Path Tracking Algorithms for Non-Convex Waiter Motion Problem

Abstract

Originally, motion planning was concerned with problems such as how to move an object from a start to a goal position without hitting anything. Later, it has extended with complications such as kinematics, dynamics, uncertainties, and also with some optimality purpose such as minimum-time, minimum-energy planning. The paper presents a time-optimal approach for robotic manipulators.A special area of motion planning is the waiter motion problem, in which a tablet is moved from one place to another as fastas possible, avoiding the slip of the object that is placed upon it. The presented method uses the direct transcription approach for the waiter problem, which means a optimization problem is formed in order to obtain a time-optimal control for the robot. Problem formulation is extended with a non-convex jerk constraints to avoid unwanted oscillations during the motion. The possible local and global solver approaches for the presented formulation are discussed, and the waiter motion problem is validated by real-life experimental results with a 6-DoF robotic arm.Keywords motion planning, minimum-time control, time-optimal control, convex optimisation, robot control 1 Introduction Time-optimal motion planning has been a topic of active research since the 1980. Minimum-time algorithms can maximize productivity, and reduce energy consumption of the robotic system. Direct approaches [1] or one step methods solve the entire problem in one step. In general it is a highly difficult task, since both the geometric constraints (including collision avoidance), and the timing along this geometric path (including dynamic limitation) have to be optimized.As an alternative to direct approach, the motion planning problem is often decoupled [2,3]. First, a high-level geometry path planner determines a path for the robot considering geometric constraints and ignoring system dynamics. In the next stage (path tracking), a velocity profile for a predefined path is generated, where all constraints of the robot are applied for the fixed path. Decoupled approach is preferred to direct approach for its lower computational time.In this paper, we will focus on the second stage of the decoupled motion planning approach. Since the desired path of the robot is already defined, a scalar path coordinate