CITATIONS.bib

@unpublished{jalletConstrainedDifferentialDynamic2022,
  title = {Constrained {{Differential Dynamic Programming}}: {{A}} Primal-Dual Augmented {{Lagrangian}} Approach},
  shorttitle = {Constrained {{Differential Dynamic Programming}}},
  author = {Jallet, Wilson and Bambade, Antoine and Mansard, Nicolas and Carpentier, Justin},
  year = {2022},
  month = mar,
  abstract = {Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver to iteratively compute its solution. On one hand, differential dynamic programming (DDP) provides an efficient approach to transcribe the optimal control problem into a finite-dimensional problem while optimally exploiting the sparsity induced by time. On the other hand, augmented Lagrangian methods make it possible to formulate efficient algorithms with advanced constraint-satisfaction strategies. In this paper, we propose to combine these two approaches into an efficient optimal control algorithm accepting both equality and inequality constraints. Based on the augmented Lagrangian literature, we first derive a generic primal-dual augmented Lagrangian strategy for nonlinear problems with equality and inequality constraints. We then apply it to the dynamic programming principle to solve the value-greedy optimization problems inherent to the backward pass of DDP, which we combine with a dedicated globalization strategy, resulting in a Newton-like algorithm for solving constrained trajectory optimization problems. Contrary to previous attempts of formulating an augmented Lagrangian version of DDP, our approach exhibits adequate convergence properties without any switch in strategies. We empirically demonstrate its interest with several case-studies from the robotics literature.},
  keywords = {Optimal control,Robotics and automation,Trajectory optimization}
}

@inproceedings{jalletProxNLPPrimaldualAugmented2022,
  title = {ProxNLP: A Primal-Dual Augmented Lagrangian Solver for Nonlinear Programming in Robotics and Beyond},
  shorttitle = {ProxNLP},
  booktitle = {6th Legged Robots Workshop},
  author = {Jallet, Wilson and Bambade, Antoine and Mansard, Nicolas and Carpentier, Justin},
  year = {2022},
  month = may,
  address = {Philadelphia, Pennsylvania, United States},
  urldate = {2022-10-10},
  abstract = {Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie groups), along with a specific requirement for robustness and speed. In recent years, augmented Lagrangian methods have seen a resurgence due to their robustness and flexibility, their connections to (inexact) proximal-point methods, and their interoperability with Newton or semismooth Newton methods. In the sequel, we present primal-dual augmented Lagrangian method for inequality-constrained problems on manifolds, which we introduced in our recent work, as well as an efficient C++ implementation suitable for use in robotics applications and beyond.}
}

@misc{jalletPROXDDPProximalConstrained2023,
  title = {PROXDDP: Proximal Constrained Trajectory Optimization},
  author = {Jallet, Wilson and Bambade, Antoine and Arlaud, Etienne and {El-Kazdadi}, Sarah and Mansard, Nicolas and Carpentier, Justin},
  year = {2023},
  abstract = {Trajectory optimization (TO) has proven, over the last decade, to be a versatile and effective framework for robot control. Several numerical solvers have been demonstrated to be fast enough to allow recomputing full-dynamics trajectories for various systems at control time, enabling model predictive control (MPC) of complex robots. These first implementations of MPC in robotics predominantly utilize some differential dynamic programming (DDP) variant for its computational speed and ease of use in constraint-free settings. Nevertheless, many scenarios in robotics call for adding hard constraints in TO problems (e.g., torque limits, obstacle avoidance), which existing solvers, based on DDP, often struggle to handle. Effectively addressing path constraints still poses optimization challenges (e.g., numerical stability, efficiency, accuracy of constraint satisfaction) that we propose to solve by combining advances in numerical optimization with the foundational efficiency of DDP. In this article, we leverage proximal methods for constrained optimization and introduce a DDP-like method to achieve fast, constrained trajectory optimization with an efficient warm-starting strategy particularly suited for MPC applications. Compared to earlier solvers, our approach effectively manages hard constraints without warm-start limitations and exhibits commendable convergence accuracy. Additionally, we leverage the computational efficiency of DDP, enabling real-time resolution of complex problems such as whole-body quadruped locomotion. We provide a complete implementation as part of an open-source and flexible C++ trajectory optimization library called ALIGATOR. These algorithmic contributions are validated through several trajectory planning scenarios from the robotics literature and the real-time whole-body MPC of a quadruped robot.},
  langid = {english}
}