Using a Kinetic Model of Human Gait in Personal Navigation Systems

Transcription

1 Using a Kinetic Model of Human Gait in Personal Navigation ystems Demoz Gebre-Egziabher Department of Aerospace Engineering and Mechanics University of Minnesota, win Cities

2 file:///c:/users/demoz/documents/projects/border/personal_navigation/presentations/ufts_march_2010/quad-firefighter-positioning-ystem.jpg file:///c:/users/demoz/documents/projects/border/personal_navigation/presentations/ufts_march_2010/ea_blind %5BConverted%5D.jpg Personal Navigation: Why? Personal navigation systems: Navigators that can be carried or worn by individuals Primarily, generate a position solution. Can provide velocity and attitude solution as well. Guidance for the Visually Impaired ignificant current interest in personal navigation systems for applications such as: ocation-based computing (e.g., cell phones, laptops, etc) Assisted iving Guidance for Visually impaired. First responders (fire fighters, EMs) Post surgery monitoring of patients aw enforcement & Military (e.g., urban navigation, cave navigation, etc.) Biometrics: Identify a person by gait. First Responder Navigation

3 Personal Navigation olutions Most current personal navigation solutions are GP-based. Work well outdoors and away from urban canyons Work poorly (or not at all) indoors olutions based on other position fixing techniques are being explored. Wi-Fi, Ultra Wide Band (UWB), Electro Optical/Infrared Cameras Advantage: Position errors do not grow with time Disadvantage: Infrastructure intensive Dead reckoning solutions are self contained and address some of the issues associated with position fixing systems tep counting (pedometer), shoe-mounted inertial navigation (Navhoe from Intersense), body-mounted inertial navigation. Advantages: elf contained. Disadvantages: Errors grow with time ( random walk )

4 Inertial Navigation ystems (IN) Inertial Navigation ystems (IN): elf-contained navigators equipped with sensors continuously measuring acceleration (a) and rotation/rotation rate (ω), from which velocity (v), position (p) b and attitude/orientation ( ) are computed. C n v v + a dt Velocity Equation t 0 0 Inertial ensor uite (small of back) p t p + v dt p0 a d τ dt t τ 0 0 Position Equation

5 IN Quality pectrum vs Error file:///c:/users/demoz/documents/projects/border/personal_navigation/presentations/ufts_march_2010/poserrcovblowup2 %5BConverted%5D.jpg ) ( ˆ t dt dt dt t t t m m v v a a v a v v a a a δ δ δ

6 file:///c:/users/demoz/documents/projects/border/personal_navigation/presentations/ufts_march_2010/nav_shoe.jpg Bounding IN Drift with ZUPs Can use zero velocity updates (ZUPs) to bound position error drift V at the end of each step is zero Advantage: Position error (Δp) is becomes a linear function of time of travel () as opposed to a quadratic or cubic growth seen by traditional IN. Problem: Direction of travel or heading can be of poor quality if not aided by information from another source.

7 tep Counting (Pedometer) Need a way to measure he distance traveled during each step (not a simple problem) he direction of travel (heading) during each step. tart top teps can be counted by using a sensor like an accelerometer. Direction of travel can be determined using a compass (magnetometer triad).

8 Motion Model: A Virtual ensor? Potential ite For measuring Kinematic tates Can knowledge of human motion be used as a sensor or constraint in personal navigation systems? What are the important parameters to characterize human motion (from a navigation point of view)? inear Acceleration Yes. his talk is about using such models to estimate step size or.

9 9 Proposed Approach

10 tep ize & Gait Kinematics ocal Vertical et us assume that we are dealing with a person walking in a straight line. No heading change tance eg ( l ) high ( d ) hank et us also assume we are dealing with normal walking No running, skipping, shuffling, etc. hen a time history of limb angles can be used to estimate step size (). l sin + d sin + ( l d ) sin

11 he Passive Walker he passive walker is an idealization of human gait. It assumes the motive force is gravity and ignores muscular inputs.

