Time-energy optimal path tracking for robots: a numerically efficient optimization approach

Abstract

This paper focuses on time-optimal and time-energy optimal path tracking, which are subproblems in optimal motion planning of robot systems. Through a nonlinear change of variables, the time-energy optimal path tracking problem is transformed here into a convex optimal control problem with a single state variable. A direct transcription method is presented that reduces finding the globally optimal trajectory to solving a second-order cone program using robust numerical algorithms that are freely available. Application to a six-DOF KUKA 361 industrial robot carrying out a writing task illustrates the practicality of the new method.

Smooth time-optimal tool trajectory generation for CNC manufacturing systems

“…With reference to Verscheure and Demeulenaere [15], we define states a and b that satisfy (12) Then, it is obvious that…”

“…Gasparetto and Zanotto [14] used the fifth-order B-splines to define the path and solved the trajectory planning problem using the sequential quadratic programming (SQP) method. Verscheure and Demeulenaere [15] converted the time-optimal path tracking problem into a second-order convex programming problem which is then solved using the direct transcription approach.…”

Online motion selection for semi-optimal stabilization using reverse-time tree

“…Many short-time control methods based on these studies have been suggested since then (for e.g. [6]). In many of these studies, a sequence of q from a given initial position/posture q 0 to a given goal position/posture q g is pre-specified.…”

Optimal motion planning for robotic manipulators with dynamic obstacles using mixed-integer linear programming

“…Shin and McKay presented a dynamic programming approach to trajectory planning for this step in [8]. Verscheure et al transformed the trajectory planning by direct transcription and used second order cone programming [9]. Moreover, it is also possible to integrate both path planning and trajectory planning in one stage by the means of mathematical programming, e.g.…”