UNSW

Estimating Lower Limb Kinematics using a Lie Group Constrained EKF and a Reduced Wearable IMU Count

Luke Wicent Sy, Nigel Lovell, Stephen Redmond

Motion Capture

Movie CG LoTR

Animation

Teleoperation

Teleoperation

Cerebral Palsy Surgery

Cerebral Palsy Surgery

Perform. Improvement

Perform. Improvement

Fall risk assessment

Fall risk assessment

Real Time Feedback

Real Time Feedback

Motion Capture Systems

Camera based

Camera based

Very accurate but limited to a small space

IMU based OSPS

Inertial Measurement Unit (IMU)

Miniaturization. Track position and orientation (albeit with drift).

IMU based OSPS

IMU based (one sensor per seg)

Can capture almost everywhere. Can be conspicuous for everyday use

Wearable based sparse Wearable based sparse

Wearable based

More comfortable

  • Soft stretch sensors
  • More & smaller IMUs
  • Sparse sensors

Wearable based

More comfortable

  • Soft stretch sensors
  • More & smaller IMUs
  • Sparse sensors

Sparse Wearable Challenge

Goal: Comfortable, Fast, and Accurate Motion Capture System

Camera based Missing sensor

One sensor per segment.

Less sensor = Missing info

Infer through biomechanical constraints

Infer through biomechanical constraints

Infer through biomechanical constraints

Infer through biomechanical constraints

Infer from additional measurements

Pose Tracking Challenge

specifically, tracking rotation

Rep.Vars.SingularityConstraints
Vector rep.Diff. geometry rep.
Euler angles3YNN
Rotation Matrix9NY ($R^TR = I$)N (Lie algebra)
Quaternions4NY ($||q|| = 1$)N (Clifford algebra)

 

$ R = \begin{bmatrix} \cos(\theta) & -\sin(\theta) & 0 \\ \sin(\theta) & \cos(\theta) & 0 \\ 0 & 0 & 1 \end{bmatrix} $ $ q = \begin{bmatrix} w & x & y & z \end{bmatrix} $
Euler

Sparse Constrained KF (CKF)

Algorithm overview of prior work

Sparse CKF

Body Model:

CKF+D Body Model

Sparse Lie Group CKF (LGCKF)

Algorithm overview of prior work

Sparse CKF

Body Model:

CKF+D Body Model

Lie Group Formulation

CKF+D Body Model

Sparse Lie Group CKF (LGCKF)

Algorithm Description

Prediction update

• Input: acceleration from IMU, zero angular velocity for simplicity

• Kinematic equations relating input to position and orientation

Measurement update

• Orientation from IMU

• Pelvis height (close to standing pelvis height)

• Zero velocity update (ankle velocity = 0)

• Flat floor assumption (ankle global z position = 0)

• Covariance limiter

Constraint update

• Constant segment length (thigh)

• Hinge knee joint

• Normal knee range of motion

Pred.

Sparse CKF Prediction

Pred.

Sparse CKF Prediction

Meas.

Sparse CKF Measurement

Pred.

Sparse CKF Prediction

Meas.

Sparse CKF Measurement

Cstr.

Sparse CKF Constraint

Sparse LGCKF - Sample

Tested on actual IMU data from Sparse CKF dataset (walking, high knee jog, jog, jumping jacks, speedskater). For walk, most deviation is at the turning motion ($t=3.5 - 5$s).

 

Sample walk Joint angle samples

Sparse LGCKF - Sample

Increase in performance in dynamic movements. Captures sagittal knee angles better.

 

Sample High Knee Jog Sample Jog

Sparse LGCKF - Sample

Jumping jacks and speedskater

 

Sample SpeedSkater Sample TUG

Sparse LGCKF - Results

Below shows the joint angle rmse and correlation coefficient for knee and hip joint angles.

results

C denotes CKF-3IMU and LG denotes LGKF-3IMU

Conclusion & Future Work

  • Lie group representation for tracking pose is indeed a promising approach
  • Code at https://git.io/Jv3oF
  • Interesting to try with additional measurements and tracking more segments.
LG7Seg Sample Walk

Lie Group based 7 segment tracking