Time Optimal Control along Specified Paths with Acceleration Continuity: A Non-Linear Time Scaling based approach

Arun Kumar Singh1    Bharath Gopalakrishnan1    K.Madhava Krishna1   

1 IIIT Hyderabad, India   

In this paper we present a non-linear time scaling based formulation for computing time optimal motions along specified paths. The primary motivation behind the current work is to introduce acceleration continuity constraints within the time optimal framework. Such constraint necessitates the use of time varying controls instead of commonly used piecewise constant controls. We propose a novel extension of our previously developed concept of non-linear time scaling through which it is possible to parametrize controls as piece-wise product of a exponential and a linear function. We show that such representation leads to a very simple optimization structure with primarily linear constraints. The non-linearity has a quasi-convex structure which we reformulate into a simple difference of convex form. A sequential convex programming framework is utilised to solve the optimization as a sequence of sparse quadratic programmes. The proposed optimization is an improvement over the current state of the art frameworks which introduces acceleration continuity constraints in the time optimal framework through highly non-linear and non-convex optimizations.