## 1.4 SPECIAL ISSUES

### 1.4.1 Optimal Motion

• Previous sections discuss common industrial methods for path planning, but these methods are generally sub-optimal.

• The example below shows two paths, and the difference in motion time for torque limited actuators. • In the example above, the arm is bent along the path to reduce the moment of inertia, and thus allows faster motions, but this would not happen with any of the simple control schemes.

• Methods to find these paths efficiently are still in research phases.

### 1.4.2 Singularities

• Common types of singularities are,

- redundant configurations lead to indefinite solutions

- joints become straight, and infinite joint velocities are required

- positions that may be reached in an infinite number of ways.

• Most of these singularities became obvious mathematically.

• A simple type of singularity often occurs at the edge of the robot workspace • Another type of robot singularity occurs when the joints flip • Some forms of solution redundancy can also be considered singularities (the solution to these is to examine the last position, and match the solution to it) 