Efficient Riccati recursion for optimal control problems with pure-state equality constraints
This work addresses a computational bottleneck in optimal control for robotics and engineering applications, offering an incremental improvement in efficiency for constrained problems.
The paper tackles the problem of efficiently handling pure-state equality constraints in optimal control problems by proposing a novel Riccati recursion algorithm that transforms these constraints into mixed state-control constraints, achieving linear time complexity in grid number compared to cubic scaling in previous methods, as demonstrated in numerical experiments on quadrupedal gait control.
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.