Redundant Kinematics for a Mobile Dual Arm Manipulator

Bryan WillimonECE 869

Outline

Previous Work Approach

Kinematics Calculations Jacobian Matrix Obstacle Avoidance Self-Collision Avoidance

Results Conclusion Future Work

Previous Work

H. Kaneko, T. Arai, K. Inoue and Y. Mae. Real-time Obstacle Avoidance for Robot Arm Using Collision Jacobian. Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 617-622, 1999.

K. Glass, R. Colbaugh, D. Lim, and H. Seraji. Real-Time Collision Avoidance for Redundant Manipulators. IEEE Transactions on Robotics and Automation, 11(3): 448–457, 1995.

H.P. Xie, R.V. Patel, S. Kalaycioglu, H. Asmer. Real-Time Collision Avoidance for a Redundant Manipulator in an Unstructured Environment. Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 1998.

M. Uchiyama, A. Konno, T. Uchiyama, S. Kanda. Development of a Flexible Dual- Arm Manipulator Testbed for Space Robotics. Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 1990.

F. Caccavale, P. Chiacchio, A. Marino, and L. Villani. Six-DOF Impedance Control of Dual-Arm Cooperative Manipulators. IEEE Transactions on Mechatronics, 13(5): 576-586, 2008.

J. Liu and K. Abdel-Malek. Robust Control of Planar Dual- Arm Cooperative Manipulators. Robotics and Computer-Integrated Manufacturing,16(2-3): 109–120, 2000.

Blanc, Y. Mezouar, and P. Martinet. Indoor navigation of a wheeled mobile robot along visual routes. In Proceedings of the International Conference on Robotics and Automation, pp. 33543359, 2005..Bonev, M. Cazorla, and F. Escolano. Robot navigation behaviors based on omnidirectional vision and information theory. Journal of Physical Agents, 1(1):2735, September 2007.Z. Chen and S. T. Birchfield. Qualitative vision-based mobile robot navigation. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), May 2006.

Approach

The robot is redundant in the fact that there are 14 joints (revolute and prismatic) and the end effectors require 12 variables.

Each end effector is calculated separately for simplicity of the kinematics.

Collision detection is calculated as to keep the manipulators from hitting themselves or an outside object.

Approach

Kinematics Calculations

Jacobian Matrix

Obstacle Avoidance

Self-Collision Avoidance

Kinematics Calculations

The kinematics of the robot is calculated by using Denavit-Hartenberg*

The axises of the various revolute and prismatic joints in a

Top view Side view Front view.

* J. Denavit and R.S. Hartenberg. A kinematic notation for lower-pair mechanisms based on matrices. Trans ASME J. Appl. Mech, 23:215- 221, 1955.

Kinematics Calculations

The axises of the robot are used to calculate the kinematics of the: Torso - The value of represents 90

for the left arm and -90 for the right arm Each arm

Kinematics Calculations

The resulting D-H matrix for the: Torso for the Left arm Torso for the Right arm Each Arm

Jacobian Matrix

The Jacobian matrix for each arm was calculated separately.

The relationship between each set of variables results in the Jacobian.

Jacobian Matrix

The Jacobian is found by using the D-H matrices

The following matrices are used to calculate the Jacobian

represent the values of from the previous iteration.

Obstacle Avoidance

When the manipulators or torso collides with another object, another Jacobian will need to be computed to determine the final velocity of the manipulator.

This new Jacobian is referred to as the collision Jacobian.*

* H. Kaneko, T. Arai, K. Inoue and Y. Mae. Real-time Obstacle Avoidance for Robot Arm Using Collision Jacobian. Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 617-622, 1999.

Obstacle Avoidance

Calculate the collision Jacobian using: and are two points, one on the robot and one on the object, that are the closest in length to each other

Obstacle Avoidance

First, calculate the distance value:

Next, differentiate across all joint values

inverse Jacobian

Obstacle Avoidance

Then, stack all values for each collision

Finally, multiply collision Jacobian to end effector velocity to compute new velocity for each collision

Self-Collision Avoidance

The algorithm of the collision Jacobian can be used for self-collision or develop a trimmed down method.

The goal of this method is to focus on the elbow joint to the end effector of each arm, since they are the only movable items that will collide with any other part of the robot.

Self-Collision Avoidance

A set of four rules can be used to avoid self collision.

The elbow joint position must be units above the height of the mobile base.

Self-Collision Avoidance

The end effector position must be units away from the torso

A set of four rules can be used to avoid self collision.

Self-Collision Avoidance

The end effector position must be units away from the mobile base

A set of four rules can be used to avoid self collision.

Self-Collision Avoidance

The area around the elbow, forearm, wrist, and end effector for each arm must be units away from everything else.

A set of four rules can be used to avoid self collision.

Results

The focus of this experiment is to implement the proposed kinematics and Jacobian within a 3D environment.

Matlab was used to create a 3D graphical interface of this approach.

Results

Nine iterations of the experiment that moves both end effectors to pre-specified locations:

Conclusion

Various sensors (e.g. cameras, sonars, etc) will be needed to calculate locations of and distances from the nearest obstacles.

The mobile base of this robot allows for reduced singularity in several cases.

The singularities that are common with standard manipulators involve end effector locations being out of reach in the horizontal plane and locations that parts of the robot system currently occupy.

The design of a dual arm mobile robot reduces singularities and increases complexity because of the redundancy of two arms and a movable base.

Future Work

Implement proposed approach

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