Interaction Torque Estimation Algorithm for Wrist Gimbal Rehabilitation Robot
Mohammadhossein Saadatzi, David C. Long and Ozkan Celik
Biomechatronics Research Laboratory, Department of Mechanical Engineering, Colorado School of Mines
 Wrist Gimbal is a two degree-of-freedom (DOF) wrist and
forearm rehabilitation exoskeleton.
 Active DOF are wrist flexion/extension and forearm
pronation/supination.
Implementation of force/torque
estimation algorithms requires a
dynamic model of the robot,
which is realized using Denavit
Hartenberg convention, and
Newton-Euler dynamics
formulation.
SolidWorks model and assigned
coordinate frames for wrist gimbal.
𝝉𝝉 = 𝑴𝑴 𝜽𝜽 𝜽𝜽̈ + 𝑪𝑪 𝜽𝜽 𝜽𝜽̇ + 𝑮𝑮(𝜽𝜽)
𝐾𝐾𝑝𝑝 𝑒𝑒𝜏𝜏 + 𝐾𝐾𝑣𝑣 𝑒𝑒𝜏𝜏̇
−
Disturbance Observer
+
𝜏𝜏̂ 𝑑𝑑 𝜏𝜏̇̂ =-L𝜏𝜏̂ + 𝐿𝐿{𝑀𝑀
� 𝜃𝜃 𝜃𝜃̈ +
𝑑𝑑
𝑑𝑑
𝐶𝐶̂ 𝜃𝜃, 𝜃𝜃̇ 𝜃𝜃̇ + 𝐺𝐺� 𝜃𝜃 }
Estimated
interaction
torques: 𝜏𝜏̂ 𝑖𝑖𝑖𝑖𝑖𝑖
0.4
Dynamic model+Simplified friction model
Motor torque
0.2
0
-0.2
Friction
Model
̇
𝜏𝜏𝑓𝑓𝑓𝑓𝑓𝑓
̂ = 𝑓𝑓(𝜃𝜃)
𝜏𝜏𝑓𝑓𝑓𝑓𝑓𝑓
̂
-0.4
2
0
4
6
8
10
12
time (sec)
14
16
18
20
14
16
18
20
Second joint
0.05
 For torque estimation, first the total disturbance torque at the robot
handle 𝜏𝜏𝑑𝑑 is estimated using a nonlinear disturbance observer
(NDO).
 The estimated torque 𝜏𝜏̂ 𝑑𝑑 includes the friction at the joints and the
torque applied by the patient/user.
 By subtracting the friction of the joints 𝜏𝜏𝑓𝑓𝑓𝑓𝑓𝑓 from the estimated
disturbance, the torque applied by the user's hand to the robot
handle can be calculated.
Friction Modeling
First joint frictional torque
Original friction model
Simplified friction model
Experimental data
Estimated motor
torques, using dynamic
and friction models,
closely track the
recorded motor torques.
0
-0.05
-0.1
-0.15
-0.2
2
0
4
6
8
12
10
time (sec)
Validation of the NDO algorithm via the same experiments:
First joint
0.2
0.1
0
-0.1
-0.2
 Friction (𝜏𝜏𝑓𝑓𝑓𝑓𝑓𝑓
̂ ) at joints is modeled as a combination of stiction
and viscous effects.
0.1
First joint
Torque (N.m)
−
+
Torque (N.m)
+
Joint
kinematics:
𝜃𝜃, 𝜃𝜃̇
+
Validation of the derived robot dynamic model and the friction
model is completed using a closed-loop sinusoidal trajectory tracking
experiment scenario under PD control.
Torque (N.m)
Device Description
Desired feedback
torque 𝜏𝜏𝑟𝑟𝑟𝑟𝑟𝑟
Torque Controller
Results and Discussion
0
2
4
6
8
10
12
time (sec)
14
16
18
20
14
16
18
20
Second joint
Estimated torque
Simplified friction model
0.1
Torque (N.m)
Wrist Gimbal mechanism, and the implemented target matching game for it.
Total external disturbances: 𝜏𝜏𝑑𝑑 = 𝜏𝜏𝑓𝑓𝑓𝑓𝑓𝑓 + 𝜏𝜏𝑖𝑖𝑖𝑖𝑖𝑖
Torque (N.m)
 Repetitive movement exercises help re-establish part of the lost
motor function in stroke and spinal cord injury patients.
 Rehabilitation robots present opportunities for lowering therapy
costs, increasing patient motivation in therapy and enabling
intensive exercise protocols.
 This work focuses on development of force/torque estimation
algorithms that will allow accurate tracking of patient interaction
torques in rehabilitation robots, without relying on force sensors.
Disturbance Observer Design
Estimated torque,
using NDO algorithm,
follows the friction
torque acting on the
robot fairly closely.
0.05
0
-0.05
0
0
-1.5
-1
-0.5
0
0.5
1
1.5
2
dθ1/dt (rad/sec)
Second joint frictional torque
0.1
0.05
0
-0.05
-0.1
-2
-1.5
-1
-0.5
0
0.5
dθ2/dt (rad/sec)
1
1.5
2
2
4
6
8
10
12
time (sec)
Conclusion
-0.1
-2
Torque (N.m)
Introduction and Motivation
 Robot dynamic model and friction model were developed.
 Correct operation of the NDO, as a force estimator, was
verified.
 It was found that the pursued NDO structure has significant
potential for enabling accurate interaction force/torque
estimations for force feedback robots.
5th
Annual Regional Meeting of the Rocky Mountain ASB
April 17-18, 2015 | Estes Park, Colorado