Time-optimal motion planning is one of the most essential problems in robotic theories. The presented direct transcription approach uses convex optimisation method to obtain a minimum-time control for robot manipulators. One subset of motion planning is the waiter motion problem that consists of moving a tablet from one place to another as fast as possible, avoiding the slip of the object that is placed upon it. In this paper the direct transcription method is presented in order to solve the waiter problem. This path tracking problem is also approximated by sequential two dimensional second-order cone programs (SOCP) using nonlinear change of variables. The computational benefit of the sequential method compared to the direct transcription approach is presented. The waiter motion problem is validated by real-life experimental results with a 6-DoF robotic arm.
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