Passive-dynamic walkers are simple mechanical devices, composed of solid parts connected by joints, that walk stably down a slope. They have no motors or controllers, yet can have remarkably humanlike motions. This suggests that these machines are useful models of human locomotion; however, they cannot walk on level ground. Here we present three robots based on passive-dynamics, with small active power sources substituted for gravity, which can walk on level ground. These robots use less control and less energy than other powered robots, yet walk more naturally, further suggesting the importance of passive-dynamics in human locomotion.

https://science.sciencemag.org/content/sci/307/5712/1082.full.pdf

Efficient bipedal robots based on passive-dynamic walkers.

Robust stability and control for systems that combine continuous-time and discrete-time dynamics. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data perturbation, external disturbances, and measurement error distinguishes the approach taken here from other approaches to hybrid systems. While we make some connections to alternative approaches, this article does not aspire to be a survey of the hybrid system literature, which is vast and multifaceted.

Hybrid dynamical systems

Biped robots form a subclass of legged or walking robots. The study of mechanical legged motion has been motivated by its potential use as a means of locomotion in rough terrain, as well as its potential benefits to prothesis development and testing. The paper concentrates on issues related to the automatic control of biped robots. More precisely, its primary goal is to contribute a means to prove asymptotically-stable walking in planar, underactuated biped robot models. Since normal walking can be viewed as a periodic solution of the robot model, the method of Poincare sections is the natural means to study asymptotic stability of a walking cycle. However, due to the complexity of the associated dynamic models, this approach has had limited success. The principal contribution of the present work is to show that the control strategy can be designed in a way that greatly simplifies the application of the method of Poincare to a class of biped models, and, in fact, to reduce the stability assessment problem to the calculation of a continuous map from a subinterval of R to itself. The mapping in question is directly computable from a simulation model. The stability analysis is based on a careful formulation of the robot model as a system with impulse effects and the extension of the method of Poincare sections to this class of models.

/pdf/asymptotically-stable-walking-for-biped-robots-analysis-via-1fe3i0vaa4.pdf

Asymptotically stable walking for biped robots: analysis via systems with impulse effects

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.

/pdf/feedback-control-of-dynamic-bipedal-robot-locomotion-2pz7pbjgsi.pdf

Feedback Control of Dynamic Bipedal Robot Locomotion

Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators. The within-step control action creates an attracting invariant set - a two-dimensional zero dynamics submanifold of the full hybrid model $whose restriction dynamics admits a scalar linear time-invariant return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed-loop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. The general theory developed in the paper is illustrated on a five link walker, consisting of a torso and two legs with knees.

/pdf/hybrid-zero-dynamics-of-planar-biped-walkers-1f08i7dzjl.pdf

Hybrid zero dynamics of planar biped walkers

Describes the design, construction and control of an experimental bipedal robot platform for the study of walking.

/pdf/rabbit-a-testbed-for-advanced-control-theory-5ce0g6ojg5.pdf

RABBIT: a testbed for advanced control theory

The primary goal of this paper is to demonstrate a means to prove asymptotically stable walking in an underactuated, planar, five-link biped robot model. The analysis assumes a rigid contact model when the swing leg impacts the ground and an instantaneous double support phase. The specific robot model analyzed corresponds to a prototype under development by the Centre National de la Recherche Scientifique (CNRS), Paris, France. A secondary goal of the paper is to establish the viability of the theoretically motivated control law. This is explored in a number of ways. First, it is shown how known time trajectories, such as those determined on the basis of walking with minimal energy consumption, can be incorporated into the proposed controller structure. Secondly, various perturbations to the walking motion are introduced to verify disturbance rejection capability. Finally, the controller is demonstrated on a detailed simulator for the prototype which includes torque limits and a compliant model of the walking surface, and thus a noninstantaneous double support phase.

Stable walking of a 7-DOF biped robot

The objective is to control a web transport system with winder and unwinder for elastic material. A physical modeling of this plant is made based on the general laws of physics. For this type of control problem, it is extremely important to prevent the occurrence of web break or fold by decoupling the web tension and the web velocity. Due to the wide-range variation of the radius and inertia of the rollers the system dynamics change considerably during the winding/unwinding process. Different strategies for web tension control and linear transport velocity control are presented. First, an H/sub /spl infin// robust control strategy which reduces the coupling between tension and velocity, is compared to the decentralized control strategy with proportional integral derivative (PID) controllers commonly used in the industry. Second, an H/sub /spl infin// robust control strategy with varying gains is shown to render the control more robust to the radius variations. Then, a linear parameter varying (LPV) control strategy with smooth scheduling of controllers is synthesized for different operating points and compared to the previous methods. Finally, this LPV control and the H/sub /spl infin// robust control strategy with varying gains are combined to give the best results on an experimental setup, for the rejection of the disturbances introduced by velocity variations and for the robustness to radius and inertia changes.

Modeling and robust control of winding systems for elastic webs

Chapter 1. Bipedal Robots and Walking. 1.1. Introduction. 1.2. Biomechanical approach. 1.3. Human walking. 1.4. Bipedal walking robots: state of the art. 1.5. Different applications. 1.6. Conclusion. 1.7. Bibliography. Chapter 2. Kinematic and Dynamic Models for Walking. 2.1. Introduction. 2.2. The kinematics of walking. 2.3. The dynamics of walking. 2.4. Dynamic constraints. 2.5. Complementary feasibility constraints. 2.6. Conclusion. 2.7. Bibliography. Chapter 3. Design Tools for Making Bipedal Robots. 3.1. Introduction. 3.2. Study of influence of robot body masses. 3.3. Mechanical design: the architectures carried out. 3.4. Actuators. 3.5. Sensors. 3.6. Conclusion. 3.7. Appendix. 3.8. Bibliography. Chapter 4. Walking Pattern Generators. 4.1. Introduction. 4.2. Passive and quasi-passive dynamic walking. 4.3. Static balance walking. 4.4. Dynamic synthesis of walking. 4.5. Walking synthesis via parametric optimization. 4.6. Conclusion. 4.7. Bibliography. Chapter 5. Control 5.1. Introduction. 5.2. Hybrid systems and stability study. 5.3. Taking into account the unilateralism of the contact constraint. 5.4. Online modification of references. 5.5. Taking an under-actuated phase into account. 5.6. Taking the double support phase into account. 5.7. Intuitive and neural network methods. 5.8. Passive movements. 5.9. Conclusion. 5.10. Bibliography. Index.

G. Abba

Papers

Asymptotically stable walking for biped robots: analysis via systems with impulse effects

RABBIT: a testbed for advanced control theory

Stable walking of a 7-DOF biped robot

Modeling and robust control of winding systems for elastic webs

Bipedal Robots : Modeling, Design and Walking Synthesis