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

Abstract

The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time version 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 objectpushing task with a quadrupedal mobile manipulator.

Versatile multicontact planning and control for legged loco-manipulation

“…This PDF file includes: Methods and Discussion Figs. S1 to S4 Tables S1 to S7 References (95)(96)(97)(98)(99)(100)(101)(102)(103)(104)(105)(106)(107)(108)(109) Other Supplementary Material for this manuscript includes the following: Movies S1 to S7 (NCCR dfab), and TenneT TSO. This work has been conducted as part of ANYmal Research, a community to advance legged robotics.…”

Agile Maneuvers in Legged Robots: a Predictive Control Approach

“…Unfortunately, this extension increases the computation time by up to four times. To improve this, Howell et al [49] proposed an augmented Lagrangian approach to boost the computational efficiency, which was later extended in [50], [51]. On the other hand, for improving the poor globalization, a modification of the Riccati equations to account for lifted dynamics was proposed in [52].…”

Agile Maneuvers in Legged Robots: a Predictive Control Approach

“…Unfortunately, this extension increases the computation time by up to four times. To improve this, Howell et al [49] proposed an augmented Lagrangian approach to boost the computational efficiency, which was later extended in [50], [51]. On the other hand, for improving the poor globalization, a modification of the Riccati equations to account for lifted 4 dynamics was proposed in [53].…”