Optimal Splines for Rigid Motion Systems: A Convex Programming Framework

Abstract

This paper develops a general framework to synthesize optimal polynomial splines for rigid motion systems driven by cams or servomotors. This framework is based on numerical optimization, and has three main characteristics: (i) Spline knot locations are optimized through an indirect approach, based on providing a large number of fixed, uniformly distributed candidate knots; (ii) in order to efficiently solve the corresponding large-scale optimization problem to global optimality, only design objectives and constraints are allowed that result in convex programs; and (iii) one-norm regularization is used as an effective tool for selecting the better (that is, having fewer active knots) solution if many equally optimal solutions exist. The framework is developed and validated based on a double-dwell benchmark problem for which an analytical solution exists.