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We propose an efficient stochastic scheme for minimum-time trajectory planning of a nonholonomic unicycle mobile robot under constraints on path curvature, velocities, and torques. This problem, which is known to be complex, often requires important runtimes, particularly if obstacles are present and if full dynamics is considered. The proposed technique is a fast variant of the random-profile approach recently applied to wheeled-mobile robots. It incorporates a trapezoidal-velocity-profile constraint that helps reduce the number of unknown parameters and that speeds up the calculation steps. Results are presented for two-and threewheel mobile robots in free/constrained workspaces. A comparison with reference solutions, which were obtained independently, shows that the proposed variant is able to achieve almost the same quality of calculated trajectories while reducing the runtime considerably.Index Terms-Stochastic optimization, trajectory planning, trapezoidalvelocity profile (TVP), wheeled-mobile robot.

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because the dynamics is simply described by the inverse dynamic model.In the present paper, we propose a new and simple direct method able to generate suboptimal trajectories for robotic manipulators minimizing the transfer time T and verifying imposed kinodynamic constraints. It can be seen as a variant of DCPM. This method is based first on the dissociation of the search of the optimal transfer time T from that of the other optimal motion parameters. This allows us to express the kinodynamic constraints as bounds on admissible values of T. Then, normalized trapezoidal velocity profiles (TVP) are used to generate trajectory profile candidates. Finally, a stochastic optimization method is used to find the best trajectory profile leading to the best approximation of the optimal time motion T. This work is motivated by the following:* The simplicity of the classical TVP and its large use in the industrial context. * The reduced number of optimization parameters which allows solving the problem in quasi real time. * The obtained trajectory can be implemented on existing robot controllers.

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