling inertia matrix 4.2 Simulation method Considering the SRA and the wrist system as the active manipulator mounted on a flexible base as shown in Figure 12, the vibration can be suppressed by the reaction force of the wrist with the above method of vibration suppression control. The input torque was calculated by a computed torque method as shown in the following equation with desired angular acceleration, velocity and angle of the wrist. (13) the generalized inertia matrix[6] defined as: : desired angular acceleration of the wrist : desired angular velocity of the wrist : desired angle of the wrist : gains Figure 12. Model for the vibration suppression control The free flying robot and the manipulator mounted the flexible base have to consider the reaction force for the base when the manipulator moves. Therefore, the input torque was calculated with the. From equation (11), the desired angular acceleration, velocity and angle of the wrist are obtained as follows. (14) The deflections between desired value and output value of the angular velocity and the angle of the wrist decrease with the proper gains. Figure 13 shows a block diagram for calculating the input torque based on the computed torque method. d d d m Stationary Base (Main Body) m * H m KV KP Figure 13. Block diagram for the calculation of the input torque 4.3 Simulated results m Direct Kinematics The numerical simulation was performed to evaluate the performance of the proposed vibration suppression control. This simulation assumes that the initial angle of the joint2 is 5 degrees and the vibration of the SRA is excited without an external force. The torque of the wrist is controlled by equation (13). Figure 14 shows the simulated results with control and without control in the case that the length of the SRA is 1.3 m. Flexible Base (SRA) Active Arm (Wrist) 824

6 less than 90 degrees in the case that the initial angle is 90 degrees. This result implies that here is the proper attitude of the wrist for this vibration suppression control. The wrist whose angle of joint4 is 45 degree could respond to the vibration control in at least two directions. 5 Conclusions Figure 14. Vibration with control and without control It is clearly observed that the vibration of the SRA with control was suppressed quicker than that without control. This result indicated that the proposed vibration suppression control method is valid for REXJ system. However, this control has not worked during at first few seconds. The cause of this phenomenon is the attitude of the wrist upon which the control method does not work. The ordered velocity of the joint4 from the control method had been negative at first. However, the wrist whose initial angle is 0 degree could not move forward to be less than 0 degree because the range is limited between 0 and 90 degree. The simulations of the vibration with the control in various cases of the different initial attitudes were executed. Figure 15 shows the comparison of the vibration with control in the cases that an initial angle of joint 4 is 0 degree and 90 degrees. Figure 15. Vibration with control (different initial angles) Figure 15 shows that the vibration in the case that an initial angle of joint4 is 90 degrees was suppressed rapidly. The wrist had been able to move forward to be This paper introduced the tether based locomotion robot and its advantages. The extendable arm used in REXJ, which is an experiment to demonstrate the locomotion capability with the extendable arm and several tethers, is described. The SRA is easy to vibrate by the external force and reaction force of the base or wrist. Dynamic model and several parameters such as stiffness and damping coefficient of the SRA were identified by analyzing the experiment data. In addition, the dynamics simulator for REXJ was built with the identified model. The vibration suppression control method was also introduced. The SRA and wrist system can be considered as a manipulator mounted on a flexible base. The vibration of the SRA was suppressed through this control method with the numerical simulation. It is revealed that a proper attitude of the wrist exists for the proposed vibration suppression control. References [1] Rod McGregor and Layi Oshinowo, Flight 6A: Deployment and Checkout of the Space Station Remote Manipulator System (SSRMS), Proc. of the 6 th International Symposium on Artificial Intelligence and Robotics & Automation in Space, Quebec, Canada, June [2] Steve E. Fredrickson, et al Application of the Mini AERCam Free Flyer for Orbital Inspection, Proc. of SPIE Vol.5419, Bellingham, WA, U.S, pp [3] Mitsusige Oda, et al Tether Based Space Walking Robot on KIBO -REX-J:Robot Experiment on JEM-, Proc. of 26 th International Symposium on Space Technology and Science (ISTS), Hamamatsu, Japan, 2008, paper ID 2008-d-08, 1-4. [4] Kazuya Yoshida, et al The SpaceDyn: a MATLAB Toolbox for Space and Mobile Robots, Journal of Robotics and Mechatronics, 2000, Vol.12 No.4, pp [5] Kazuya Yoshida, Dragomir N Nenchev, and Masaru Uchiyama Vibration suppression and zero reaction maneuvers of flexible space structure mounted manipulators, Smart Materials and Structures, 8-6 (1999/12), pp [6] Y. Masutani, F. Miyazaki, and S. Arimoto, Sensory feedback for space manipulators, Proc. of 1989 IEEE Conf. on Robotics and Automation, Scottsdale, Arizona, USA, 1989, pp