Example (3)

• Performance Criteria:
  • Maximum acceleration ( ).
  • Minimum position error (e).
  • Minimize power consumption for the motors (P).
• Optimization Parameters:
  • Link lengths.
  • Link masses.
• Optimization Functions:

  The overall objective function is:

• Constraints:
  • Feedback gains.
  • Update frequency.
  • Feedback frequency.
  • Friction.
  • Set of available densities for the link material.
  • Catalog of available motors.
• Strategy:

  This problem is solved in two stages: first the manipulability and the structured length index can be used to determine the optimum link lengths (as in the first example); then, we use these lengths to get the optimum masses. From the assumptions stated before, there is a finite set of densities, and the links are uniform, which means we need to select the density that gives optimum performance, since we already have the lengths. This problem can be solved using pattern search on the densities, or using some other integer optimization techniques.

  The power consumption of the motor is related to the torque, which means we need to minimize the maximum torque. Also, here we use the simulation program to get a quantitative measure for the overall objective function.