INPUT SHAPING EXPERIMENT FOR DAMPING VIBRATION IN MANUAL OPERATION OF A LARGE ROBOTIC ARM

Transcription

1 INPUT SHAPING EXPERIMENT FOR DAMPING VIBRATION IN MANUAL OPERATION OF A LARGE ROBOTIC ARM Hirotaka Sawada (), Kazuya Konoue (), Saburo Matunaga (), Hiroshi Ueno (), Mitsushige Oda () () Institute of Space Technology and Aeronautics, Japan Aerospace Exploration Agency -- Sengen, Tsukuba-shi, Ibaraki-ken, 5-855, JAPAN, sawada.hirotaka@jaxa.jp () Mechanical and Aerospace Engineering, Tokyo Institute of Technology -- O-okayama, Meguro-ku, Tokyo, Japan, 5-855, Matunaga.Saburo@mes.titech.ac.jp ABSTRACT This paper describes a method for operating large robotic manipulators, which generally has flexible links and joints in space. Vibration induced by flexibility is a serious problem when operating a long manipulator in orbit. Once vibration has occurred while a manipulator is handling a payload, the operator must wait for the vibration to be damped before proceeding, which decreases working efficiency. We studied a control method to suppress vibration during both manual and automatic operations. We investigated an Input Shaping feed-forward control method for damping residual vibration during operation. We discuss in detail the results of the pre-shaping vibration suppression and manual operation experiments in this paper. We can shape a velocity commands for the joint beforehand (pre-shaping) in automatic operation mode to suppress residual vibration in both the first and second modes of the arm. However, problems that differ from those of the pre-shaping application arise when we apply Input Shaping during manual control using a joystick. We could not use a pre-shaped command profile because the input from the joystick could not be predicted accurately. The shaped command profile was treated as a future command and it was superposed on every alteration of joystick input. We implemented this algorithm in the experimental system and demonstrated that the deflection of the arm s tip can be damped well during operation, although the operator sensed that its responsiveness declined.. INTRODUCTION Robotic manipulators are indispensable technology for space application. For example, the Space Station Manipulator System (SSRMS) and JEM Remote Manipulator System (JEMRMS) perform important roles on the International Space Station (ISS). Vibration induced by flexibility is a serious problem when a long manipulator is used. In fact, an operator on the ISS must move the manipulator very slowly, which decreases working efficiency and can present a burden for the astronaut. Once vibration has occurs during manipulator operation, the operator must wait for the vibration to be damped before proceeding. We specifically investigated an Input Shaping feedforward control method for damping residual vibration during operation, and conducted practical examinations of its application feasibility using an experimental model arm (-DOF) similar in length to JEMRMS. Input Shaping can be applied to the existing control system without any modification, which is greatly advantageous, given the limited resources in orbit.. EXPERIMENTAL SETUP Fig.. depicts an overview of the long arm system for the ground experiment, which has two links similar in length to JEMRMS at 4m-long and kg in weight. The root joint is driven by an AC servo motor, and the other joints are fixed at 45deg, 9deg, and 45deg, respectively (Fig..). The gross weight of the arm is balanced with a counter mass set at the opposite side of the arm. Vibration of the arm is measured by an acceleration sensor, a laser sensor, and a strain gauge. We conducted a modal test to observe characteristic vibration of the arm system by measuring the alteration of three points, the end-effector, the center joint, and the root of the arm. Fig. 4. presents the result of the test. The first mode of natural frequency, approximately.5hz, was predominant at the end-effector, as shown in the figure. However, the second mode, approximately.hz, can not be ignored at the center joint and the root. Thus, we considered both the first and second modes of the natural frequency in the Input Shaping application. Proc. of 'The 8th International Symposium on Artifical Intelligence, Robotics and Automation in Space - isairas, Munich, Germany. 5-8 September 5, (ESA SP-6, August 5)

2 . INPUT SHAPING APPLICATION Counter Mass -DOF Fig.. Overview of Experimental Setup DOF AC Servo Motor 4m 9 4m Motor Driver PC Fig.. DOF Manipulator System Joystick. Pre-Shaping Application The principle of the Input Shaping control method is introduced in this section. Input Shaping is a theory for suppression of residual vibration of a system by the appropriate shaped command. If the system response to an impulse input can be expressed as an equation (), the system response can be represented by equation () after n times impulses are inputted. ςωt h( t) = Ae sin ω * t ς () n h( t) = Ai e i= ςωti sin ω ς * ( t t i ) = Asin ( ω t φ) () The residual vibration of the system will be zero, if we can derive an input command profile that will make amplitude A be zero. For example, we can calculate amplitude d A i and time A = and location t i from constraint equations A + A = if we want to suppress residual vibration by two times the impulses. We then obtain the following command profile. π ω d ςπ ti = ς e () A i ςπ ςπ ς ς + e + e Fig. 5. shows examples of schematic image of convolving a desired system command signal with impulses profile Velocity Command * t t t t t + D FE + Shaping t t t Transfer Func End-Effector of Arm Root of Arm Fig.. Joystick LRF/Input Acc/Input Strain/Input.. Joint of Arm..5Hz... Frequency[Hz].Hz.5Hz Fig. 4. Result of Modal Test Fig. 5. Input Shaping of the Command Signal. Post-Shaping Application We generally give the velocity command to the endeffector or each joints of the manipulator from a controller when we operate a manipulator using a manual controller, such as a joystick. However, we can not shape the command in advance because the operator always adjusts the command inputs from the controller according to the situation. Therefore, we use a future command profile to apply Input Shaping for manual operation. We first calculate the acceleration command from the alteration of velocity command of the joystick inputs, as indicated in Fig. 6. We then -

