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

Animation

Teleoperation

Cerebral Palsy Surgery

Perform. Improvement

Fall risk assessment

Real Time Feedback

Motion Capture Systems

Camera based

Very accurate but limited to a small space

Inertial Measurement Unit (IMU)

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

IMU based (one sensor per seg)

Can capture almost everywhere. Can be conspicuous for everyday use

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

One sensor per segment.

Less sensor = Missing info

Infer through biomechanical constraints

Infer through biomechanical constraints

Infer from additional measurements

Pose Tracking Challenge

specifically, tracking rotation

Rep.

Vars.

Singularity

Constraints

Vector rep.

Diff. geometry rep.

Euler angles

3

Y

N

N

Rotation Matrix

9

N

Y ($R^TR = I$)

N (Lie algebra)

Quaternions

4

N

Y ($||q|| = 1$)

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} $

Sparse Constrained KF (CKF)

Algorithm overview of prior work

Body Model:

Sparse Lie Group CKF (LGCKF)

Algorithm overview of prior work

Body Model:

Lie Group Formulation

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.

Pred.

Meas.

Pred.

Meas.

Cstr.

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).

Sparse LGCKF - Sample

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

Sparse LGCKF - Sample

Jumping jacks and speedskater

Sparse LGCKF - Results

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

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

Conclusion & Future Work

Lie group representation for tracking pose is indeed a promising approach