Efficient Riccati recursion for optimal control problems with pure-state equality constraints

by   Sotaro Katayama, et al.

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.


page 1

page 2

page 3

page 4


Equality Constrained Linear Optimal Control With Factor Graphs

This paper presents a novel factor graph-based approach to solve the dis...

Lifted contact dynamics for efficient direct optimal control of rigid body systems with contacts

We propose a novel and efficient lifting approach for the direct optimal...

A Projection Approach to Equality Constrained Iterative Linear Quadratic Optimal Control

This paper presents a state and state-input constrained variant of the d...

A New Continuous-Time Equality-Constrained Optimization Method to Avoid Singularity

In equality-constrained optimization, a standard regularity assumption i...

Sample Average Approximation for Stochastic Programming with Equality Constraints

We revisit the sample average approximation (SAA) approach for general n...

Locally Imposing Function for Generalized Constraint Neural Networks - A Study on Equality Constraints

This work is a further study on the Generalized Constraint Neural Networ...

Phase-field fracture irreversibility using the slack variable approach

In this manuscript, the phase-field fracture irreversibility constraint ...

Please sign up or login with your details

Forgot password? Click here to reset