Philippe Sardain

An anthropomorphic biped robot: dynamic concepts and technological design

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.

A Parametric Optimization Approach to Walking Pattern Synthesis

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.

Optimal Gait Synthesis of a Seven-Link Planar Biped:

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, comprising starting, cyclic, and stopping steps, is generated in the form of a numerical simulation.

Foot contact event detection using kinematic data in cerebral palsy children and normal adults gait

Initial contact (IC) and toe off (TO) times are essential measurements in the analysis of temporal gait parameters, especially in cerebral palsy (CP) gait analysis. A new gait event detection algorithm, called the high pass algorithm (HPA) has been developed and is discussed in this paper. Kinematics of markers on the heel and metatarsal are used. Their forward components are high pass filtered, to amplify the contact discontinuities, thus the local extrema of the processed signal correspond to IC and TO. The accuracy and precision of HPA are compared with the gold standard of foot contact event detection, that is, force plate measurements. Furthermore HPA is compared with two other kinematics methods. This study has been conducted on 20 CP children and on eight normal adults. For normal subjects all the methods performed equally well. True errors in HPA (mean+/-standard deviation) were found to be 1+/-23 ms for IC and 2+/-25 ms for TO in CP children. These results were significantly (p<0.05) more accurate and precise than those obtained using the other algorithms. Moreover, in the case of pathological gaits, the other methods are not suitable for IC detection when IC is flatfoot or forefoot. In conclusion, the HPA is a simple and robust algorithm, which performs equally well for adults and actually performs better when applied to the gait of CP children. It is therefore recommended as the method of choice.

Gait analysis of a human walker wearing robot feet as shoes

This work takes part in the project of development of an anthropomorphic biped robot, Bip. The technological construction has been completed and the robot has performed some slow static walks. The next stage is the implementation of fast and dynamic walking gaits, in other words anthropomorphic gaits. The robot feet have been designed with a three-axes force-moment sensor for reconstructing the center of pressure-zero moment point. To study and test these feet, the idea is simple: the experimental setup consists of a human walker wearing the Bip feet as shoes, a force-plate and a motion analysis system. The purpose is double. The first one is aimed at comparing the contact pressure forces reconstructed with the Bip sensor feet, with the data recorded by the force-plate. The second one consists in determining the influence of (relatively) heavy and rigid metallic shoes on the gait of a human walker. If these feet were proving to be a handicap for efficient and elegant human walking gaits, how could it be any different for the robot Bip? Fortunately the analysis shows that they do not really handicap the walker.

Parametric-based dynamic synthesis of 3d-gait

This paper describes a dynamic synthesis method for generating optimal walking patterns of biped robots having a human-like locomotion system. The generating principle of gait is based on the minimisation of driving torques. A parametric optimisation technique is used to solve the underlying optimal control problem. Special attention is devoted to foot-ground interactions in order to ensure a steady dynamic balance of the biped. Transition states between step sub-phases are fully optimised together with step length and sub-phase lengths with respect to a given walking velocity. The data needed to generate purely cyclic steps can be reduced to the forward velocity.

Optimal Motion Synthesis – Dynamic Modelling and Numerical Solving Aspects

A general approach for generating optimal movements of actuatedmulti-jointed systems is presented. The method is based on theimplementation of the Pontryagin Maximum Principle (PMP) used as amathematical optimization tool. It applies to mechanical systems withkinematic tree-like topology such as serial robots, walking machines,and articulated biosystems. Emphasis is put on the choice of anappropriate dynamic model of the multibody system, together with thechoice of relevant performance criteria to be minimized for generatingthe optimal motion. It is shown that the Hamiltonian formalism isperfectly suitable to deal with the optimization problem using the PMP.On the other hand, prominence is given to performance criteria ensuringsoft and efficient functioning of the articulated systems. Two computingtechniques for solving the optimization problem are presented. Threenumerical simulations demonstrate the applicability of the method.

The convex wrapping algorithm: a method for identifying muscle paths using the underlying bone mesh.

Associating musculoskeletal models to motion analysis data enables the determination of the muscular lengths, lengthening rates and moment arms of the muscles during the studied movement. Therefore, those models must be anatomically personalized and able to identify realistic muscular paths. Different kinds of algorithms exist to achieve this last issue, such as the wired models and the finite elements ones. After having studied the advantages and drawbacks of each one, we present the convex wrapping algorithm. Its purpose is to identify the shortest path from the origin to the insertion of a muscle wrapping over the underlying skeleton mesh while respecting possible non-sliding constraints. After the presentation of the algorithm, the results obtained are compared to a classically used wrapping surface algorithm (obstacle set method) by measuring the length and moment arm of the semitendinosus muscle during an asymptomatic gait. The convex wrapping algorithm gives an efficient and realistic way of identifying the muscular paths with respect to the underlying bones mesh without the need to define simplified geometric forms. It also enables the identification of the centroid path of the muscles if their thickness evolution function is known. All this presents a particular interest when studying populations presenting noticeable bone deformations, such as those observed in cerebral palsy or rheumatic pathologies.

MODELING OF FRICTIONS IN THE TRANSMISSION ELEMENTS OF A ROBOT AXIS FOR ITS IDENTIFICATION

Abstract Control in robotics needs more and more precise models of the mechanical parts of the structure and specially for a complex system such as a biped robot. An important but difficult aspect of this work is the modeling of the mechanical loss due to friction in the chain of transmission from the motor to the axis. Each part losses are defined as a sum of three terms, one constant, another depending only on the speed and the last depending on the torque transmitted. The robot joint kinematic chain is modeled with three elements: the motor, the gearbox and a rotational joint at the leg. The results show a good adequacy between measurement and simulation with the proposed identification method in comparison with a classic least square identification method.

Optimal Gait Synthesis of a Planar Biped

Abstract This paper deals with dynamic optimization of biped locomotion, and is focused on the unipodal phase planning in the sagittal plane. The optimal motion is generated by minimizing the joint actuating torques. It must obey hard state constraints to prevent counter-flexing of the swing leg, as well as collision of the foot with the ground or an obstacle. The minimization technique used to solve this problem is the Pontryagin Maximum Principle. Numerical simulations presented are applied to a biped robot whose mechanical characteristics are closely related to those of the human biped. The patterns of the gait generated are similar to human gait in the sagittal plane.