The paper addresses a velocity planning problem for autonomous vehicles. Appropriate bounds on velocities and accelerations have to be considered in order to avoid wheels skidding and actuators saturation. Planned profiles fulfill an assigned travelling time, while longitudinal jerk is minimized in order to increase the motion smoothness. In the paper it is shown that the velocity planning problem can be formulated as a nonlinear semi-infinite optimization to be solved in real time by means of an appositely devised algorithm characterized by a light computational burden.

The paper deals with the generation of smooth paths for the inversion-based motion control of wheeled mobile robots. A new path primitive, called$ { \mmb{\eta } }^{3}$-spline, is proposed. It is a seventh order polynomial spline which permits the interpolation of an arbitrary sequence of points with associated arbitrary tangent directions, curvatures, and curvature derivatives, so that an overall$\mmb G^{3}$-path is planned. A$\mmb G^{3}$-path or path with third order geometric continuity has continuous tangent vector, curvature, and curvature derivative along the arc length. Adopting this planning scheme and a dynamic path inversion technique, the robot's command velocities are continuous with continuous accelerations. The new primitive depends on a vector ($ { \mmb{\eta } }$) of six parameters that can be used to finely shape the path. The$ { \mmb{\eta } }^{3}$-spline can generate or approximate, in a unified framework, a variety of curve primitives such as circular arcs, clothoids, spirals, etc. The paper includes theoretical results, path planning examples, and a note on general$ { \mmb{\eta } }^{k}$-splines.

The path-velocity decomposition scheme is frequently adopted in the context of trajectory planning. A technique for the optimal velocity planning, to be used that framework, is proposed in this paper. Differentiable velocity profiles, which fulfil assigned initial and final boundary conditions on the velocity itself and on its first derivative, are obtained by means of the proposed strategy. Moreover, profiles are constrained between assigned bounds, i.e. velocity is limited, and its second derivative (the longitudinal jerk) is minimized by means of an optimization algorithm. The extensive use of closed form expressions makes this approach suitable to be implemented in real-time applications.

A new motion-generation approach is proposed for wheeled mobile robots described by the unicycle kinematic model. This approach permits the generation of smooth continuous-acceleration controls using a dynamic path-inversion procedure that exploits the concept of G/sup 3/ -paths, i.e., Cartesian paths with third-order geometric continuity (both the curvature function and its derivative, with respect to the arc length, are continuous). The exposed steering method is well suited to be adopted for the robot's iterative steering within a supervisory control architecture for sensor-based autonomous navigation. A worked example illustrates the approach.