DOCSLIB.ORG

An Inverse Dynamics Model for the Analysis, Reconstruction and Prediction of Bipedal Walking

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
An Inverse Dynamics Model for the Analysis, Reconstruction and Prediction of Bipedal Walking Pergamon J. Biomechanics, Vol. 28, No. 11, pp. 1369%1376,1995 Copyri& 0 1995 Elsevicr Science Ltd hinted in Great Britain. All rifits reserved 0021-9290/95 $9.50 + .oO 0021-9290(94)00185-J AN INVERSE DYNAMICS MODEL FOR THE ANALYSIS, RECONSTRUCTION AND PREDICTION OF BIPEDAL WALKING Bart Koopman, Henk .I. Grootenboer and Henk J. de Jongh University of Twente, Faculty of Mechanical Engineering, Laboratory of Biomedical Engineering, P.O. Box 217,750O AE Enschede, The Netherlands Abstract-Walkingis a constrainedmovement which may best be observed during the double stance phase when both feet contact the floor. When analyzing a measured movement with an inverse dynamics model, a violation of these constraints will always occur due to measuring errors and deviations of the segments model from reality, leading to inconsistent results. Consistency is obtained by implementing the constraints into the model. This makes it possible to combine the inverse dynamics model with optimization techniques in order to predict walking patterns or to reconstruct non-measured rotations when only a part of the three-dimensional joint rotations is measured. In this paper the outlines of the extended inverse dynamics method are presented, the constraints which detine walking are defined and the optimization procedure is described. The model is applied to analyze a normal walking pattern of which only the hip, knee and ankle flexions/extensions are measured. This input movement is reconstructed to a kinematically and dynam- ically consistent three-dimensional movement, and the joint forces (including the ground reaction forces) and joint moments of force, needed to bring about thts movement are estimated. INTRODUCIION are, except for the double support phase,completely determinedby the segmentaldisplacements. However, Numerous models have been developed to simulate sincethe measureddisplacements have to be differen- human walking, based on segment models in varying tiated twice with respectto time in order to obtain the complexity from three (McMahon, 1984) up to 17 accelerations,this may resultin large numericalerrors segments (Hatze, 198la). Symmetry betweenthe right when no precautionsare taken. To avoid theseerrors, and left leg is often assumed to reduce complexity (e.g. Chao and Rim (1973)combined optimization tech- Brand et al., 1982),and the movement is often re- niqueswith the direct dynamicsmethod to calculate stricted to the sagittal plane only. the joint momentsof force in normal walking. The two ways to apply the equationsof motion to Optimization techniquesare also usedin predictive the segmentsmodel are usually referred to as the models,where both the movement and the internal ‘direct dynamics method’ and the ‘inverse dynamics forces have to be calculated.This approachmay find method’. In the direct dynamicsmethod, the move- a wide application in rehabilitation technology, for ments of the segmentsare calculated by integrating example,to calculate the effect of prosthetic compo- the equationsof motion. This is only possiblewhen nentson the walking pattern or in functional electrical the joint momentsof force are known or assumed to stimulation. Chow and Jacobson(1971) were the first be zero. The latter is the case in ballistic walking to developa (semi)predictive modelfor walking: with (McMahon, 1984).It is alsopossible to choosefor the prescribedhip trajectories,ground reaction forcesand internal forces such values that a normal walking ankle momentsof force they predicted the hip and pattern results (e.g. Pandy and Berme, 1988) or to knee angles and moments of force by minimizing calculatethe joint momentsof force from estimations a criterion reflecting the mechanicalenergy expendi- of the muscle forces (e.g. Olney and Winter, 1985). ture. The complex model of Hatze (1981b) includes In the inverse dynamics method, the joint forces muscledynamics and is applied to predict the long and joint momentsof force are calculatedfrom a pre- jump. scribedmovement. Since the segmentalmovements, in The predictive model presentedhere is, in contrast contrast to the internal forces, can be measured,this to other existing models,based on a combination of method is commonly appliedfor the analysisof meas- inverse dynamics and optimization techniques. There ured movements.Hereby the measuredground reac- are two reasonsfor choosing the inverse dynamics tion forces are used as an input for most of these method instead of the direct dynamicsmethod: first, models(e.g. Brand et al., 1982).This, however, is not sincemovements can be measuredand internal forces a necessityfor a bipedal model, as was shown by and moments of force cannot, the inverse dynamics Hardt and Mann (1980).The ground reaction forces part of the model can be usedseparately for the gait analysis of measurement.Second, walking is a con- strained movement, and it is easier to implement Received in jinal form 21 March 