A Projection Approach to Equality Constrained Iterative Linear Quadratic Optimal Control
This work addresses constrained optimal control for robotics applications, but it is incremental as it extends an existing algorithm with a specific constraint-handling method.
The paper tackles the problem of incorporating state and state-input constraints into the iterative Linear Quadratic Regulator (iLQR) algorithm by proposing a projection-based method that ensures linear time-complexity. It demonstrates the approach through simulations, such as a 6 DoF robotic arm, to validate performance.
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.