ALTRO: A Fast Solver for Constrained Trajectory Optimization

Howell, Taylor A.; Jackson, Brian E.; Manchester, Zachary

doi:10.1109/iros40897.2019.8967788

Cited by 126 publications

(103 citation statements)

References 14 publications

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“…Contact sequences can even be optimized simultaneously, using relaxations of the contact model [66,67]. Thanks to efficient open-source numerical solvers [68][69][70] exploiting the sparsity of the trajectory optimization problem and exact derivatives of the dynamic models [71][72][73], wholebody motions can be computed online in less than 7 ms [70,74,75].…”

Section: Recent Progress With Whole-body Modelsmentioning

confidence: 99%

Recent Progress in Legged Robots Locomotion Control

Carpentier

Wieber

2021

Curr Robot Rep

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Purpose of review In recent years, legged robots locomotion has been transitioning from mostly flat ground in controlled settings to generic indoor and outdoor environments, approaching now real industrial scenarios. This paper aims at documenting some of the key progress made in legged locomotion control that enabled this transition.Recent findings Legged locomotion control makes extensive use of numerical trajectory optimization and its online implementation, model predictive control. A key progress has been how this optimization is handled, with refined models and refined numerical methods. This led the legged locomotion research community to heavily invest in and contribute to the development of new optimization methods and efficient numerical software. SummaryWe present an overview of the typical approach to legged locomotion control, which involves primarily planning a sequence of contacts with the environment and computing a corresponding dynamically feasible trajectory of the Center of Mass of the robot. We then detail recent progress in contact planning and trajectory optimization with either the full Lagrangian dynamics of legged robots or with reduced models.

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Section: Recent Progress With Whole-body Modelsmentioning

confidence: 99%

Recent Progress in Legged Robots Locomotion Control

Carpentier

Wieber

2021

Curr Robot Rep

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“…Besides, they propose to use an Augmented Lagrangian method. Another Augmented Lagrangian extension called ALTRO [15] has been proposed recently.…”

Section: A Motivation and Related Workmentioning

confidence: 99%

“…Now, the aim is to find an expression for g that is bounded (14), monotonic (15) and, importantly for the convergence of FDDP, continuously differentiable. For the rest of this paper, our sigmoid function has the form (see Fig.…”

Section: A Squashing Functionmentioning

confidence: 99%

Squash-Box Feasibility Driven Differential Dynamic Programming

Marti-Saumell

Solà

Mastalli

et al. 2020

2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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Recently, Differential Dynamic Programming (DDP) and other similar algorithms have become the solvers of choice when performing non-linear Model Predictive Control (nMPC) with modern robotic devices. The reason is that they have a lower computational cost per iteration when compared with off-the-shelf Non-Linear Programming (NLP) solvers, which enables its online operation. However, they cannot handle constraints, and are known to have poor convergence capabilities. In this paper, we propose a method to solve the optimal control problem with control bounds through a squashing function (i.e., a sigmoid, which is bounded by construction). It has been shown that a naive use of squashing functions damage the convergence rate. To tackle this, we first propose to add a quadratic barrier that avoids the difficulty of the plateau produced by the sigmoid. Second, we add an outer loop that adapts both the sigmoid and the barrier; it makes the optimal control problem with the squashing function converge to the original control-bounded problem. To validate our method, we present simulation results for different types of platforms including a multi-rotor, a biped, a quadruped and a humanoid robot.

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“…Classical DDP was initially limited to unconstrained problems. Recent works have proposed using various optimization strategies to handle different levels of constraints: box control constraints (aka box-DDP) [8] via box Quadratic Programming (QP), nonlinear equality constraints [9], [10], [11], [12], a mix of box constraints and equality constraints, and generic nonlinear constraints [13], [14], [15] via either AL, penalty, or SQP methods. However, these solutions either provide limited convergence guarantees (no globalization strategies [3]) or require a significant amount of iterations of the DDP algorithm or the internal numerical routines to converge to a feasible solution, limiting then the deployment of these methods for online Model Predictive Control for instance.…”

Section: Introductionmentioning

confidence: 99%

Equality Constrained Differential Dynamic Programming

Kazdadi

Carpentier

Ponce

2021

2021 IEEE International Conference on Robotics and Automation (ICRA)

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Trajectory optimization is an important tool in task-based robot motion planning, due to its generality and convergence guarantees under some mild conditions. It is often used as a post-processing operation to smooth out trajectories that are generated by probabilistic methods or to directly control the robot motion. Unconstrained trajectory optimization problems have been well studied, and are commonly solved using Differential Dynamic Programming methods that allow for fast convergence at a relatively low computational cost. In this paper, we propose an augmented Lagrangian approach that extends these ideas to equality-constrained trajectory optimization problems, while maintaining a balance between convergence speed and numerical stability. We illustrate our contributions on various standard robotic problems and highlights their benefits compared to standard approaches.

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ALTRO: A Fast Solver for Constrained Trajectory Optimization

Cited by 126 publications

References 14 publications

Recent Progress in Legged Robots Locomotion Control

Recent Progress in Legged Robots Locomotion Control

Squash-Box Feasibility Driven Differential Dynamic Programming

Equality Constrained Differential Dynamic Programming

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