Motion primitives in the trajectory planning problem with kinematic constraints

Automatic trajectory planning is an urgent scientific and technical problem, whose solutions are in demand in many fields: unmanned transportation, robotic logistics, social robotics, etc. Often, when planning a trajectory, it is necessary to consider the fact that the agent (robot, unmanned car, etc.) cannot arbitrarily change its orientation while moving, in other words, it is necessary to consider kinematic constraints when planning. One widespread approach to solving this problem is the approach that relies on the construction of a trajectory from prepared parts, motion primitives, each of which satisfies kinematic constraints. Often, the emphasis in the development of methods implementing this approach is on reducing the combinations of choices in planning (heuristic search), with the set of available primitives itself being regarded as externally defined. In this paper, on the contrary, we aim to investigate and analyze the effect of different available motion primitives on the quality of solving the planning problem with a fixed search algorithm. Specifically, we consider 3 different sets of motion primitives for a wheeled robot with differential drive. As a search algorithm, the A* algorithm well known in artificial intelligence and robotics is used. The solution quality is evaluated by 6 metrics, including planning time, length and curvature of the resulting trajectory. Based on the study, conclusions are made about the factors that have the strongest influence on the planning result, and recommendations are given on the construction of motion primitives, the use of which allows to achieve a balance between the speed of the planning algorithm and the quality of the trajectories found.