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Simulated Annealing for Redundant Robot Inverse Kinematics (page 1)

Abstract ó The assist interface suggests configuration options to the systemís operator. As an example, this paper develops an assist interface for a robotic system called the Dual-Arm Work Module (DAWM). The DAWM has seventeen independent Degrees Of Freedom (DOF) arranged to give the system five degrees of kinematic redundancy. These five extra kinematic resources (extra joints) give the DAWM the versatility to perform a wide range of tasks, including: disassembly, cutting, material transport, and decontamination. In the current application scenario, the operator positions each redundant joint directly and independently of the other joints. Because of obstacles and kinematic coupling, even an experienced operator may need to reposition the extra joints several times while performing a task. The simulated annealing optimization algorithm considers obstacles and performance criteria while generating suggested options for positioning the extra joints (configuration options). The operator interface then presents these options using computer graphics. The interface should reduce the amount of time the operator spends positioning the extra joints and perhaps improve the quality of the work.

Introduction - Implementing the configuration advisor represents a challenging global optimization problem. There are a number of complicating factors, including:
1. seventeen DOF is a very large solution space
2. the robot operates in an obstacle-strewn environment
3. the need for response time of a few seconds or less.

Through the assist interface, the operator establishes End-EFfector (EEF) locations for the robotís two arms. These two EEF locations represent twelve equality constraints (six per EEF). The optimization combines these constraints with inverse kinematics to reduce the solution space from seventeen DOF to five DOF. In other words, the algorithm only looks for optima within the robotís null-space (self-motion space). This technique dramatically increases the speed of the optimization. Implementing it for the assist interface, however, requires solving an inverse kinematics problem.

The inverse kinematics problem enjoys a rich history. Dimentberg in the 1950s and Freudenstein in the 1960s and 1970ís were seminal authors. With the realization in the late 1960s that a serial robot could be modeled as a spatial mechanism, the disciplined and analytical theory of mechanisms was applied to the exciting new field of robotics. This work dominated inverse kinematics research during the 1970ís as the search for a general closed-form solution for
robots with six DOF became the ďMount EverestĒ of kinematics problems (Freudenstein, 1972). Duffy, Pieper, and Roth were at the forefront of inverse kinematics research during this time.

Within the context of redundant robots, the inverse kinematics focus shifted towards optimization and linear algebra. Whitney (1969) pioneered this work with his resolved motion rate control that suggests the use of the pseudo-inverse to resolve redundancy. Liegeois (1977) showed the extension of this method to include self-motions via the null-space. A number of other researchers have developed and implemented rate control methods. Notable approaches include: Serajiís (1992) configuration control, Baillieulís (1986) extended Jacobian, and the Jacobian transpose (Das, Slotine, and Sheridan, 1988). Several approaches optimize task-based performance measures in the redundancy resolution (Dubey and Luh, 1988). Maciejewski (1989) discusses the kinetic limitations of redundant robots.

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