Three-Dimensional Kneed Bipedal Walking: A Hybrid Geometric Approach

Ames, Aaron D.; Sinnet, Ryan W.; Wendel, Eric

doi:10.1007/978-3-642-00602-9_2

Cited by 31 publications

(36 citation statements)

References 14 publications

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“…Our second application to periodic systems is a controlled planar biped with locking knees walking on flat ground, as studied in [30]. It may be considered the augmentation of the planar compass biped with an additional domain where the stance leg is locked and the non-stance leg is unlocked at the knee.…”

Section: Planar Kneed Bipedmentioning

confidence: 99%

Rank deficiency and superstability of hybrid systems

Wendel

Ames

2012

Nonlinear Analysis: Hybrid Systems

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Section: Planar Kneed Bipedmentioning

confidence: 99%

Rank deficiency and superstability of hybrid systems

Wendel

Ames

2012

Nonlinear Analysis: Hybrid Systems

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“…Furthermore, hypothesis H5 for a symmetric periodic orbit O immediately implies that z * L = S z z * R and z * R = S z z * L . 7 We remark thatSS = I 26×26 .…”

Section: Time-invariant One-step Event-based Controllermentioning

confidence: 99%

Event-Based Stabilization of Periodic Orbits for Underactuated 3-D Bipedal Robots With Left-Right Symmetry

Hamed

Grizzle

2014

IEEE Trans. Robot.

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Abstract-Models of robotic bipedal walking are hybrid, with a differential equation describing the stance phase and a discrete map describing the impact event, that is, the non-stance leg contacting the walking surface. The feedback controllers for these systems can be hybrid as well, including both continuous and discrete (event-based) actions. This paper concentrates on the eventbased portion of the feedback design problem for 3D bipedal walking. The results are developed in the context of robustly stabilizing periodic orbits for a simulation model of ATRIAS 2.1, a highly underactuated 3D bipedal robot with series-compliant actuators and point feet, against external disturbances as well as parametric and nonparametric uncertainty. It is shown that leftright symmetry of the model can be used to both simplify and improve the design of event-based controllers. Here, the eventbased control is developed on the basis of the Poincaré map, linear matrix inequalities (LMIs), and robust optimal control (ROC). The results are illustrated by designing a controller that enhances the lateral stability of ATRIAS 2.1.

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“…In certain cases, they are used to capture the interaction between discrete and analog components of the physical system, for example the use of switching elements in the control of electrical and mechanical systems (Aimer et al, 2007). In other cases, they are used to capture sharp changes in the continuous behavior of a dynamical system, for example the operation modes of an automotive engine (Balluchi et al, 2000), or the phases of bipedal walking (Ames et al, 2009). Finally, perhaps most relevant for our discussions, they have been used as a mathematical formalism to integrate discrete and continuous abstractions in a hierarchical control architecture (Gollu and Varaiya, 1989;Lygeros, 1996;Caines and Wei, 1998;Alur et al, 2001).…”

Section: High-confidence Controller Design As Hybrid Reachability Promentioning

confidence: 99%

“…elastic impacts). Examples of such systems range from automotive engines (Balluchi et al, 2000), power electronics (Aimer et al, 2007), to bipedal walkers (Ames et al, 2009). However, the consideration of autonomous switching for continuous time systems is also accompanied by a significant increase in the difficulty of analyzing system properties.…”

Section: Accounting For Autonomous Switches In Deterministic Continuomentioning

confidence: 99%

Methods for Reachability-based Hybrid Controller Design

Ding¹

2012

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With the increasing complexity of systems found in practical applications, the problem of controller design is often approached in a hierarchical fashion, with discrete abstractions and design methods used to satisfy high level task specifications, and continuous abstractions and design techniques used to satisfy low level control objectives. Although such a separation allows the application of mature theoretical and computational tools from the realms of computer science and control theory, the task of ensuring desired closed-loop behaviors, which results from the composition between discrete and continuous designs, often requires costly and time consuming verification and validation. This problem becomes especially acute in safety-critical applications, in which design specifications are often subject to rigorous industry standards and government regulations. Hybrid systems, which feature state trajectories evolving on a combination of discrete and continuous state spaces, have been proposed as a possible approach to reconcile the analysis and design techniques from the discrete and continuous domains under a rigorous theoretical framework. However, designing controllers for general classes of hybrid systems is a highly nontrivial task, as such a design problem inherits both the difficulty of nonlinear control, as well as the range of theoretical and computational issues introduced by the consideration of discrete switching.This dissertation describes several efforts aimed towards the development of theoretical analysis tools and computational synthesis techniques to facilitate the systematic design of feedback control policies satisfying safety and target attainability specifications with respect to subclasses of hybrid system models. The main types of problems we consider are safety/invariance problems, which involve keeping the closed-loop state trajectory within a safe set in the hybrid state space, and reach-avoid problems, which involve driving the state trajectory into a target set subject to a safety constraint. These problems are addressed within the context of continuous time switched nonlinear systems and discrete time stochastic hybrid systems, as motivated by application scenarios arising in autonomous vehicle control and air traffic management.First, we provide several design techniques and synthesis algorithms for deterministic reachability problems formulated in the setting of switched nonlinear systems, with controlled switches between discrete modes, and bounded continuous disturbances. For scenarios in which the mode transitions proceed in a known sequence, a method is discussed for designing controllers to satisfy 1 sequential reachability specifications, consisting of a temporally ordered sequence of invariance and reach-avoid objectives. In particular, we use continuous time reachable sets to inform choices of feedback control policies within each discrete mode to satisfy both individual reachability objectives and compatibility conditions between successive modes. This technique is illus...

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Three-Dimensional Kneed Bipedal Walking: A Hybrid Geometric Approach

Cited by 31 publications

References 14 publications

Rank deficiency and superstability of hybrid systems

Rank deficiency and superstability of hybrid systems

Event-Based Stabilization of Periodic Orbits for Underactuated 3-D Bipedal Robots With Left-Right Symmetry

Methods for Reachability-based Hybrid Controller Design

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