An optimization approach to rough terrain locomotion

Zucker, Matt; Bagnell, J. Andrew; Atkeson, Christopher G.; Kuffner, James

doi:10.1109/robot.2010.5509176

Cited by 69 publications

(53 citation statements)

References 14 publications

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“…Indeed, it is important to note that while we have made a minimal usage of modelbased techniques in the applications that we have presented, more complex task could be performed through the combination of motor primitives and model-based approach dealing with multiple constraints, as for instance whole-body control approaches such as in Sentis and Khatib (2005) or in the case of locomotion, such as Zico Kolter and Ng (2009), Kalakrishnan et al (2010) or Zucker et al (2010) . Since our framework simply generates desired policies, it could be easily integrated with modern torque control techniques, in a similar way that Zico Kolter and Ng (2009) and Zucker et al (2010) used splines. The main advantage of using differential equations over splines is that external signals can be embedded into the dynamics (e.g.…”

Section: Discussionmentioning

confidence: 99%

Toward simple control for complex, autonomous robotic applications: combining discrete and rhythmic motor primitives

2011

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Vertebrates are able to quickly adapt to new environments in a very robust, seemingly effortless way. To explain both this adaptivity and robustness, a very promising perspective in neurosciences is the modular approach to movement generation: Movements results from combinations of a finite set of stable motor primitives organized at the spinal level. In this article we apply this concept of modular generation of movements to the control of robots with a high number of degrees of freedom, an issue that is challenging notably because planning complex, multidimensional trajectories in time-varying environments is a laborious and costly process. We thus propose to decrease the complexity of the planning phase through the use of a combination of discrete and rhythmic motor primitives, leading to the decoupling of the planning phase (i.e. the choice of behavior) and the actual trajectory generation. Such implementation eases the control of, and the switch between, different behaviors by reducing the dimensionality of the high-level commands. Moreover, since the motor primitives are generated by dynamical systems, the trajectories can be smoothly modulated, either by high-level commands to change the current behavior or by sensory feedback information to adapt to environmental constraints. In order to show the generality of our approach, we apply the framework to interactive drumming and infant crawling in a humanoid robot. These experiments illustrate the simplicity of the control architecture in terms of planning, the integration of different types * This work was supported by the European Commission's Cognition Unit, projects RobotCub and AMARSi. S.G. is funded by a IST-EPFL grant.of feedback (vision and contact) and the capacity of autonomously switching between different behaviors (crawling and simple reaching).

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Section: Discussionmentioning

confidence: 99%

Toward simple control for complex, autonomous robotic applications: combining discrete and rhythmic motor primitives

2011

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“…In [18], the authors explore the design of pasitivity-based controllers to achieve walking on different ground slopes. Optimization-based techniques for locomotion in rough terrains are presented in [19]. Locomotion in very rough terrain is presented in [20], where the authors exploit optimization and static models as a means to plan locomotion.…”

Section: State Of the Artmentioning

confidence: 99%

“…(18) we find an expression of the perturbation in terms of the velocities and acceleration, ≈ (ẋ k+1 −ẋ k )/ẍ k , and substituting in Eq. (19), withẍ k = f (x k ), we get…”

