# A Projection Approach to Equality Constrained Iterative Linear Quadratic Optimal Control

arXiv: https://arxiv.org/abs/1805.09403 · HTML: https://mlsanity.com/paper/1805.09403/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 1 of 1)

- [Constrained Stein Variational Trajectory Optimization](https://mlsanity.com/paper/2308.12110/) (2023)

## Abstract (arXiv)

This paper presents a state and state-input constrained variant of the discrete-time iterative Linear Quadratic Regulator (iLQR) algorithm, with linear time-complexity in the number of time steps. The approach is based on a projection of the control input onto the nullspace of the linearized constraints. We derive a fully constraint-compliant feedforward-feedback control update rule, for which we can solve efficiently with Riccati-style difference equations. We assume that the relative degree of all constraints in the discrete-time system model is equal to one, which often holds for robotics problems employing rigid-body dynamic models. Simulation examples, including a 6 DoF robotic arm, are given to validate and illustrate the performance of the method.