Hybrid Systems Differential Dynamic Programming for Whole-Body Motion Planning of Legged Robots

He, Li; Wensing, Patrick M.

doi:10.1109/lra.2020.3007475

Cited by 69 publications

(71 citation statements)

References 42 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%

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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%

“…In [24], a hierarchical trajectory optimization is also inverting directly the constrained system with real-time applications. In [33], a similar approach is used and extended to account for constrained impact dynamics and switching constraints.…”

Section: Introductionmentioning

confidence: 99%

Proximal and Sparse Resolution of Constrained Dynamic Equations

Carpentier¹,

Budhiraja²,

Mansard³

2021

Robotics: Science and Systems XVII

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show abstract

“…The empirical effectiveness of DDP for highly nonlinear systems has been well-demonstrated in the robotics literature: DDP has been used to control quadrupeds [13], [18], humanoids [12], [14], and other high-DoF robots [11], [15].…”

Section: Differential Dynamic Programmingmentioning

confidence: 99%

Trajectory Optimization for High-Dimensional Nonlinear Systems Under STL Specifications

Kurtz

Lin

2021

IEEE Control Syst. Lett.

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Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis problemgenerating a trajectory that satisfies a given specification-can be formulated as a trajectory optimization problem. Unfortunately, the associated cost function is nonsmooth and non-convex. As a result, existing synthesis methods scale poorly to high-dimensional nonlinear systems. In this letter, we present a new trajectory optimization approach for STL synthesis based on Differential Dynamic Programming (DDP). It is well known that DDP scales well to extremely high-dimensional nonlinear systems like robotic quadrupeds and humanoids: we show that these advantages can be harnessed for STL synthesis. We prove the soundness of our proposed approach, demonstrate order-of-magnitude speed improvements over the state-of-the-art on several benchmark problems, and demonstrate the scalability of our approach to the full nonlinear dynamics of a 7 degree-of-freedom robot arm.

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“…The main drawbacks of DDP based approaches is the difficulty in implementing hard-inequality and switching constraints. Hard-inequality constraints need to be implemented as penalties (e.g., with relaxed-barriers) [22] while the switching constraints are formulated using Augmented Lagrangian methods [23,24].…”

Section: Introductionmentioning

confidence: 99%