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 coleman powermate air tool set path, the robot requires observing 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 kiara sky allure obtained in closed-form.Simulations several experiments show that the resulting high-degree trajectories satisfy the initial and final zero velocity conditions as well as acceleration constraint.