建立在Udwadia和Kalaba方程上的伺服约束跟踪控制方法要求系统的初始条件必须与跟踪约束方程相容。针对该问题，利用广义虚位移投影分解方法，将跟踪约束误差转化为广义坐标误差与广义速度误差，通过提出系统跟踪控制总误差的概念，提出一种可以消除该误差的控制力计算方法。该方法可以实现对系统初始误差的补偿。利用该算法对系统初始跟踪误差的可控性，将其与基于Udwadia和Kalaba方程的伺服约束跟踪控制算法结合，实现了不相容初始条件下的约束系统轨迹跟踪控制。以平面2自由度机械手臂为仿真算例，对该控制算法在轨迹跟踪控制中的应用进行仿真研究。仿真结果表明，该方法可以解决机械系统跟踪控制中的初值不相容问题，同时对约束违约进行了抑制，提高了控制精度及稳定性。

The servo constraint following control algorithm based on Udwadia and Kalaba equation requires the consistent initial conditions. To solve this problem, the principle of generalized virtual displacement decomposition is used to transform constraint errors into generalized coordinate errors and generalized velocity errors. The concept of total error of trajectory tracking for mechanical systems is proposed, and the explicit control forces formulae are deduced to eliminate this error. The method proposed here can compensate the initial tracking errors. Because of the controllability of this tracking control algorithm on initial errors, it can be combined with servo constraint following control which is based on the Udwadia and Kalaba equation. This method can handle the trajectory tracking control under inconsistent initial conditions effectively. The numerical simulation of a mechanical manipulator with two degrees of freedom is made and the results show that the algorithm can solve problems caused by the inconsistent initial conditions, also solve constraint violation problem, and improve the control precision and stability.