1994. kinematic constraints in an inverse method than in 1369 1370 B. Koopmanet al. a direct method. One kinematic constraint is, for segments(Fig. 2): the upper legs,lower legs,feet, pelvis example, that the feet must be exactly on the floor and the head, arms and trunk (HAT) segment.The during the stance phase. However, the distinction number of segmentsis a compromisebetween the betweeninverse and direct dynamics is not essential wish to avoid unnecessarycomplexity and large com- sinceboth methodsshould eventually yield the same putation times, on the one hand, and to simulatethe results. movement adequately on the other hand. The seg- Dynamic constraintsare appliedto achievethat the mentsare connectedin the joints; the point of contact segmentsmodel is in balancefor the completewalking betweenthe foot and the floor is modeledas if it were cycle, which may bestbe explainedin the frontal plane a joint aswell. In this view, the floor is a segmentwith (Fig. 1). With an input consistingof the sagittal hip, zero velocity and infinite mass,which makesit pos- knee and ankle rotations only, the foot will move sible to calculate the ground reaction forces in the straight under the hip joint. Sincethe ground reaction sameway as the joint forces. A referenceframe is forces can only apply to the foot and are in general attached to the floor, with the x-axis pointing in the not in the line of action of the static and dynamic walking direction, the y-axis pointing upward and the forces acting on the total center of massof the seg- z-axis perpendicular to the xy-plane in the lateral mentsmodel, an imbalancemoment M is necessaryto direction (Fig. 2). keep the body upright [Fig. l(a)]. This imbalanceis In each segmenta local frame is defined according reducedby estimatingthe leg adduction in an optim- to the method usedby Brand et al. (1982),which is ization schemeand thus meeting the dynamic con- basedon the location of someanatomical landmarks. straints [Fig. l(b)]. It is extended with definitions for the segmentsof the The application of kinematic and dynamic con- feet and the HAT segment.A detailed description of straints eventually results in a movement of the the construction of theseframes, as well as a list of all segmentsmodel which is consistent with physical segmental parameters, has been given elsewhere demands:all deviations due to measuringerrors and (Koopman, 1989). approximationsin the segmentsmodel are corrected The mass,the position of the center of massin the for. As an example,the model is applied to a normal local frame and the moment of inertia tensor are gait pattern which is basically two-dimensional:only determinedwith the regressionequations of Chandler the hip, knee and ankle flexions/extensionsare meas- et al. (1975). These relations depend on the local ured. The non-measuredrotations are estimatedwith dimensionsof the segmentsand the total body weight, the constraints, and the resulting three-dimensional and are in some respectsadapted to the segments movementis analyzed. model usedin this study: the properties for the foot- segmentare corrected for the influence of the shoe, METHODS and a distinction is madefor the HAT and the pelvis. The segmentsmodel In the segmentsmodel the human body is modeled as a coupled systemof right bodiescontaining eight Fig. 2. The segmentsmodel for the body at rest,with seg- ments: pelvis (I), R-L femur (2-31, R-L tibia (4-5), R-L foot Fig. 1. Imbalanceof the segmentsmodel. The imbalance (6-7) and HAT (8);with joints: R-L hip (l-2), R-L knee(3-4), momentM canbe viewed as resulting from an eccentricity of R-L ankle (5-6), R-L foot-floor (7-8) and HAT-pelvis(9); the groundreaction force FR with the body weightF, (a) and the definition .of the. reference. frame: forward axis (x), andis correctedwith a hip adduction(b). verticalaxis (y) andlateral axis (2). An inverse dynamics model of bipedal walking 1371 [t is assumed that the axes of the local frames of the With known joint rotations, all segmental move- segments are in the principal directions, so that ments are defined relative to an arbitrary reference the principal moments of inertia as determined by point and with an unknown reference orientation. Chandler et al. can be used. These are constructed by applying the kinematic All joints are modeled as potential ball-hinges with constraints. three independent rotational degrees of freedom. -The reference orientation (as a function of time) However, the nature of the joint (ball-hinge, line- is deduced from the demands that at the time of heel hinge) is determined by the input joint rotations of the contact, both feet touch the floor and during a part of inverse dynamics model and the constraints: when the single stance phase (foot flat) the rotation of the the joint angular velocity vector has a fixed direction, foot relative to the floor is zero. the joint will effectively act as a line-hinge. The posi- -The displacement of the reference point is cal- tions of the joints in the local frames of the segments culated from the constraint that during the stance may depend on the joint rotation and thus vary impli- phase no slipping between foot and floor may occur.
