Learning to jump in granular media: Unifying optimal control synthesis with Gaussian process-based regression

Chang, Alexander H.; Hubicki, Christian; Aguilar, Jeff J.; Goldman, Daniel I.; Ames, Aaron D.; Vela, Patricio A.

doi:10.1109/icra.2017.7989248

Cited by 15 publications

(16 citation statements)

References 26 publications

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“…Most of the aforementioned works lack a general approach that can deal with multiple terrain compliances or with transitions between them. Perhaps, one noticeable work (to date) in online soft terrain adaptation was proposed by Chang et al [14]. In that work, an iterative soft terrain adaptation approach was proposed.…”

Section: A Related Work -Soft Terrain Adaptation For Legged Robotsmentioning

confidence: 99%

“…Compared to previous work on soft terrain adaptation [10], STANCE can adapt to soft terrain online and was tested on multiple terrains with different compliances and with transitions between them. Compared to [14], our TCE is computationally inexpensive, which allows STANCE to run real-time in experiments and simulations. Compared to the previous work done on compliance estimation, we implemented our TCE on a legged robot which is, to the best of our knowledge, the first experimental validation of this approach.…”

Section: Proposed Approach and Contributionmentioning

confidence: 99%

“…7) Torque and Joint Limits: The torque and joint limits are enforced in the inequality constraints (14) and (15), respectively.…”

Section: ) Stance Taskmentioning

confidence: 99%

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STANCE: Locomotion Adaptation Over Soft Terrain

et al. 2020

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Whole-Body Control (WBC) has emerged as an important framework in locomotion control for legged robots. However, most WBC frameworks fail to generalize beyond rigid terrains. Legged locomotion over soft terrain is difficult due to the presence of unmodeled contact dynamics that WBCs do not account for. This introduces uncertainty in locomotion and affects the stability and performance of the system. In this paper, we propose a novel soft terrain adaptation algorithm called STANCE: Soft Terrain Adaptation and Compliance Estimation. STANCE consists of a WBC that exploits the knowledge of the terrain to generate an optimal solution that is contact consistent and an online terrain compliance estimator that provides the WBC with terrain knowledge. We validated STANCE both in simulation and experiment on the Hydraulically actuated Quadruped (HyQ) robot, and we compared it against the state of the art WBC. We demonstrated the capabilities of STANCE with multiple terrains of different compliances, aggressive maneuvers, different forward velocities, and external disturbances. STANCE allowed HyQ to adapt online to terrains with different compliances (rigid and soft) without pre-tuning. HyQ was able to successfully deal with the transition between different terrains and showed the ability to differentiate between compliances under each foot.

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Section: A Related Work -Soft Terrain Adaptation For Legged Robotsmentioning

confidence: 99%

Section: Proposed Approach and Contributionmentioning

confidence: 99%

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STANCE: Locomotion Adaptation Over Soft Terrain

et al. 2020

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“…GPs applied to learn substrate forcing, in the context of jumping on a particular simulated GM model, previously suggested that online learning would occur rapidly [35]. As opposed to learning the dynamics of the entire system from scratch, online learning targeted the unknown external forcing component.…”

Section: A Review Of Related Work 1) Locomotion On Soft Terrainmentioning

confidence: 99%

Learning Terrain Dynamics: A Gaussian Process Modeling and Optimal Control Adaptation Framework Applied to Robotic Jumping

Chang

Hubicki

Aguilar

et al. 2021

IEEE Trans. Contr. Syst. Technol.

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The complex dynamics characterizing deformable terrain presents significant impediments toward the real-world viability of locomotive robotics, particularly for legged machines. We explore vertical, robotic jumping as a model task for legged locomotion on presumed-uncharacterized, nonrigid terrain. By integrating Gaussian process (GP)-based regression and evaluation to estimate ground reaction forces as a function of the state, a 1-D jumper acquires the capability to learn forcing profiles exerted by its environment in tandem with achieving its control objective. The GP-based dynamical model initially assumes a baseline rigid, noncompliant surface. As part of an iterative procedure, the optimizer employing this model generates an optimal control strategy to achieve a target jump height. Experiential data recovered from execution on the true surface model are applied to train the GP, in turn, providing the optimizer a more richly informed dynamical model of the environment. The iterative control-learning procedure was rigorously evaluated in experiment, over different surface types, whereby a robotic hopper was challenged to jump to several different target heights. Each task was achieved within ten attempts, over which the terrain's dynamics were learned. With each iteration, GP predictions of ground forcing became incrementally refined, rapidly matching experimental force measurements. The few-iteration convergence demonstrates a fundamental capacity to both estimate and adapt to unknown terrain dynamics in application-realistic time scales, all with control tools amenable to robotic legged locomotion.

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“…In general, bulk-behavior models of the plastic flows of granular media are accurate when the size of the intruder far exceeds the size of the grains [11], and the results scale well with different sizes and masses of intruders [12]. Bulk-behavior models can now predict the terrain response with sufficient accuracy to allow optimal control methods to generate robot motion trajectories that result in jumps to a desired height [13], [14]. Although powerful, results using optimal control have limited applicability to robot locomotion on real deserts, as they assume granular media preparations that are homogeneous within and between steps -an assumption which cannot be made for locomotion in real deserts with unknown ground properties [5], [3], [2] -and experiments in the laboratory are not much affected by the dissipation of electrical energy to heat, which is a very real concern for a robot running long distances in a desert.…”

Section: B Previous Research Has Produced Bulk-behavior Models With mentioning

confidence: 99%

Reactive velocity control reduces energetic cost of jumping with a virtual leg spring on simulated granular media

Roberts

Koditschek²

2018

2018 IEEE International Conference on Robotics and Biomimetics (ROBIO)

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Robots capable of dynamic locomotion behaviors and high-bandwidth sensing with their limbs have a high cost of transport, especially when locomoting over highly dissipative substrates such as sand. We formulate the problem of reducing the energetic cost of locomotion by a Minitaur robot on sand, reacting to robot state variables in the inertial world frame without modeling the ground online. Using a bulkbehavior model of high-velocity intrusions into dry granular media, we simulated single jumps by a onelegged hopper using a Raibert-style compression-extension virtual leg spring. We compose this controller with a controller that added damping to the leg spring in proportion to the intrusion velocity of the robot's foot into the simulated sand while the robot is pushing off in the second half of stance. This has the effect of both reducing the torque exerted by the motors because the added virtual "active damping" force acts in opposition to the virtual leg spring force, and reducing the transfer of energy from the robot to the sand by slowing the intrusion velocity of the foot. Varying the simulated robot's initial conditions and the simulated ground parameters, we gained a consistent 20% energy savings by adding active damping with no cost in apex height. For more information, see the Kod*lab website: kodlab.seas.upenn.edu

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Learning to jump in granular media: Unifying optimal control synthesis with Gaussian process-based regression

Cited by 15 publications

References 26 publications

STANCE: Locomotion Adaptation Over Soft Terrain

STANCE: Locomotion Adaptation Over Soft Terrain

Learning Terrain Dynamics: A Gaussian Process Modeling and Optimal Control Adaptation Framework Applied to Robotic Jumping

Reactive velocity control reduces energetic cost of jumping with a virtual leg spring on simulated granular media

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