Differentiable Simulation for Physical System Identification

Lidec, Quentin Le; Kalevatykh, Igor; Laptev, Ivan; Schmid, Cordelia; Carpentier, Justin

doi:10.1109/lra.2021.3062323

Cited by 43 publications

(38 citation statements)

References 20 publications

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“…We also want to propose an efficient way of differentiating our algorithm and compute the derivatives of the constrained dynamics, going beyond classic derivatives of unconstrained forward or inverse dynamics [8]. This necessary for efficient use in an optimization problem, for example for optimal control or model predictive control of complex legged robots [6,26,31,33,36].…”

Section: Discussionmentioning

confidence: 99%

Proximal and Sparse Resolution of Constrained Dynamic Equations

Carpentier¹,

Budhiraja²,

Mansard³

2021

Robotics: Science and Systems XVII

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Control of robots with kinematic constraints like loop-closure constraints or interactions with the environment requires solving the underlying constrained dynamics equations of motion. Several approaches have been proposed so far in the literature to solve these constrained optimization problems, for instance by either taking advantage in part of the sparsity of the kinematic tree or by considering an explicit formulation of the constraints in the problem resolution. Yet, not all the constraints allow an explicit formulation and in general, approaches of the state of the art suffer from singularity issues, especially in the context of redundant or singular constraints. In this paper, we propose a unified approach to solve forward dynamics equations involving constraints in an efficient, generic and robust manner. To this aim, we first (i) propose a proximal formulation of the constrained dynamics which converges to an optimal solution in the least-square sense even in the presence of singularities. Based on this proximal formulation, we introduce (ii) a sparse Cholesky factorization of the underlying Karush-Kuhn-Tucker matrix related to the constrained dynamics, which exploits at best the sparsity of the kinematic structure of the robot. We also show (iii) that it is possible to extract from this factorization the Cholesky decomposition associated to the so-called Operational Space Inertia Matrix, inherent to task-based control frameworks or physic simulations. These new formulation and factorization, implemented within the Pinocchio library, are benchmark on various robotic platforms, ranging from classic robotic arms or quadrupeds to humanoid robots with closed kinematic chains, and show how they significantly outperform alternative solutions of the state of the art by a factor 2 or more.

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Section: Discussionmentioning

confidence: 99%

Proximal and Sparse Resolution of Constrained Dynamic Equations

Carpentier¹,

Budhiraja²,

Mansard³

2021

Robotics: Science and Systems XVII

Self Cite

View full text Add to dashboard Cite

show abstract

“…We would like to avoid computing H −1 , even storing a precomputed inverse for all iterations would be unpractical because often dense (except when H is a diagonal mass matrix M). So we propose to replace (31) with an equivalent saddle point problem: Theorem 1. Let k+1 be a solution to (31), then it is also a solution to [ H D…”

Section: The Admm Solvermentioning

confidence: 99%

“…So we propose to replace (31) with an equivalent saddle point problem: Theorem 1. Let k+1 be a solution to (31), then it is also a solution to [ H D…”

Section: The Admm Solvermentioning

confidence: 99%

“…The linear system (32) introduces an auxiliary variable v ∈ R n v , however, the matrix is very sparse and does not require storing or computing any H −1 matrix as we should do if using (31).…”

Section: The Admm Solvermentioning

confidence: 99%

“…26 ADMM methods have been used in many fields, with recent and notable examples in computer graphics, 27 computational fluid dynamics, 28 simulation of deformable structures, 29 and contact dynamics. 30,31 In the field of robotics, a sequential unconstrained minimization technique (SUMT) method based on augmented Lagrangian has been discussed in References 32,33, to our knowledge for the first time in a context of nonsmooth dynamics: SUMT leads to an iteration with the same structure of ADMM, for the same type of constraints.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solving variational inequalities and cone complementarity problems in nonsmooth dynamics using the alternating direction method of multipliers

Tasora

Mangoni

Benatti

et al. 2021

Numerical Meth Engineering

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This work presents a numerical method for the solution of variational inequalities arising in nonsmooth flexible multibody problems that involve set-valued forces. For the special case of hard frictional contacts, the method solves a second order cone complementarity problem. We ground our algorithm on the Alternating Direction Method of Multipliers (ADMM), an efficient and robust optimization method that draws on few computational primitives. In order to improve computational performance, we reformulated the original ADMM scheme in order to exploit the sparsity of constraint jacobians and we added optimizations such as warm starting and adaptive step scaling. The proposed method can be used in scenarios that pose major difficulties to other methods available in literature for complementarity in contact dynamics, namely when using very stiff finite elements and when simulating articulated mechanisms with odd mass ratios. The method can have applications in the fields of robotics, vehicle dynamics, virtual reality, and multiphysics simulation in general.

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ORCANet: Differentiable multi‐parameter learning for crowd simulation

Zhang

Wang

et al. 2022

Computer Animation & Virtual

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Realistic crowd simulation has always been an important research field in computer graphics. While both agent-based motion models and data-driven behavior models have made some progress, they are still suffering from either huge effort of multi-parameter tuning or limited realistic motion. In this article, we propose a novel and differentiable multi-parameter learning method for crowd simulation, which is called ORCANet. The main idea is to learn from real data and inverse evaluating the multi-parameter for subsequent simulation.ORCANet uses classic optimal reciprocal collision avoidance (ORCA) as a basic motion model which is integrated into the deep learning framework. Addressing the feature of linear programming and non-differentiable operation, a Gaussian kernel is added to approximate the role of neighbor distance in collision avoidance, which turns the original discrete operation into a fully differentiable forward simulation. Furthermore, we leverage ORCANet to optimize the multi-parameter combination in synthetic and real-world datasets. ORCANet is proved to rapidly converge to correct parameter values and regenerate the input synthetic sequence. Moreover, experiments on real-world datasets by the metric of pedestrian trajectories verified that a more realistic crowd simulation has been generated through ORCANet.

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Differentiable Simulation for Physical System Identification

Cited by 43 publications

References 20 publications

Proximal and Sparse Resolution of Constrained Dynamic Equations

Proximal and Sparse Resolution of Constrained Dynamic Equations

Solving variational inequalities and cone complementarity problems in nonsmooth dynamics using the alternating direction method of multipliers

ORCANet: Differentiable multi‐parameter learning for crowd simulation

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