Load more

Recommended publications
  • Chapter 3 Dynamics of Rigid Body Systems
    Rigid Body Dynamics Algorithms Roy Featherstone Rigid Body Dynamics Algorithms Roy Featherstone The Austrailian National University Canberra, ACT Austrailia Library of Congress Control Number: 2007936980 ISBN 978-0-387-74314-1 ISBN 978-1-4899-7560-7 (eBook) Printed on acid-free paper. @ 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com Preface The purpose of this book is to present a substantial collection of the most efficient algorithms for calculating rigid-body dynamics, and to explain them in enough detail that the reader can understand how they work, and how to adapt them (or create new algorithms) to suit the reader’s needs. The collection includes the following well-known algorithms: the recursive Newton-Euler algo- rithm, the composite-rigid-body algorithm and the articulated-body algorithm. It also includes algorithms for kinematic loops and floating bases.
    [Show full text]
  • Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism
    sensors Article Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism Linkang Wang 1 , Jingjing You 1,* , Xiaolong Yang 2, Huaxin Chen 1, Chenggang Li 3 and Hongtao Wu 3 1 College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China; [email protected] (L.W.); [email protected] (H.C.) 2 School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210037, China; [email protected] 3 School of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; [email protected] (C.L.); [email protected] (H.W.) * Correspondence: [email protected] Abstract: The solution of the dynamic equations of the six-axis accelerometer is a prerequisite for sensor calibration, structural optimization, and practical application. However, the forward dynamic equations (FDEs) and inverse dynamic equations (IDEs) of this type of system have not been completely solved due to the strongly nonlinear coupling relationship between the inputs and outputs. This article presents a comprehensive study of the FDEs and IDEs of the six-axis accelerometer based on a parallel mechanism. Firstly, two sets of dynamic equations of the sensor are constructed based on the Newton–Euler method in the configuration space. Secondly, based on the analytical solution of the sensor branch chain length, the coordination equation between the output signals of the branch chain is constructed. The FDEs of the sensor are established by combining the coordination equations and two sets of dynamic equations. Furthermore, by introducing generalized momentum and Hamiltonian function and using Legendre transformation, the vibration differential equations (VDEs) of the sensor are derived.
