Robotics and Automation Expert
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Optimal Control of Teleoperated Redundant Robots (page 5)

The compliance criteria describe the robotís ability to perform precision operations under load. They also correspond to the vibratory modes of the robot. Of the compliance criteria, the potential energy partition values are particularly important. The potential energy partition values measure the distribution of compliance energy and how it changes as the robot moves. An unusually high compliance energy content in any part of the robot indicates a problem with the robotís design. Rapid changes in compliance energy indicate large local forces, which correspond to large actuator demands and decreased precision.

The kinetic energy performance criteria address high-level issues represented in relatively simply formulations. Large changes in kinetic energy correspond to very large demands on actuator power. Very rapid changes in the kinetic energy represent shocks to the robot.

Simulated Annealing - The operator assist interface must solve a global optimization problem. Options for finding global optima include: a ďshotgunĒ approach tracking gradients from different starting places, simulated annealing based on models of the physical annealing process, genetic algorithms based on models of biological genetics, brute force exhaustive evaluation,and the Monte Carlo based on randomness and statistics. All of these methods will solve global optimization problems. The difficulty lies in the need for interactive response (a few seconds) from the configuration advisor. In an optimization with seventeen DOF, none of these methods would have interactive response on available computer hardware. With constraint tracking, all of the methods except brute force will have interactive response in a configuration advisor application. This section discusses an implementation of the simulated annealing method. Even in complex environments with multiple obstacles and competing performance criteria, the implementation has proven

Annealing describes a process of heating a material to an elevated temperature and then cooling it slowly. The slow cooling allows the material to reach a low energy state in which it is ductile. With no intelligence or systematic strategy, some materials minimize energy state during the slow cooling. Simulated annealing models this process on a computer. The model is based on the Boltzmann probability distribution equation. In this equation, E is the energy of the system, k is Boltzmannís constant, and T is the temperature. Essentially, Boltzmann states that a systemís energy probabilistically distributes depending upon the temperature. As the temperature increases, the probability of the system assuming a higher energy state increases. As the temperature decreases, the probability of the system leaving a lower energy state decreases. Each configuration option corresponds to an energy state. Because simulated annealing algorithms sometimes leave lower energy states for higher ones, they can escape from local minima. Simulated annealing algorithms typically include a method of generating random changes in the systemís configuration. The random changes represent trial configurations evaluated using the Boltzmann probability distribution. If the distribution indicates, the system assumes the trial configuration; otherwise it is discarded.

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