An Analytic Closed-form Solution for Trajectory Generation on a Path along an Arc of a Circle

An Analytic Closed-form Solution for Trajectory Generation on a Path along an Arc of a Circle

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A polynomial trajectory is a time-traveled distance function used to describe trajectory of the robot.Optimal high-degree polynomial trajectories considering initial and the final velocity conditions besides the acceleration constraints are desired.In this paper, a trajectory optimization problem aiming travel maximum distance for a robot that follows an arc based path is formulated.Along the path, the robot requires observing higgs bookcase initial and final zero velocity conditions as well as certain acceleration limits.

A high-degree polynomial equation along the trajectory is proposed inside of the optimization problem.The closed-form solution of the problem had been obtained analytically.The solution includes the coefficients of the any high-degree trajectory polynomial equation where the coefficients are obtained in closed-form.Simulations several experiments show that the resulting high-degree trajectories satisfy the initial ultrastar dc hc550 and final zero velocity conditions as well as acceleration constraint.