Philippe Sardain

Bio: Philippe Sardain is an academic researcher from University of Poitiers. The author has contributed to research in topics: Optimization problem & Robot. The author has an hindex of 15, co-authored 29 publications receiving 1198 citations. Previous affiliations of Philippe Sardain include Centre national de la recherche scientifique.

Forces acting on a biped robot. Center of pressure-zero moment point

Abstract: In the area of biped robot research, much progress has been made in the past few years. However, some difficulties remain to be dealt with, particularly about the implementation of fast and dynamic walking gaits, in other words anthropomorphic gaits, especially on uneven terrain. In this perspective, both concepts of center of pressure (CoP) and zero moment point (ZMP) are obviously useful. In this paper, the two concepts are strictly defined, the CoP with respect to ground-feet contact forces, the ZMP with respect to gravity plus inertia forces. Then, the coincidence of CoP and ZMP is proven, and related control aspects are examined. Finally, a virtual CoP-ZMP is defined, allowing us to extend the concept when walking on uneven terrain. This paper is a theoretical study. Experimental results are presented in a companion paper, analyzing the evolution of the ground contact forces obtained from a human walker wearing robot feet as shoes.

A Parametric Optimization Approach to Walking Pattern Synthesis

Abstract: Walking pattern synthesis is carried out using a spline-based parametric optimization technique. Generalized coordinates are approximated by spline functions of class C3fitted at knots uniformly distributed along the motion time. This high-order differentiability eliminates jerky variations of actuating torques. Through connecting conditions, spline polynomial coefficients are determined as a linear function of the joint coordinates at knots. These values are then dealt with as optimization parameters. An optimal control problem is formulated on the basis of a performance criterion to be minimized, representing an integral quadratic amount of driving torques. Using the above spline approximations, this primary problem is recast into a constrained non-linear optimization problem of mathematical programming, which is solved using a computing code implementing an SQP algorithm. As numerical simulations, complete gait cycles are generated for a seven-link planar biped. The only kinematic data to be accounted for are the walking speeds. Optimization of both phases of gait is carried out globally; it includes the optimization of transition configurations of the biped between successive phases of the gait cycle.

An anthropomorphic biped robot: dynamic concepts and technological design

Abstract: The authors of this study are a part of a joint project, involving four French laboratories, whose goal is the design and construction of a mechanical biped robot with anthropomorphic characteristics. In the first section of this paper, we will examine mechanical architectures of some representatives of state-of-the art biped robots by focusing on their kinematic arrangement. It is widely known that the existence of natural gaits is closely linked to the intrinsic dynamic characteristics of the mechanical structure of the biped robot. In order to further develop this idea, two studies will be presented in the second section: the first is relative to the lateral instability of the system while the second deals with the existence of passive pendular gaits during the swing phase of walking in the sagittal plane. In the last section, in correlation with the observations made, we will gain insight into main characteristics of the mechanical architecture that we have designed for the BIP project: 15 active degrees of freedom (DOF), joints actuated by special transmission system, anthropometric mass distribution.

Optimal Gait Synthesis of a Seven-Link Planar Biped:

Abstract: In this paper, we carry out the dynamics-based optimization of sagittal gait cycles of a planar seven-link biped using the Pontryagin maximum principle. Special attention is devoted to the double-support phase of the gait, during which the movement is subjected to severe limiting conditions. In particular, due to the fact that the biped moves as a closed kinematic chain, overactuation must be compatible with double, non-sliding unilateral contacts with the supporting ground. The closed chain is considered as open at front foot level. A full set of joint coordinates is introduced to formulate a complete Hamiltonian dynamic model of the biped. Contact forces at the front foot are considered as additional control variables of the stated optimal control problem. This is restated as a state-unconstrained optimization problem which is finally recast, using the Pontryagin maximum principle, as a two-point boundary value problem. This final problem is solved using a standard computing code. A gait sequence, compr...

Feedback Control of Dynamic Bipedal Robot Locomotion

Abstract: 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.

Hybrid zero dynamics of planar biped walkers

Abstract: 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.

RABBIT: a testbed for advanced control theory

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

Forces acting on a biped robot. Center of pressure-zero moment point

Abstract: In the area of biped robot research, much progress has been made in the past few years. However, some difficulties remain to be dealt with, particularly about the implementation of fast and dynamic walking gaits, in other words anthropomorphic gaits, especially on uneven terrain. In this perspective, both concepts of center of pressure (CoP) and zero moment point (ZMP) are obviously useful. In this paper, the two concepts are strictly defined, the CoP with respect to ground-feet contact forces, the ZMP with respect to gravity plus inertia forces. Then, the coincidence of CoP and ZMP is proven, and related control aspects are examined. Finally, a virtual CoP-ZMP is defined, allowing us to extend the concept when walking on uneven terrain. This paper is a theoretical study. Experimental results are presented in a companion paper, analyzing the evolution of the ground contact forces obtained from a human walker wearing robot feet as shoes.

Morphological Muscle and joint parameters for musculoskeletal modelling of the lower extremity

Abstract: Background: To assist in the treatment of gait disorders, an inverse and forward 3D musculoskeletal model of the lower extremity will be useful that allows to evaluate if–then scenarios. Currently available anatomical datasets do not comprise sufficiently accurate and complete information to construct such a model. The aim of this paper is to present a complete and consistent anatomical dataset, containing the orientations of joints (hip, knee, ankle and subtalar joints), muscle parameters (optimum length, physiological cross sectional area), and geometrical parameters (attachment sites, ‘via’ points). Methods: One lower extremity, taken from a male embalmed specimen, was studied. Position and geometry were measured with a 3D-digitizer. Optotrak was used for measurement of rotation axes of joints. Sarcomere length was measured by laser diffraction. Findings: A total of 38 muscles were measured. Each muscle was divided in different muscle lines of action based on muscle morphology. 14 Ligaments of the hip, knee and ankle were included. Interpretation: The presented anatomical dataset embraces all necessary data for state of the art musculoskeletal modelling of the lower extremity. Implementation of these data into an (existing) model is likely to significantly improve the estimation of muscle forces and will thus make the use of the model as a clinical tool more feasible.