基于时间最优的PTP轨迹规划问题

摘要

When dealing with a minimum-time traj ectory planning for a point to point (PTP)task,parametric interpolation func-tions are usually used to join the target points.But whether the interpolation function itself can describe the fastest path is a problem.To solve this problem,a proposition that cubic spline function can describe a path which can be the fastest one among all the possible paths when the number of segments between each two points is 7 was proved.When the number of segments between each two points is 11,the jerks of the path can be constant with the same property.Using this kind of cubic spline,a penalty function was built.With conjugate gradient method,the result obtained is satisfactory.%针对PTP(point to point)问题中,插值函数可能无法描述时间最短的轨迹的问题,通过形式逻辑,证明在使用三次样条函数作为插值函数连接目标点时,在每两个相邻的目标点之间构造分段数为7的三次样条函数,可以使插值函数有能力描述时间最短的轨迹;在不丢失这种描述能力的前提下,当每两个相邻的目标点之间构造的三次样条函数的分段数为11时,各段三次样条函数的三次项系数可以为定值.在此基础上构造优化模型,用BFGS方法进行优化计算,优化结果表明,上述三次样条函数能有效满足轨迹规划的要求.