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Acceleration-based optimal trajectory planning in 3D environments

An approach to generating acceleration-based optimal smooth piecewise trajectories is proposed. Given two configurations (position and orientation) in 3D, we search for the minimal energy trajectory that minimizes the integral of the squared acceleration, opposed to curvature, which is widely investigated. The variation in both components of acceleration controls the smoothness of generated trajectories. Our objective is to search for the trajectory along which a free moving robot is able to accelerate (decelerate) to a safe speed in an optimal way. A numerical iterative procedure is devised for computing the optimal piecewise trajectory as a solution of a constrained boundary value problem.