In this dissertation, we study the time-optimal trajectory planning which is based on dynamics for differential-driven wheeled mobile robots with current or voltage input constraints.
First, we investigate the time-optimal trajectory planning in the environment with one polygonal-shaped obstacle satisfying both motor's current and voltage constraints. We divide the trajectory into three section with constant input depending on the robot's motion. In case that DWMR has a sudden change of input, the current is saturated with its maximum value before the voltage. Hence, each section is divided into two intervals where one is for current saturation subsection and the other is for the voltage saturation subsection. We apply the bang-bang principle in all subsections which have not achieved in previous works. To illustrate the effectiveness of the proposed solution, we conduct simulations for various path deviation and compare the results with that of ECA.
Second, the time-optimal trajectory planning is suggested in the environment with two polygonal obstacles satisfying motor's voltage input constraints. In the first problem, it is assumed that the roads before and after the corner are long enough. To eliminate this assumption, we introduce the concept of the 'transition angle' which is used in a search loop. The simulation results are compared with the results of the 3-2-3 method, where the near-optimal arc trajectory section is used.
Third, we propose an efficient time-optimal trajectory planning algorithm for an environment with multiple static circular obstacles satisfying motor's voltage input constraints. This problem is known to be complex particularly if obstacles are present and if full dynamics including actuators is considered. Given a homotopy class, the proposed technique solves this problem with the assumption that two obstacles are apart from each other up to a certain distance by defining a portion of trajectory between obstacles as a section and combining multiple sections with arcs while treating the case of multiple consecutive obstacles without arcs. This method helps to treat complex environment considering dynamics with actuators. Simulation results are shown to validate the efficiency of the proposed algorithm.
To remove the distance assumption and a homotopy class condition in the previous problem, we proposed $V^*$ algorithm. To handling the distance assumption, we add one loop for the out-curve interval in OO, SO, OF section planning. Also, we use the existing visibility graph and $A^*$ algorithm to find the optimal path among all possible homotopy classes not visiting the all classes using the real travel time as a cost to determine the next visit obstacle.
Finally, we conduct the experience corresponding to the last algorithm. Modifying the Kobuki hardware, we can give PWM input to the robot directly. The experiment results showed that the proposed algorithm gives a proper reference trajectory which the robot can follow while satisfying not only the robot's kinematics and dynamics but also motor's voltage constraint.