一种新的基于spatial高斯最小约束原理的正动力学算法

A NEW POSITIVE DYNAMICS ALGORITHM BASED ON SPATIAL GAUSSIAN PRINCIPLE OF LEAST CONSTRAINT

本文首先利用 spatial notation 理论建立了刚体的达朗伯原理、高斯原理和高斯最小拘束原理.然后,将其用于机器人端杆加速度受约束时的动力学分析和建模,并利用动态规划方法求解机器人的正动力学问题,得到了计算关节加速度的线性递推公式.用简单而统一的办法来处理附加于机器人系统的约束条件,特别适合于分析空间、水下和冗余机器人的复杂运动.

Based-on the spatial notation theory,D Alembert's principle,Gauss principle and Gaussian principle ofleast constraint for rigid body are discussed.These principles are applied to the dynamic analysis and mod-elling of the robot while the accelerations of the manipulator are constrainted.In solving the positive dy-namics problem of robot,dynamic planning method is also used.As a result,linear recursion formulae ofcomputing the joint accelerations are obtained.The algorithm is simple and general,can be used conve-niently in analyzing the complicate,motions for spatial,underwater and redundant robots.