3 obtain a command profile for t seconds since current time by applying Input Shaping to the acceleration command. Here, t is a different value depending on the type of Input Shaper and the natural frequency period. The command profile is held in the control program as a future command profile. The Future command profile is updated at every alteration of velocity command input, i.e., whenever the acceleration command is input, by superimposing a newly calculated future profile over the old one, as illustrated in Fig. 7. The velocity command to a joint is calculated at every implementation in the control program according to the current velocity command and acceleration command of the future profile. Voltage Voltage Convert to Acceleration Shaped Command Profile ( Velocity Input ) Input Shaping of Acceleration T ( Shaper) Current Acceleration T Actual Input OutPut Future Command Current Current T: a half of natural freq. period Fig. 6. and Future Profile Current Acceleration Actual Input Shaped Input Current Fig. 7. Update of Future Profile OutPut Future Command Current 4. VIBRATION SUPPRESSION EXPERIMENT 4. Automatic Operation Experiment We first conducted experiments using a trapezoidshaped velocity command profile, which is often applied to industrial robots on the ground. The rise time of the velocity command we used was sec. Fig. 8. shows the velocity command profile and acceleration profile. We shaped the velocity command profile by applying a shaper that targets the first mode and a shaper that targets both the first and second modes. All velocity profiles had the same average velocity deg/sec, and the same rotation angle of deg. Fig. 9. and Table provide the experiment results of the end-effector alteration measured by laser sensor and the suppression rate of each shaper, respectively. Applying shaper enables us to suppress the residual vibration to less than % of that for an unshaped case. However, the residual vibration can not be suppressed well since the influence of the second mode is not ignored. The shaper can suppress the residual vibration to less than.4%, which indicates that Input Shaping is very effective but we must consider to a higher mode when using the trapezoid-shaped profile in this system. Acceleration Commands, [deg/sec ] - - Displacement[cm] UnShaped 5 5 Fig. 8. Trapezoid-Shaped Velocity Command Unshaped Shaped_freq Shaped_freq UnShaped - Shaper Shaper -.5 [sec] Fig. 9. Experiment Result of Alteration of the Tip Table Suppression Rate Shaper Residual Vibration, [cm] Suppression Rate, [%] Trapezoid UnShaped 4. Trapezoid.95.6 Trapezoid..4 Next, we applied Input Shaping to a spline curve velocity profile, such as the sine curve profile in Fig.. These profiles have the same average velocity (deg/sec) and rotation angle (deg) as the trapezoidshaped profile. Fig.. and Table present the experiment results and suppression rate, respectively. The residual vibration can be damped by only applying the sine curve profile compared with that of the trapezoid profile. In addition, the shaper can suppress the residual vibration to less than 5%, which means approximately % of that of shaper application to a trapezoid-shaped profile. We could demonstrate the validity and the feasibility of Input Shaping application to a long arm system in automatic operation mode in these experiments. Acceleration Commands, [deg/sec ] UnShaped 5 5 Fig.. Sine Curve Velocity Command

4 Displacement[cm] Unshaped [sec] Shaped Fig.. Experiment Result of Alteration of the Tip Table Suppression Rate Shaper Residual Vibration, [cm] Suppression Rate, [%] Trapezoid UnShaped 4. Sin Wave UnShaped Sin Wave Manual Operation Experiment The operator drove the arm manually using the joystick in manual experiments by visual observation of the end-effector position. The target position of the end-effector was set deg from the initial position, and the operator attempted to move the end-effector in 5sec (average velocity: deg/sec). The graphs in Fig.. indicate the residual vibration of the end-effector position at the target position, and Table provides the suppression rate of each shaper. The velocity command profile in Fig.. is similar to a trapezoid shape, in that the operator drives manually without Input Shaping, which causes residual vibration of approximately 5cm in amplitude. However, the residual vibration can be damped to % in maximum with Input Shaping. One of the most important issues in these experiments is the manipulation responsiveness. The operator sensed that the response worsened while Input Shaping was applied. Shaped velocity command profiles and practical command inputs from joystick are illustrated in Figs The time delay is.86sec in minimum, and.7sec in maximum. For example, it takes a half period of the natural frequency (in this case:.86sec) before the velocity command to the joint reaches the actual command from the operator in applying the Shaper. Thus, the operator perceives a time delay to the own sense of operation. Although residual vibration can be suppressed by applying Input Shaping, we must pay attention to decelerate the arm in case the time delay is long, since the arm moves for t sec depending on the shaper type, after the operator inputs a zero velocity command. Residual Vibration of E.E., [cm] sec Fig.. Experimental Result UnShape D D Table Suppression Rate Shaper Residual Vibration, [cm] Suppression Rate, [%] UnShaped D D.8. Fig.. Velocity Command Profile of UnShaped.86sec Fig. 4. Velocity Command Profile of

