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= P (if 180° <= <= 0°)

To compensate for the maximum torque here, an Inequalitry Constraint will be used, so that the torque avoids approaching the maximum torque value.

PΤ = Torque Penalty Coefficient

n

Torque Constraint = PΤ ∑ (ei / Tmax)2

i=1

Every torque value is considered and if the torque approaches a maximum, then the torque constraint will grow considerably, and make the overall cost high.

To complete the description the optimization process will be described. The path could be split into 2 segments (n = 2), the first segment goes from 0° to 90°, the second segment goes from 90° to 180°. The process is simple, we choose start values for ′1 and ′2 (these will

both be of the same magnitude, but opposite sign in this example). The next step is to calculate the value for cost,

COST = Measurement of Performance + Motion Constraint + Torque Constraint

We would continue choosing new values for ′1 and ′2 until COST has obtained a minimum

value. This would provide an optimal path plan. The next factor of importance is to be able to express the difference between various path planning methods.

40.1.4 EVALUATION OF PATH PLANNERS

It is valuable to have a number of criteria to determine the value of a path planning method. These values should reflect the information required, the time (and complexity) of the method, the type of results, and the level of abstraction from the manipulator.

GENERAL REQUIREMENTS EVALUATION CRITERIA:

-Dimensions of Space (2D, 2.5D, 3D)

-Collision Avoidance (None, Contact Detection, Proximity Calculation)

-Multilink Manipulators

-Rotations of Payload

-Moving Workspace Obstacles

-Multi Robot Coordination

-Degree of Automation

INFORMATION SETUP EVALUATION CRITERIA:

-Information Source (Knowledge Based, Sensor Based)

-World Modelling

METHOD EVALUATION CRITERIA: