A novel approach to efficiently treat pure-state equality constraints in optimal control problems (OCPs) using a Riccati recursion algorithm is proposed. The proposed method transforms a pure-state equality constraint into a mixed state-control constraint such that the constraint is expressed by variables at a certain previous time stage. It is showed that if the solution satisfies the second-order sufficient conditions of the OCP with the transformed mixed state-control constraints, it is a local minimum of the OCP with the original pure-state constraints. A Riccati recursion algorithm is derived to solve the OCP using the transformed constraints with linear time complexity in the grid number of the horizon, in contrast to a previous approach that scales cubically with respect to the total dimension of the pure-state equality constraints. Numerical experiments on the whole-body optimal control of quadrupedal gaits that involve pure-state equality constraints owing to contact switches demonstrate the effectiveness of the proposed method over existing approaches.

翻译：提议采用一种新颖的方法,在最佳控制问题中有效处理纯国家平等限制,使用Riccati累回算法,在最佳控制问题中有效处理纯国家平等限制; 提议的方法将纯国家平等限制转变为混合国家控制限制,从而在以前某个时间阶段以变量表示这种限制; 表明如果解决办法满足了OCP的第二阶充分条件,而转变了混合国家控制限制,它就是OCP的当地最低条件,而原始的纯国家限制; 产生Riccati累回算法,利用地平线网数线性时间复杂性的转变限制来解决OCP,而以前的做法则在纯国家平等限制的全方位方面是三成的; 对涉及纯国家平等限制的四肢进行整体最佳控制试验,因为接触开关而导致纯国家平等限制; 利用Riccati递解算法对现行方法的有效性。