12 l high & hank Free Body l Diagrams Hip H R H H m a m g G G m g H G H G m a MH : r r HG HG m g + rhg m g m a + r HG m a + H + G H G

13 hank Free Body Diagram Knee K R K K m a M K G m g H G MK : r g + M K KG m r CG m a + H G

14 Passive Walker Kinematics G u a G C a C u H Τ G K a u a a G ω k ω k a a + ω r + ω ω r G H C C CG a a + ω r + ω ω r a u a H ω u 0 CH a G a H + ω rhg + ω ω r a K ah + ω rhk + ω ω r a a + ω r + ω ω r G K K k Ignoring orso way CH HG HK K CG

15 Passive Walker Equations he passive walker equations from the previous slides can be recast into a the following form: his form, in turn, can be recast in a non-linear, state-space form which looks like: ), ( ), ( ), ( ) ( G G G ω ω ω ω ω ω x f x ( ) ( ) [ ] A M A M,, 1

16 file:///c:/users/demoz/documents/projects/border/personal_navigation/presentations/ufts_march_2010/foot_and_accel_convention.jpg Gait-Cycle: Ankle Acceleration 1. Pick Up and Go 2. wing Phase 3. Impact 4. Weight ransfer 5. tance Phase ample # (50 Hz sampling Rate)

17 Modified Passive Walker We can use the acceleration at the ankle (a), input to the passive walker equations (an indirect measure of muscular torques) a d dt ( ) ( l sin + d sin + ( l d ) sin ) We also augment the state vector with an additional set of states to account for applied torques at the knee and ankle of the swing leg (assume quadratic over the step). M k p k 0 + p k 1 t + p k 2 t 2 M c p c 0 + p c 1 t + p c 2 t 2 he unknowns in these moment equations are the coefficients of the quadratic moment model.

18 olving Modified PW Equations Given the initial conditions on angular velocities, we can use the accelerometer outputs to integrate the modified passive walker equations. What are the initial conditions? For angles: we assume initial conditions for the current step are the angles at the end of the last step. Angular rates: We solve for them. Basically, we solve an optimization problem Unknowns are the initial conditions for angular rates and the moment coefficients olution is based on a set of terminal constraints. Heuristic as well as physics based constraints For example, the height of the foot at the end of the step should be zero.

19 Experimental Results One way we tested out results is by using data collected at the James R. Gage Center for Gait and Motion Analysis (Gillette Children s Hospital in t. Paul). Data collected from subjects walking in straight line and their motion was tracked using a Vicon motion tracking systems. Data was used to generate time history of limb kinematic states (position, velocity, accelerations, angular rates). Data was replayed in modified passive walker equations developed for this work.

20 Five tep ime History for [ ]

21 tep Counting Experiments Performed a series of experiments to assess the viability of estimating step size or stride length in-situ indoors. ubject (C. Matthews) had an IMU strapped to each ankle MIDG II IN/GP unit ile count/size provided truth reference while CPU time on the MIDG is used as the time base.

22 Basement Navigation Experiment ravel Path Akerman Hall Basement (Concrete Building) MIDG II IN/GP Unit

23 file:///c:/users/demoz/documents/projects/border/personal_navigation/presentations/ufts_march_2010/indoor_step.jpg In-itu tep ize Estimates Figures show that the model does a reasonable job of estimating the two varying step sizes (24 61 cm and cm) Note that in this case, a measurement from a single accelerometer is used to augment the state vector:

24 Distance raveled (Integrated tep ize) file:///c:/users/demoz/documents/projects/border/personal_navigation/presentations/ufts_march_2010/indoor_test3 %5BConverted%5D.jpg

25 ummary & Future Work Developed an approach for in-situ step size estimation (c.f., C. J. Matthews, et al, In-itu tride ength Estimation Using a Kinetic Model of Human Gait, ION-GN 2010) Based on a kinetic model of gait and driven by a single acceleration measurement. Adequate for normal step sizes Cannot deal with turns or non-normal gait. On going work attempts to address turning motion as well as other nonnormal gait patterns. Another thrust is to examine how gait characteristics can be used as means of identifying of persons.

26 Model Identification or Biometrics 26

27 Acknowledgments Chris Matthews (M.. candidate in AEM) Prof. Yohannes Ketema, (Associate Professor AEM). Prof. Michael chwartz (Department of Orthopedic urgery, UMN) he work described in this presentation was sponsored by grants from: Honeywell International Inc. U Department of Homeland ecurity cience & echnology Directorate.