Optimal Constant Acceleration Motion Primitives

This paper proposes new motion primitives that are time optimal and feasible for a vehicle (wheeled-mobile robot). They are parameterized by a constant acceleration and a constant deceleration in an obstacle-free environment between an initial and a final configuration with given poses and velocities. The derived compact parametric solution has an implicit optimal velocity profile, is continuous in C-2, considers driving constraints, and is computationally efficient. The path is derived analytically considering constraints on maximal allowable driving velocity and accelerations. The obtained motion primitives have continuous transition of curvature and are, thus, easily drivable by the vehicle. The proposed motion primitives are evaluated on several path-planning examples, and the obtained solutions are compared to a numerically expensive planner using Bernstein-Bezier curve with path shape and velocity profile optimization. Numerous experiments have been conducted not only in the simulation environment, but also during testing and comparisons on the actual mobile robot platforms. It is shown that the proposed solution is computationally efficient, time optimal under given constraints and trapezoidal velocity profile assumptions, and is close to globally optimal solution with an arbitrary velocity profile.