    [Show full text]
  • Existence and Uniqueness of Rigid-Body Dynamics With
    EXISTENCE AND UNIQUENESS OF RIGIDBODY DYNAMICS WITH COULOMB FRICTION Pierre E Dup ont Aerospace and Mechanical Engineering Boston University Boston MA USA ABSTRACT For motion planning and verication as well as for mo delbased control it is imp ortanttohavean accurate dynamic system mo del In many cases friction is a signicant comp onent of the mo del When considering the solution of the rigidb o dy forward dynamics problem in systems such as rob ots wecan often app eal to the fundamental theorem of dierential equations to prove the existence and uniqueness of the solution It is known however that when Coulomb friction is added to the dynamic equations the forward dynamic solution may not exist and if it exists it is not necessarily unique In these situations the inverse dynamic problem is illp osed as well Thus there is the need to understand the nature of the existence and uniqueness problems and to know under what conditions these problems arise In this pap er we show that even single degree of freedom systems can exhibit existence and uniqueness problems Next weintro duce compliance in the otherwise rigidb o dy mo del This has two eects First the forward and inverse problems b ecome wellp osed Thus we are guaranteed unique solutions Secondlyweshow that the extra dynamic solutions asso ciated with the rigid mo del are unstable INTRODUCTION To plan motions one needs to know what dynamic b ehavior will o ccur as the result of applying given forces or torques to the system In addition the simulation of motions is useful to verify motion
    [Show full text]
  • Newton Euler Equations of Motion Examples
    Newton Euler Equations Of Motion Examples Alto and onymous Antonino often interloping some obligations excursively or outstrikes sunward. Pasteboard and Sarmatia Kincaid never flits his redwood! Potatory and larboard Leighton never roller-skating otherwhile when Trip notarizes his counterproofs. Velocity thus resulting in the tumbling motion of rigid bodies. Equations of motion Euler-Lagrange Newton-Euler Equations of motion. Motion of examples of experiments that a random walker uses cookies. Forces by each other two examples of example are second kind, we will refer to specify any parameter in. 213 Translational and Rotational Equations of Motion. Robotics Lecture Dynamics. Independence from a thorough description and angular velocity as expected or tofollowa userdefined behaviour does it only be loaded geometry in an appropriate cuts in. An interface to derive a particular instance: divide and author provides a positive moment is to express to output side can be run at all previous step. The analysis of rotational motions which make necessary to decide whether rotations are. For xddot and whatnot in which a very much easier in which together or arena where to use them in two backwards operation complies with respect to rotations. Which influence of examples are true, is due to independent coordinates. On sameor adjacent joints at each moment equation is also be more specific white ellipses represent rotations are unconditionally stable, for motion break down direction. Unit quaternions or Euler parameters are known to be well suited for the. The angular momentum and time and runnable python code. The example will be run physics examples are models can be symbolic generator runs faster rotation kinetic energy.
    [Show full text]
  • Investigation Into the Utility of the MSC ADAMS Dynamic Software for Simulating
    Investigation into the Utility of the MSC ADAMS Dynamic Software for Simulating Robots and Mechanisms A thesis presented to The faculty of The Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirements for the degree Master of Science Xiao Xue May 2013 © 2013 Xiao Xue. All Rights Reserved 2 This thesis titled Investigation into the Utility of the MSC ADAMS Dynamic Software for Simulating Robots and Mechanisms by XIAO XUE has been approved for the Department of Mechanical Engineering and the Russ College of Engineering and Technology by Robert L. Williams II Professor of Mechanical Engineering Dennis Irwin Dean, Russ College of Engineering and Technology 3 ABSTRACT XUE, XIAO, M.S., May 2013, Mechanical Engineering Investigation into the Utility of the MSC ADAMS Dynamic Software for Simulating Robots and Mechanisms (pp.143) Director of Thesis: Robert L. Williams II A Slider-Crank mechanism, a 4-bar mechanism, a 2R planar serial robot and a Stewart-Gough parallel manipulator are modeled and simulated in MSC ADAMS/View. Forward dynamics simulation is done on the Stewart-Gough parallel manipulator; Inverse dynamics simulation is done on Slider-Crank mechanism, 2R planar serial robot and 4- bar mechanism. In forward dynamics simulation, the forces are applied in prismatic joints and the Stewart-Gough parallel manipulator is actuated to perform 4 different expected motions. The motion of the platform is measured and compared with the results in MATLAB. An example of inverse dynamics simulation is also performed on it. In the inverse dynamics simulation, the Slider-Crank mechanism and four-bar mechanism both run with constant input angular velocity and the actuating forces are measured and compared with the results in MATLAB.
