Constraint Handling in Continuous-Time DDP-Based Model Predictive Control

TL;DR

This paper introduces a constrained continuous-time SLQ algorithm that effectively incorporates path constraints into DDP-based model predictive control, enabling real-time applications in robotics.

Contribution

It develops a novel augmented-Lagrangian approach with multiplier updates for constrained SLQ, improving constraint handling in DDP-based MPC.

Findings

Effective constraint handling in real-time MPC

Benchmarking shows improved performance over relaxed log-barrier methods

Successful application to robotics tasks like obstacle avoidance and object pushing

Abstract

The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time variant of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the robotics community due to its efficiency in solving complex trajectory optimization problems. However, one major drawback of DDP-based formulations is their inability to properly incorporate path constraints. In this paper, we address this issue by devising a constrained SLQ algorithm that handles a mixture of constraints with a previously implemented projection technique and a new augmented-Lagrangian approach. By providing an appropriate multiplier update law, and by solving a single inner and outer loop iteration, we are able to retrieve suboptimal solutions at rates suitable for real-time model-predictive control applications. We particularly focus on the inequality-constrained case, where three augmented-Lagrangian penalty functions are introduced, along with their corresponding multiplier update rules. These are then benchmarked against a relaxed log-barrier formulation in a cart-pole swing up example, an obstacle-avoidance task, and an object-pushing task with a quadrupedal mobile manipulator.