Smooth curves and motions defined and optimised using point-based techniques

Smooth motions are important in many areas of engineering, including robotics and machine design. Typically there are conflicting requirements and the design task can be formulated as a constrained optimisation problem. Examples of requirements include: smooth motion, minimal time of travel, minimal peak acceleration and jerk, and obstacle avoidance. Rather deal with Bézier or B-spline control points, it can be easier to deal with actual points along the motion and use variation of these to achieve performance requirements and functional constraints. The paper investigates the applicability of point-based techniques for design optimisation. Three strategies for doing this are proposed and evaluated by means of case study examples.