Time-Optimal Path Following for Robots With Convex–Concave Constraints Using Sequential Convex Programming

Abstract

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time. In the case of a robotic manipulator with simplified constraints a convex reformulation of this optimal control problem has been derived previously. However, many applications in robotics feature constraints such as velocity-dependent torque constraints or torque rate constraints that destroy the convexity. The present paper proposes an efficient sequential convex programming (SCP) approach to solve the corresponding nonconvex optimal control problems by writing the non-convex constraints as a difference of convex (DC) functions, resulting in convex-concave constraints. We consider seven practical applications that fit into the proposed framework even when mutually combined, illustrating the flexibility and practicality of the proposed framework. Furthermore, numerical simulations for some typical applications illustrate the fast convergence of the proposed method in only a few SCP iterations, confirming the efficiency of the proposed framework.

Path Tracking Algorithms for Non-Convex Waiter Motion Problem

“…In the presented approach, a mathematical optimisation problem is formed based on the work of Verscheure et al [5], Debrouwere et al [14].…”

“…Otherwise an approximation method is necessary for the derivatives (e.q. : numerical derivation, spline interpolation) [6,14].…”

“…Therefore an another approximation is applied for T , in which b(θ) is linear in θ . This technique is also used in the work of Debrouwere et al [14]. So the approximated T is a convex function of b i…”

“…In this section a Sequential Convex Programming (SCP) algorithm [14] is presented as a local solver for the waiter motion problem.…”

“…In Section 2 the time-optimal waiter motion problem is presented with non-convex jerk constraint. The formulation is based on the work of Verscheure et al [5], Debrouwere et al [14]. A possible solver methods for the presented problem are discussed in Section 3.…”