    [Show full text]
  • AN ALGORITHM for the INVERSE DYNAMICS of N-AXIS GENERAL MANIPULATORS USING KANE's EQUATIONS
    Computers Math. Applic. Vol. 17, No. 12, pp. 1545-1561, 1989 0097-4943/89 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright © 1989 Pergamon Press plc AN ALGORITHM FOR THE INVERSE DYNAMICS OF n-AXIS GENERAL MANIPULATORS USING KANE'S EQUATIONS J. ANGELES and O. MA Department of Mechanical Engineering, Robotic Mechanical Systems Laboratory, McGill Research Centre for Intelligent Machines, McGill University, Montrral, Qurbec, Canada A. ROJAS National Autonomous University of Mexico, Villa Obregrn, Mexico (Received 4 April 1988) Abstract--Presented in this paper is an algorithm for the numerical solution of the inverse dynamics of robotic manipulators of the serial type, but otherwise arbitrary. The algorithm is applicable to manipulators containing n joints of the rotational or the prismatic type. For a given set of Hartenberg- Denavit and inertial parameters, as well as for a given trajectory in the space of joint coordinates, the algorithm produces the time histories of the n torques or forces required to drive the manipulator through the prescribed trajectory. The algorithm is based on Kane's dynamical equations of mechanical multibody systems. Moreover, the complexityof the algorithm presented here is lower than that of the most ett~cient inverse-dynamics algorithm reported in the literature. Finally, the applicability of the algorithm is illustrated with two fully solved examples. 1. INTRODUCTION The inverse dynamics of robotic manipulators has been approached with a variety of methods, the most widely applied being those based on the Newton-Euler (NE) and the Euler-Lagrange (EL) formulations [1-11]. Although essentially equivalent [12], the two said formulations regard the dynamics problems associated with rigid-link manipulators from very different viewpoints.
    [Show full text]
  • Forward and Inverse Dynamics Reconstruction of a Staged Rugby Tackle
    IRC-19-90 IRCOBI conference 2019 Forward and Inverse Dynamics Reconstruction of a Staged Rugby Tackle C. Weldon* & K. Archbold*, G. Tierney, D. Cazzola, E. Preatoni, K. Denvir, CK. Simms I. INTRODUCTION Sports participation is crucial to population health, but injuries carry short and long-term health consequences. In elite schoolboy rugby, injury incidence is 77/1000 match hours with concussions at 20/1000 hours [1], while in adult competitions the injured player proportion per year is around 50%, with tackles being the main injury cause [2]. However, little is known about contact forces/body kinematics leading to injuries in sporting collisions. Wearable sensors are promising, but challenges remain. Physics-based models with force predictions are subject to validation challenges [3-4]. We previously reported on staged rugby tackles recorded using a motion capture system [5]. Simulating these tackles using MADYMO (Helmond, The Netherlands) forward dynamics modelling highlighted challenges with the absence of muscle activation in the MADYMO pedestrian model [3]. Here our aim is to test whether combined inverse and forward dynamics modelling of a staged rugby tackle can yield a realistic estimate of tackle contact force. II. METHODS A combined forward and inverse dynamics approach was taken to estimate tackle contact forces without a direct load sensor, as impact force is challenging to measure in sporting collisions. To test this integrated approach, a staged tackle from [5] was chosen for forward and inverse dynamics model reconstruction. For forward dynamics, the MADYMO pedestrian model applied by [4] was used, with pelvis initial position, orientation and velocity and the principal joint DOFs and their time derivatives extracted from the Vicon motion capture data using the Plug-in-Gait Model [5].
