Robust Stabilization of Periodic Gaits for Quadrupedal Locomotion via QP-Based Virtual Constraint Controllers

Fawcett, Randall T.; Pandala, Abhishek; Ames, Aaron D.; Hamed, Kaveh Akbari

doi:10.1109/lcsys.2021.3133198

Cited by 12 publications

(12 citation statements)

References 31 publications

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“…The use of a single training environment is motivated by the following justification. The QP-based virtual constraints controller employed at the low level of the hierarchical control algorithm can result in stable locomotion patterns on flat terrains, as studied in our previous work [36]. The integration of the low-level controller with the high-level RMPC algorithm improves the robust stability of gaits over different sets of terrains.…”

Section: B Training Of the Mlpmentioning

confidence: 90%

“…The current work differs from our previous work [36] in that it only considers low-level and QP-based nonlinear controllers for quadrupedal locomotion while addressing their continuous differentiability, but not the RMPC framework and the proposed hierarchical control algorithm. The work is also different from [16] in that it does not address the robust planning subject to modeling uncertainties.…”

Section: B Objectives and Contributionsmentioning

confidence: 95%

“…At the lower level, a nonlinear controller, developed based on virtual constraints and QP, maps the generated desired GRFs to the full-order dynamical model while regulating some output functions for whole-body motion control. The use of virtual constraints-based controller is motivated by the successful hardware implementation on various bipedal [32]- [35] and quadrupedal [36], [37] robots and powered prosthetic legs [38], [39]. The proposed robust control strategy can bridge the gap between reduced-and full-order models while learning the uncertainty at the trajectory planning level.…”

Section: B Objectives and Contributionsmentioning

confidence: 99%

See 2 more Smart Citations

Robust Predictive Control for Quadrupedal Locomotion: Learning to Close the Gap Between Reduced- and Full-Order Models

Pandala

Fawcett

Rosolia

et al. 2022

IEEE Robot. Autom. Lett.

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Template-based reduced-order models have provided a popular methodology for real-time trajectory planning of dynamic quadrupedal locomotion. However, the abstraction and unmodeled dynamics in template models significantly increase the gap between reduced-and full-order models. This letter presents a computationally tractable robust model predictive control (RMPC) formulation, based on convex quadratic programs (QP), to bridge this gap. The RMPC framework considers the single rigid body model subject to a set of unmodeled dynamics and plans for the optimal reduced-order trajectory and ground reaction forces (GRFs). The generated optimal GRFs of the highlevel RMPC are then mapped to the full-order model using a lowlevel nonlinear controller based on virtual constraints and QP. The proposed hierarchical control framework is employed for locomotion over rough terrains. We leverage deep reinforcement learning to train a neural network to compute the set of unmodeled dynamics for the RMPC framework. The proposed controller is finally validated via extensive numerical simulations and experiments for robust and blind locomotion of the A1 quadrupedal robot on different terrains.

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Section: B Training Of the Mlpmentioning

confidence: 90%

Section: B Objectives and Contributionsmentioning

confidence: 95%

Section: B Objectives and Contributionsmentioning

confidence: 99%

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Robust Predictive Control for Quadrupedal Locomotion: Learning to Close the Gap Between Reduced- and Full-Order Models

Pandala

Fawcett

Rosolia

et al. 2022

IEEE Robot. Autom. Lett.

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“…A promising solution is to augment the controller described in Sec. V, which does not explicitly guarantee the feasibility of necessary constraints (e.g., ground contact forces), with an optimization-based controller [2], [4] that explicitly ensures the feasibility for actual walking.…”

Section: Discussionmentioning

confidence: 99%

Real-Time Walking Pattern Generation of Quadrupedal Dynamic-Surface Locomotion based on a Linear Time-Varying Pendulum Model

Iqbal¹,

Veer²,

Gu³

2023

Preprint

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This study introduces an analytically tractable and computationally efficient model of the legged robot dynamics associated with locomotion on a dynamic rigid surface (DRS), and develops a real-time motion planner based on the proposed model and its analytical solution. This study first theoretically extends the classical linear inverted pendulum (LIP) model from legged locomotion on a static surface to DRS locomotion, by relaxing the LIP's underlying assumption that the surface is static. The resulting model, which we call "DRS-LIP", is explicitly time-varying. After converting the DRS-LIP into Mathieu's equation, an approximate analytical solution of the DRS-LIP is obtained, which is reasonably accurate with a low computational cost. Furthermore, to illustrate the practical uses of the analytical results, they are exploited to develop a hierarchical motion planner that efficiently generates physically feasible trajectories for DRS locomotion. Finally, the effectiveness of the proposed theoretical results and motion planner is demonstrated both through PyBullet simulations and experimentally on a Laikago quadrupedal robot that walks on a rocking treadmill. The videos of simulations and hardware experiments are available at https://youtu.be/u2Q_u2pR99c.

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“…The goal is to solve for the minimum 2-norm torques while imposing the virtual constraints and tracking the desired forces, as well as abiding by the feasible torques and friction cone. To this end, the following strictly convex QP is employed [36] min…”

Section: B Virtual Constraints Controllermentioning

confidence: 99%

Toward a Data-Driven Template Model for Quadrupedal Locomotion

Fawcett

Afsari

Ames

et al. 2022

IEEE Robot. Autom. Lett.

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This work investigates a data-driven template model for trajectory planning of dynamic quadrupedal robots. Many state-of-the-art approaches involve using a reduced-order model, primarily due to computational tractability. The spirit of the trajectory planning approach in this work draws on recent advancements in the area of behavioral systems theory. Here, we aim to capitalize on the knowledge of well-known template models to construct a data-driven model, enabling us to obtain an information rich reduced-order model. In particular, this work considers input-output states similar to that of the single rigid body model and proceeds to develop a data-driven representation of the system, which is then used in a predictive control framework to plan a trajectory for quadrupeds. The optimal trajectory is passed to a low-level and nonlinear model-based controller to be tracked. Preliminary experimental results are provided to establish the efficacy of this hierarchical control approach for trotting and walking gaits of a high-dimensional quadrupedal robot on unknown terrains and in the presence of disturbances.

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Robust Stabilization of Periodic Gaits for Quadrupedal Locomotion via QP-Based Virtual Constraint Controllers

Cited by 12 publications

References 31 publications

Robust Predictive Control for Quadrupedal Locomotion: Learning to Close the Gap Between Reduced- and Full-Order Models

Robust Predictive Control for Quadrupedal Locomotion: Learning to Close the Gap Between Reduced- and Full-Order Models

Real-Time Walking Pattern Generation of Quadrupedal Dynamic-Surface Locomotion based on a Linear Time-Varying Pendulum Model

Toward a Data-Driven Template Model for Quadrupedal Locomotion

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