Section: State-space Behavior Prediction From Perturbation Theorymentioning

confidence: 99%

Perturbation theory to plan dynamic locomotion in very rough terrains

Sentis¹,

Fernández²

2011

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-Although the problem of dynamic locomotion in very rough terrain is critical to the advancement of various areas in robotics and health devices, little progress has been made on generalizing gait behavior with arbitrary paths. Here, we report that perturbation theory, a set of approximation schemes that has roots in celestial mechanics and nonlinear dynamical systems, can be adapted to predict the behavior of nonintegrable state-space trajectories of a robot's center of mass, given its arbitrary contact state and center of mass (CoM) kinematic path. Given an arbitrary kinematic path of the CoM and known step locations, we use perturbation theory to determine phase curves of CoM behavior. We determine step transitions as the points of intersection between adjacent phase curves. To discover intersection points, we fit polynomials to the phase curves of neighboring steps and solve their differential roots. The resulting multi-step phase diagram is the locomotion plan suited to drive the behavior of a robot or device maneuvering in the rough terrain. We provide two main contributions to legged locomotion: (1) predicting CoM state-space behavior for arbitrary paths by means of perturbation theory, and (2) finding step transitions by locating common intersection points between neighboring phase curves. Because these points are continuous in phase they correspond to the desired contact switching policy. We validate our results on a human-size avatar navigating in a very rough environment and compare its behavior to a human subject maneuvering through the same terrain. I. STATE OF THE ARTIn dynamic walking we can classify techniques in various categories: (1) trajectory-based techniques, (2) limit cycle-based techniques, (3) prediction of contact, and (4) hybrids of the previous three.Trajectory-based techniques are techniques that track a timebased joint or task space trajectory according to some locomotion model such as the Zero Moment Point (ZMP). The state of the art of these methods includes generalized multi-contact locomotion behaviors, developed in [1] and more recenlty, a time delay extension to the ZMP method for locomotin in moderately uneven terrain, developed by [2].Prediction of contact placement are techniques that use dynamics to estimate suitable contact transitions to produce locomotion or regain balance. In [3], simple dynamic models are used to predict the placement of next contacts to achieve desire gait patterns. Finding feasible CoM static placements given frictional constraints was tackled in [4], [5]. In [6], stable locomotion, in the wide sense of not falling down, is studied by providing velocity based stability margins. This work is used to regain stability when the robot's is pushed out, and lead to the concept of Capture Point.Limit cycle based techniques were pioneered by McGeer [7] through the field of passive dynamic walking. In [8] the authors study orbital stability, and the effect of feedback control to achieve asymptotic stability. Optimization of open-loop stability is in...

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“…In order to realize this vision, robots must be able to (1) accurately predict the actions of humans in their environment, (2) quickly learn the preferences of human agents in their proximity and act accordingly, and (3) learn how to accomplish new tasks from human demonstrations. Inverse Reinforcement Learning (IRL) [41,32,2,29,38,50,16] is a powerful and flexible framework for tackling these challenges and has been previously used for tasks such as modeling and mimicking human driver behavior [1,28,43], pedestrian trajectory prediction [51,31], and legged robot locomotion [52,27,35]. The underlying assumption behind IRL is that humans act optimally with respect to an (unknown) cost function.…”

Section: Introductionmentioning

confidence: 99%

Risk-sensitive Inverse Reinforcement Learning via Coherent Risk Models

Majumdar¹,

Singh²,

Mandlekar³

et al. 2017

Robotics: Science and Systems XIII

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Abstract-The literature on Inverse Reinforcement Learning (IRL) typically assumes that humans take actions in order to minimize the expected value of a cost function, i.e., that humans are risk neutral. Yet, in practice, humans are often far from being risk neutral. To fill this gap, the objective of this paper is to devise a framework for risk-sensitive IRL in order to explicitly account for an expert's risk sensitivity. To this end, we propose a flexible class of models based on coherent risk metrics, which allow us to capture an entire spectrum of risk preferences from risk-neutral to worst-case. We propose efficient algorithms based on Linear Programming for inferring an expert's underlying risk metric and cost function for a rich class of static and dynamic decision-making settings. The resulting approach is demonstrated on a simulated driving game with ten human participants. Our method is able to infer and mimic a wide range of qualitatively different driving styles from highly risk-averse to risk-neutral in a data-efficient manner. Moreover, comparisons of the RiskSensitive (RS) IRL approach with a risk-neutral model show that the RS-IRL framework more accurately captures observed participant behavior both qualitatively and quantitatively.

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An optimization approach to rough terrain locomotion

Cited by 69 publications

References 14 publications

Toward simple control for complex, autonomous robotic applications: combining discrete and rhythmic motor primitives

Toward simple control for complex, autonomous robotic applications: combining discrete and rhythmic motor primitives

Perturbation theory to plan dynamic locomotion in very rough terrains

Risk-sensitive Inverse Reinforcement Learning via Coherent Risk Models

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