Structure-Exploiting Sequential Quadratic Programming for Model-Predictive Control
Armand Jordana, Sebastien Kleff, Avadesh Meduri, Justin Carpentier, Nicolas Mansard, Ludovic Righetti
AI summary
Problem
Robotics MPC heavily relies on DDP/iLQR variants, often ignoring established optimization techniques like SQP, making it difficult to efficiently enforce hard constraints and lacking a clear connection to standard optimization methods.
Approach
The authors reformulate nonlinear MPC as a multiple-shooting SQP problem and implement a custom, sparsity-exploiting ADMM-based QP solver that maintains linear complexity over the time horizon while handling arbitrary constraints.
Key results
- Clarifies mathematical equivalence between multiple-shooting DDP and standard SQP
- Demonstrates stagewise SQP outperforming state-of-the-art FDDP in benchmarks
- Introduces a novel stagewise ADMM QP solver leveraging Riccati recursions
- Achieves first closed-loop nonlinear MPC with hard constraints on a real manipulator
Why it matters
Provides robotics researchers with a robust, theoretically grounded alternative to DDP for real-time constrained control, enabling reliable hardware deployment without heuristic constraint tuning.
Abstract
The promise of model-predictive control in robotics has led to extensive development of efficient numerical op- timal control solvers in line with differential dynamic pro- gramming because it exploits the sparsity induced by time. In this work, we argue that this effervescence has hidden the fact that sparsity can be equally exploited by standard nonlinear optimization. In particular, we show how a tailored implementation of sequential quadratic programming achieves state-of-the-art model-predictive control. Then, we clarify the connections between popular algorithms from the robotics com- munity and well-established optimization techniques. Further, the sequential quadratic program formulation naturally encompasses the constrained case, a notoriously difficult problem in the robotics community. Specifically, we show that it only requires a sparsity-exploiting implementation of a state-of-the-art quadratic programming solver. We illustrate the validity of this approach in a comparative study and experiments on a torque-controlled manipulator. To the best of our knowledge, this is the first demonstration of closed loop nonlinear model-predictive control with constraints on a real robot.