The content of the doctoral dissertation is divided into three parts. In the first part, the problem of computationally efficient planning of the minimum-time velocity profile for autonomous mobile systems on a given plane curve is discussed. In doing so, the movement must take into account the velocity, acceleration and jerk limitations. In the following chapter, the problem of planning minimum-time trajectories is discussed, whereby the success and efficiency of execution is influenced by the selection of the family of curves and their parametric description. In the third part, we studied the trajectory tracking problem for a real autonomous mobile robot moving along a minimum-time trajectory with velocity, acceleration and jerk constraints. The discussed examples of curves in the geometric sense are representative path sections in real industrial environments.
The simulation environment Matlab was used in the research. We developed an algorithm that generates a velocity profile by taking into account velocity, acceleration and jerk constraints, which were expressed by components in tangent and radial form. The basic methodology in solving this problem was to numerically solve a given differential equation with known initial conditions. In the first step, the presented algorithm determines the values of speed and radial and tangential acceleration in the points of maximum curvature and determines the local velocity profiles in the vicinity of these points, from where the minimum-time velocity profile with velocity and acceleration limitations is determined. In the second step of the algorithm, the existing velocity profile is modified in such a way that the jerk constraints are also taken into account. We solved the trajectory planning problem by combining a procedure that generates smooth paths consisting of Bézier curves and the algorithm that ensures the minimum-time velocity profiles on individual segments of a limited space. We made sure that the velocities and accelerations in the joints of the segments are continuous. The methodology of the work included the description of a new way of constructing fifth order Bézier curves, which enabled easy and intuitive parameterization. The advantages of using the developed trajectory planning algorithm were demonstrated in two simulations: on a race track and in an automated warehouse. The main motivation for the implementation of the minimum-time trajectory tracking was to test the developed path and trajectory planning methods on a real robot. We proposed a trajectory tracking algorithm based on an error model of a tricycle drive. Tracking of the reference trajectory was performed using model-based predictive control, where the criterion function was minimized by particle swarm optimization. We verified the presented approaches with simulations and experiments on a real robot.
The main advantages and novelties of the proposed algorithm for the calculation of the velocity profile are the computationally efficient two-step approach and the complete treatment of the jerk by components. We also included a statistical analysis in the study to demonstrate the low computational complexity. When planning trajectories, we demonstrated the efficiency and ease of implementation of the presented construction of fifth order Bézier curves. Together with the algorithm for calculating the velocity profile, they form an extremely useful tool for constructing minimum-time trajectories, as evidenced by the results of simulations on the race track and in the automated warehouse. Simulation results of minimum-time trajectory following proved robust performance in the presence of various non-ideal conditions, such as measurement noise, delays and limited control speeds, and experimental results confirmed the possibility of real-time use. The approaches presented in this PhD thesis have many possible applications. They are especially useful in cases where driving comfort is an important factor or in time-critical transports; especially for vehicles in autonomous warehouses where travel time is a key factor for efficient operation.
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