Bipedal locomotion is among the most difficult challenges in control engineering. Most books treat the subject from a quasi-static perspective, overlooking the hybrid nature of bipedal mechanics. Feedback Control of Dynamic Bipedal Robot Locomotion is the first book to present a comprehensive and mathematically sound treatment of feedback design for achieving stable, agile, and efficient locomotion in bipedal robots.In this unique and groundbreaking treatise, expert authors lead you systematically through every step of the process, including:Mathematical modeling of walking and running gaits in planar robotsAnalysis of periodic orbits in hybrid systemsDesign and analysis of feedback systems for achieving stable periodic motionsAlgorithms for synthesizing feedback controllersDetailed simulation examplesExperimental implementations on two bipedal test bedsThe elegance of the authors' approach is evident in the marriage of control theory and mechanics, uniting control-based presentation and mathematical custom with a mechanics-based approach to the problem and computational rendering. Concrete examples and numerous illustrations complement and clarify the mathematical discussion. A supporting Web site offers links to videos of several experiments along with MATLAB® code for several of the models. This one-of-a-kind book builds a solid understanding of the theoretical and practical aspects of truly dynamic locomotion in planar bipedal robots.

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Feedback Control of Dynamic Bipedal Robot Locomotion

The authors have built the first three-dimensional, kneed, two-legged, passive-dynamic walking machine. Since the work of Tad McGeer in the late 1980s, the concept of passive dynamics has added insight into animal locomotion and the design of anthropomorphic robots. Various analyses and machines that demonstrate efficient human-like walking have been developed using this strategy. Human-like passive machines, however, have only operated in two dimensions (i.e., within the fore-aft or sagittal plane). Three-dimensional passive walking devices, mostly toys, have not had human-like motions but instead a stiff legged waddle. In the present three-dimensional device, the authors preserve features of McGeer’s two-dimensional models, including mechanical simplicity, human-like knee flexure, and passive gravitational power from descending a shallow slope. They then add specially curved feet, a compliant heel, and mechanically constrained arms to achieve a harmonious and stable gait. The device stands 85 cm tall. I...

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A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees

Power electronics is a discipline spawned by real-life applications in industrial, commercial, residential, and aerospace environments. Much of its development revolves around some immediate need for solving specific power conversion problems. This comprehensive book focuses on the typical bifurcation scenarios and nonlinear behavior observed in switching power converters, expounding on their most relevant aspects from a practical viewpoint. A balanced emphasis on theory, computer methods, and laboratory experiments bridges the gap between the theoretical research and practical engineering applications.

Complex Behavior of Switching Power Converters

We give an overview of all codim 1 bifurcations in generic planar discontinuous piecewise smooth autonomous systems, here called Filippov systems. Bifurcations are defined using the classical approach of topological equivalence. This allows the development of a simple geometric criterion for classifying sliding bifurcations, i.e. bifurcations in which some sliding on the discontinuity boundary is critically involved. The full catalog of local and global bifurcations is given, together with explicit topological normal forms for the local ones. Moreover, for each bifurcation, a defining system is proposed that can be used to numerically compute the corresponding bifurcation curve with standard continuation techniques. A problem of exploitation of a predator–prey community is analyzed with the proposed methods.

https://www.staff.science.uu.nl/~kouzn101/MiniFilippov/Filippov2D.pdf

One-Parameter Bifurcations in Planar Filippov Systems

Power electronics circuits are rich in nonlinear dynamics. Their operation is characterized by cyclic switching of circuit topologies, which gives rise to a variety of nonlinear behavior. This paper provides an overview of the chaotic dynamics and bifurcation scenarios observed in power converter circuits, emphasizing the salient features of the circuit operation and the modeling strategies. In particular this paper surveys the key publications in this field, reviews the main modeling approaches, and discusses the salient bifurcation behaviors of power converters with particular emphasis on the disruption of standard bifurcation patterns by border collisions.

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Complex behavior in switching power converters

https://hal.archives-ouvertes.fr/hal-02546986/document

Non-periodic motion caused by grazing incidence in an impact oscillator

A review is presented of the one-parameter, nonsmooth bifurcations that occur in a variety of continuous-time piecewise-smooth dynamical systems. Motivated by applications, a pragmatic approach is taken to defining a discontinuity-induced bifurcation (DIB) as a nontrivial interaction of a limit set with respect to a codimension-one discontinuity boundary in phase space. Only DIBs that are local are considered, that is, bifurcations involving equilibria or a single point of boundary interaction along a limit cycle for flows. Three classes of systems are considered, involving either state jumps, jumps in the vector field, or jumps in some derivative of the vector field. A rich array of dynamics are revealed, involving the sudden creation or disappearance of attractors, jumps to chaos, bifurcation diagrams with sharp corners, and cascades of period adding. For each kind of bifurcation identified, where possible, a kind of “normal form” or discontinuity mapping (DM) is given, together with a canonical example and an application. The goal is always to explain dynamics that may be observed in simulations of systems which include friction oscillators, impact oscillators, DC-DC converters, and problems in control theory.

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Bifurcations in Nonsmooth Dynamical Systems

/pdf/bifurcations-of-dynamical-systems-with-sliding-derivation-of-1kc21b4r2l.pdf

Bifurcations of dynamical systems with sliding: derivation of normal-form mappings

On the origin and bifurcations of stick-slip oscillations

Grazing bifurcations are nonsmooth bifurcations that occur in impacting mechanical oscillators. A sign of the lack of smoothness is a square root expression that arises in mappings describing the dynamics. Certain types of grazing bifurcations involve chaotic bands, or period adding cascades with or without chaotic bands. There is also a characteristic scaling behavior present. Here this type of bifurcation is investigated, and the self-similarity under scaling is used to derive a renormalized limit mapping. A study of the dynamics of the limit mapping identifying all attractors for all parameter values is also presented.

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Arne Nordmark

Papers

Non-periodic motion caused by grazing incidence in an impact oscillator

Bifurcations in Nonsmooth Dynamical Systems

Bifurcations of dynamical systems with sliding: derivation of normal-form mappings

On the origin and bifurcations of stick-slip oscillations

Universal limit mapping in grazing bifurcations