# 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

## 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)

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

## 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
• Code at https://git.io/Jv3oF
• Interesting to try with additional measurements and tracking more segments.

Lie Group based 7 segment tracking