5 .7sec Fig. 5. Velocity Command Profile of D.6sec Fig. 6. Velocity Command Profile of.sec Fig. 7. Velocity Command Profile of D.7sec Fig. 8. Velocity Command Profile of DD 4. Natural Frequency Identification One advantage of Input Shaping is that it can be applied to an existing system without modification, such as additional sensors. However, the frequency characteristics must be identified in case they change, such as when the arm grasps a payload or a posture of the arm is altered. A counter mass of approximately 5kg was connected to the end-effector to alter the frequency characteristics in the experiment, as illustrated in Fig. 9. We monitored the motor current of the AC servo motor to identify the natural frequency, eliminating the need for an additional sensor. However, we cannot measure the motor current frequency while the arm is driven because of the offset current induced by the driven current of the motor. Thus, the sequence of the experiments was as follows. ) Move the arm without identifying the natural frequency. ) Stop the arm at the first target point and monitor the motor current of residual vibration. Next, identify the natural frequency. ) The operator sets the measured natural frequency in the operation program. 4) Move the arm to the next target position, applying Input Shaping. Mass (5kg) Fig. 9. End-Effector Mass Default Setting Parameter (nd Mode, [Hz]) Default Setting Parameter (st Mode, [Hz]) Input Shaper Selector Fig.. GUI of Operation Program Measured Natural Frequency, [Hz] Fig.. presents the experiment result of the endeffector position. A large residual vibration occurred in the first step after the arm was moved approximately 8cm from the initial position as a result of neglecting the natural frequency. The natural frequency could be identified as approximately 4.5Hz by monitoring the motor current during the residual vibration. We then moved the arm to the next target point, applying the Shaper of the updated natural frequency, the shaper suppressed the residual vibration well, as evident in the graph. In addition, the Shaper was applied while the arm was driven to the

6 third target point, and only minimal residual vibration occurred at the target point. Fig.. indicates the residual vibration at each point. Fig.. and 4. provide the measurement results of the velocity command profiles and the motor current, respectively. We demonstrated that the residual vibration of the arm can be suppressed without any modification of the existing system, even though the frequency characteristics change during operation. Positon of End-Effector, [cm] - Shaper - Natural Frequency Identification Fig.. Natural Frequency Identification Experiment Position of E.E., [cm] Shaper -9 Position of E.E., [cm] Position of E.E., [cm] - - Fig.. Residual Vibration Fig.. Velocity Command Profile Current, [A] Fig. 4. Measurement of Motor Current 5. CONCLUSION We applied Input Shaping to long arm operation as a method to suppress residual vibration in both automatic operation mode and manual operation mode. We shaped the velocity of the joint in advance (preshaping) in automatic operation mode, and conducted experiments using a trapezoid-shaped velocity command and sine curve velocity command profile. The residual vibration could be suppressed to less than.5% at maximum by applying Input Shaping to both the types of command profile by considering to the second mode of the natural frequency. We could not apply pre-shaping when we used a joystick in manual operation mode, and thus we applied Input Shaping to a velocity command based on alteration of the current input from the joystick, which is treated as a future command profile. The residual vibration could be suppressed to less than %, similar to that of preshaping, although the operator perceived worse response induced by the time delay of Input Shaping application. We consider the operational efficiency to be improved since the time delay, which was.6 when the Shaper was applied, was minimal considering that it takes more than sec to damp the residual vibration. We conducted natural frequency identification experiments and demonstrated that the residual vibration can be suppressed in manual operation by monitoring the motor current, even when the frequency characteristics changed.

7 6. REFERENCES. H. Ueno, T. Nishimaki, M. Oda and N. Inaba, "Autonomous Cooperative Robots for Space Structure Assembly and Maintenance," Proc. 7th Int. Symp. on Artificial Intelligence, Robotics and Automation in Space:i-SAIRAS, Nara, Japan, May 9-, CD- ROM,.. Kazuo MACHIDA, et al In Orbit Servicing Experiment by ARH/ERA Connected Configuration on ETS-VII, The 4rd Space Science and Technology Conference, 999. W.J.Book and S.H.Lee, Vibration Control of a large flexible manipulator by small robotic arm, in Proc. American Control Conference, Pittsburgh, PA, pp.77-8, K. L. Hillsley and S. Yurkovich, "Vibration Control of a Two-Link Flexible Robot Arm," Dynamics and Control, Vol., pp. 6-8, W. Singhose, E. Biediger, H. Okada, and S. Matunaga, Control of Flexible Satellites Using Analytic On-Off Thruster Commands, AIAA Guidance, Navigation, and Control Conference and Exhibit,, AIAA Paper Hirotaka SAWADA and Saburo MATUNAGA Experiment of Flexible Payload Translation by Space Robotic Manipulator, 5th Workshop on JAXA Astrodynamics and Flight Mechanics, 4