    [Show full text]
  • Estimation of Ground Reaction Forces and Moments During Gait Using Only Inertial Motion Capture
    Article Estimation of Ground Reaction Forces and Moments During Gait Using Only Inertial Motion Capture Angelos Karatsidis 1,4,*, Giovanni Bellusci 1, H. Martin Schepers 1, Mark de Zee 2, Michael S. Andersen 3 and Peter H. Veltink 4 1 Xsens Technologies B.V., Enschede 7521 PR, The Netherlands; [email protected] (G.B.); [email protected] (H.M.S.) 2 Department of Health Science and Technology, Aalborg University, Aalborg 9220, Denmark; [email protected] 3 Department of Mechanical and Manufacturing Engineering, Aalborg University, Aalborg 9220, Denmark; [email protected] 4 Institute for Biomedical Technology and Technical Medicine (MIRA), University of Twente, Enschede 7500 AE, The Netherlands; [email protected] * Correspondence: [email protected]; Tel.: +31-53-489-3316 Academic Editor: Vittorio M. N. Passaro Received: 29 September 2016; Accepted: 28 December 2016; Published: 31 December 2016 Abstract: Ground reaction forces and moments (GRF&M) are important measures used as input in biomechanical analysis to estimate joint kinetics, which often are used to infer information for many musculoskeletal diseases. Their assessment is conventionally achieved using laboratory-based equipment that cannot be applied in daily life monitoring. In this study, we propose a method to predict GRF&M during walking, using exclusively kinematic information from fully-ambulatory inertial motion capture (IMC). From the equations of motion, we derive the total external forces and moments. Then, we solve the indeterminacy problem during double stance using a distribution algorithm based on a smooth transition assumption. The agreement between the IMC-predicted and reference GRF&M was categorized over normal walking speed as excellent for the vertical (r = 0.992, rRMSE = 5.3%), anterior (r = 0.965, rRMSE = 9.4%) and sagittal (r = 0.933, rRMSE = 12.4%) GRF&M components and as strong for the lateral (r = 0.862, rRMSE = 13.1%), frontal (r = 0.710, rRMSE = 29.6%), and transverse GRF&M (r = 0.826, rRMSE = 18.2%).
    [Show full text]
  • A Unified Method for Solving Inverse, Forward, and Hybridmanipulator
    A Unified Method for Solving Inverse, Forward, and HybridManipulator Dynamics using Factor Graphs Mandy Xie, Frank Dellaert (presented by Dominic Guri) Introduction 1. Inverse Dynamics I solve for forces & torques (for control and planning) for a desired trajectories (positions, velocities, and accelerations) I often used by Newton-Euler N_E — very efficient, and recursion-based 2. Forward Dynamics I solves joint accelerations when torques are applied at known positions and velocities I different from simulation problem with requires motion integration to obtain positions and velocities I solutions: I Composite-Rigid-Body Algorithm (CRBA) — can be numerically unstable I Articulated-Body Algorithm (ABA) — takes advantage of sparsity 3. Hybrid Dynamics (partially both inverse and forward) I solves for unknown forces and accelerations, given forces at some joints and accelerations at other joints NB: all the above methods do not handle kinematic loops NB: rare for a single algorithm to solve all 3 problems — proposed methods use filtering and smoothing Dynamics Problems: Figure 1: QUT Robot Academy Existing Methods 1. Inverse Dynamics I Recursive Newton-Euler [42,21] I others [49, 57] 2. Forward Dynamics I Composite-Rigid-Body Algorithm (CRBA) [60,20] I Articulated-Body Algorithm (ABA) [18] 3. Hybrid Dynamics (partially both inverse and forward) I Articulated-Body Hybrid Dynamics Algorithm [19] 4. Kinematic Loops I [19] I Rodriguez [52,51] — filtering and smoothing based, inverse & forward I applied to loops in [53] I Rodriguez [54] ⇒ I Jain [33] — serial chain dynamics I Ascher [4] — CRBA & ABA as elimination methods for solving forward dynamics Contributions I factor graph as a unified description of classical dynamics algorithms and new algorithms (graph theory-based ⇒ sparse linear systems) 1.
