Model-based control of the Mitsubishi PA-10 robot arm 
Motivation: The purpose of this research is to develop a dynamic model of the Mitsubishi PA-10 robot arm for the purpose of low velocity trajectory tracking using very low feedback gains. The targeted application was to be able to perform vision and force feedback based graft placement on a moving target using visual servoing and low feedback gains (to minimize interaction forces in a surgical setting).
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| Mitsubishi PA-10 robot arm and servo driver. | Flowchart of Mitsubishi PA-10 four layer control architecture. |
Robot Description: The Mitsubishi PA-10 robot arm is a 7 degree-of-freedom robot arm with open control architecture and is manufactured by Mitsubishi Heavy Industries. The four layer control architecture is made up of the robot arm, servo controller, motion control card, and the upper control computer. The Mitsubishi PA-10’s joints are actuated by harmonic drives. Harmonic drives are composed of three components: the wave generator, the flexspline and the circular spline.
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| Proposed control system including model of friction, gravity, and compliance of wave generator. |
Harmonic Drive Model for the PA-10: We consider the model of the harmonic drive to be composed only of friction, gravity, and stiffness. The non-linear expression for torque transmission in harmonic drives is then given by:
Kinematic Transmission Error - Harmonic drives display kinematic error caused by a number of factors such as tooth-placement errors on both the circular spline and flexspline and misalignment during assembly. The error function including two harmonics of wave generator rotation is given by:
Friction in Harmonic Drives - Because we are primarily concerned with controlling the robot at low velocities, we model friction in the robot joints using a Stribeck curve at low velocities and a linear relationship at high velocities. Coulomb friction is assumed to be the torque required to maintain very low velocity. The expression for this model is given by:
Torsional Stiffness in Harmonic Drives - Harmonic drives exhibit significant compliance when externally loaded due to deformation of the wave generator. Our experimental tests on the Mitsubishi PA-10 robot arm reveal that the effect of the non-linear stiffness profile of the wave generator is prevalent when the load on the wave generator is below a critical point where a dramatic decrease in stiffness occurs.
Findings: We determine the components of the harmonic drive model by successively subtracting known quantities from the feedback torque required to following a specified trajectory. The friction torque for these motions is nearly identical to the coulomb friction, hence we can eliminate friction. The gravity torque is also known from the estimated masses of the robot arm link. This leaves the remaining torque equal to the torque used to deform the wave generator.
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| Steps in model identification process. |
Model Verification- To verify our model, we fed forward the computed torques to track a trapezoidal velocity profile at 0.1 rad/s. The gains were set to 0.5 N and .15 Ns for the proportional and derivative gains respectively.
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| Desired and actual trajectory of robot during experiment. | Feedback torque results for trajectory following experiment. |
Video: The video demonstrates the ease of movement of the PA-10 robot arm with model-based controller in operation.
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Application note: The experimental system decouples ‘macro’ motion for motion-cancellation and ‘micro’ motion for teleoperation. Visual servo control is accomplished by the micro-camera on the left PA-10 robot end-effector and force feedback is provided by the PHANToM haptic feedback device. The random motion of the PA-10 robot arm on the right side is tracked by the microcamera on the left PA-10 robot arm.
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| Experimental platform with macro (PA-10 robot) and micro position (2-DOF robot at the end-effector) control. | |
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| 2-DOF micro positioning robot on PA-10 end-effector for fine motion. |
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| Teleoperation control strategy. |
Relevant archival publications:
- Christopher W. Kennedy and Jaydev P. Desai, “Modeling and Control of the Mitsubishi PA-10 Robot Arm Harmonic Drive System”, IEEE/ASME Transactions on Mechatronics, 10(3): 263-274, 2005.
- C. W. Kennedy and J. P. Desai, “A vision-based approach for estimating contact forces: Applications to robot-assisted surgery”, Applied Bionics and Biomechanics, 2(1): 53-60, 2005.
- Christopher W. Kennedy, Tie Hu, Jaydev P. Desai, Andrew S. Wechsler, and J. Yasha Kresh, “A Novel approach to Robotic Cardiac Surgery using Haptics and Vision”, Cardiovascular Engineering: An International Journal, 2(1): 15-22, 2002.
For further information, please contact:
Prof. Jaydev P. Desai
Director, RAMS Laboratory
Department of Mechanical Engineering
Room 0160, Building 088
Glenn L. Martin Hall
University of Maryland
College Park, MD, 20742
Email: jaydev (at) umd.edu
Phone: 301-405-4427
Fax: 301-314-9477