Time-optimal cornering trajectory planning avoiding slip for differential-wheeled mobile robots

Abstract

Autonomous mobile robots now perform various tasks covering a vast area of applications, including exploration in unknown area, reconnaissance, rescue, industrial automation, security, military, rehabilitation, logistics, cleaning, and human welfare. The topics of this dissertation are the time-optimal cornering trajectory planning of DWMRs avoiding slip. Based on dynamics including actuator motors, our cornering trajectory is planned which avoids slip while passing corner obstacles starting from initial state and reaching final state. We also use both the PWM signal and force bounds for the analysis of time-optimality. Our studies are configured as three sub-problems according to the number of turns and given corner environment. We analyze each problem with the Pontryagin's maximum principle based on PWM signal and force bounds. First, we formulate the time-optimal cornering trajectory planning problem, only utilizing a single turn which is the minimum number of turn for cornering motion, satisfying motor's voltage constraint and force constraints to avoid slip. We divide the trajectory into three sections, several intervals and sub-intervals to achieve goals and satisfy all constraints. Then we establish the time-optimal trajectory planning algorithm using the bang-bang principle or an extreme value of the force constraints. To validate the efficiency of the proposed solution, we conduct the simulations using the time-optimal trajectory compared with a TP-4PCI algorithm utilizing a single turn for cornering without slip avoidance. Also a trajectory control system for DWMRs is implemented using a resolved-acceleration controller with direct PWM signals to verify the proposed time-optimal trajectory. Second, we investigate the time-optimal trajectory planning problem utilizing three turns. Our trajectories allow additional initial and final rotations to use various turning radius for cornering. We then analyze two local minima of arrival time considering both traveled distance and velocity decrease in rotation. Based on the local minima, we proposed an algorithm of time-optimal trajectory planning avoiding slip. To demonstrate the effectiveness of the algorithm, simulations and experiments using the proposed algorithm are performed and compared with that of TOTP algorithm, which is the recent algorithm utilizing three turns without slip avoidance. Finally, we establish an efficient algorithm for time-optimal trajectory planning avoiding slip for an environment with multiple corners, based on the dynamics. We propose a hierarchical algorithm that is composed of trajectory parameter determination (TPD) and trajectory planning synthesis (TPS). TPD determines parameters of clipping point, which enable trajectory division into independent sections between corners to adopt divide-and-conquer strategy. TPS plans and integrates sections in the trajectory efficiently. To verify the validity of the proposed solution, simulations and experiments are also performed and compared with that of TOTP algorithm.