    [Show full text]
  • Inverse Dynamics Vs. Forward Dynamics in Direct Transcription Formulations for Trajectory Optimization
    Inverse Dynamics vs. Forward Dynamics in Direct Transcription Formulations for Trajectory Optimization Henrique Ferrolho1, Vladimir Ivan1, Wolfgang Merkt2, Ioannis Havoutis2, Sethu Vijayakumar1 Abstract— Benchmarks of state-of-the-art rigid-body dynam- ics libraries report better performance solving the inverse dynamics problem than the forward alternative. Those bench- marks encouraged us to question whether that computational advantage would translate to direct transcription, where cal- culating rigid-body dynamics and their derivatives accounts for a significant share of computation time. In this work, we implement an optimization framework where both approaches for enforcing the system dynamics are available. We evaluate the performance of each approach for systems of varying complexity, for domains with rigid contacts. Our tests reveal that formulations using inverse dynamics converge faster, re- quire less iterations, and are more robust to coarse problem discretization. These results indicate that inverse dynamics should be preferred to enforce the nonlinear system dynamics in simultaneous methods, such as direct transcription. I. INTRODUCTION Fig. 1: Snapshots of the humanoid TALOS [2] jumping. Direct transcription [1] is an effective approach to for- mulate and solve trajectory optimization problems. It works constraints are usually at the very core of optimal control by converting the original trajectory optimization problem formulations, and require computing rigid-body dynamics (which is continuous in time) into a numerical optimization and their derivatives—which account for a significant portion problem that is discrete in time, and which in turn can be of the optimization computation time. Therefore, it is of solved using an off-the-shelf nonlinear programming (NLP) utmost importance to use an algorithm that allows to compute solver.
    [Show full text]
  • A Foot/Ground Contact Model for Biomechanical Inverse Dynamics Analysis
    A foot/ground contact model for biomechanical inverse dynamics analysis Romain Van Hulle∗, Cédric Schwartz∗, Vincent Denoël∗, Jean-Louis Croisier∗, Bénédicte Forthomme∗, Olivier Brüls∗ Laboratory of Human Motion Analysis, University of Liège, Belgium Abstract The inverse dynamics simulation of the musculoskeletal system is a common method to understand and analyse human motion. The ground reaction forces can be accurately estimated by experimental measurements using force platforms. However, the number of steps is limited by the number of force platforms available in the laboratory. Several numerical methods have been proposed to estimate the ground reaction forces without force platforms, i.e., solely based on kinematic data combined with a model of the foot-ground contact. The purpose of this work is to provide a more efficient method, using a unilaterally constrained model of the foot at the center of pressure to compute the ground reaction forces. The proposed model does not require any data related with the compliance of the foot- ground contact and is kept as simple as possible. The indeterminacy in the force estimation is handled using a least square approach with filtering. The relative root mean square error (rRMSE) between the numerical estimations and experimental measurements are 4:1% for the vertical component of the ground reaction forces (GRF), 11:2% for the anterior component and 5:3% for the ground reaction moment (GRM) in the sagittal plane. Keywords: Musculoskeletal model, Inverse dynamics, Ground reaction forces, Contact constraint, Rigid foot model 1. Introduction Inverse dynamics simulation based on musculoskeletal models is a common and important method to study and understand the human motion as it can estimate joint torques based on experimental motion analysis data.
    [Show full text]
  • An Inverse Dynamics Satellite Attitude Determination and Control System with Autonomous Calibration
    SSC15-VIII-4 An Inverse Dynamics Satellite Attitude Determination and Control System with Autonomous Calibration Sanny R. Omar1 Faculty Advisors: Dr. David Beale2 and Dr. JM Wersinger3 Auburn University, Auburn, Alabama, 36849 Attitude determination and control systems (ADACS) are responsible for establishing desired satellite orientations. Proper satellite orientation is necessary for many science instruments and communication systems. Popular sensors include magnetometers, sun sensors, and rate gyros, and popular actuators include reaction wheels and magnetorquers. This paper investigates an ADACS design using these sensors and actuators that could feasibly be implemented on a CubeSat. The B-Dot law is used for satellite de- tumbling, and a linear inverse dynamics PD controller is utilized for steady state pointing, allowing for the analytical estimation of optimal controller gains. The inverse dynamics controller calculates desired satellite angular accelerations and then calculates the torques required to achieve these angular accelerations. This makes controller performance independent of initial conditions or system inertia properties. This system uses the magnetorquers to dump reaction wheel momentum and analyzes the satellite’s kinematic response to applied torques in order to calibrate the rate gyros and estimate system moments of inertia. Simulation results corresponded well to the analytical predictions. Often, an oscillating equilibrium would occur when controller gains were low, but this oscillation could be mitigated by
    [Show full text]