IEEE Robotics & Automation Magazine - December 2014 - 97

Remote Controller

2-D LUT Early Stance Stance
2-D LUT Midstance Control
i
2-D LUT Late Stance BM
T
T
i
i
#
v
v

Amputee

Finite-State
Machine

Walking-Speed
and Cadence
Estimator

Tdes

Swing
Control

MinimumJerk
Trajectory
Generator
+
-

Robotic
Prosthesis

Leg Dynamic
Model

Embedded
Sensors:
Position, Torque,
GRF, IMU

Embedded
Control:
Closed-Loop
Torque Control

Ground
CAN Bus

Figure 2. The block diagram of the robotic prosthesis controller. The controller receives input signals from embedded sensors on the
prosthesis through a high-speed CAN bus. By combining the prosthesis outputs with the joint angle and GRF, the remote walking-speed
estimator computes the forward speed in the sagittal plane ^v h . At the same time, based on the joint angle, velocity, and GRF, the finite-state
machine segments the gait cycle into four parts: early, midstance and late stance and swing phase. For each stance subphase, two 2-D LUTs,
implementing normalized able-bodied torque-angle curves for ankle and knee joints, provide the desired torques as a function of current angle
^i h, walking speed ^v h, and patient BM. In the swing phase, a minimum-jerk trajectory generator defines the desired angle for the ankle and
knee joints based on the stance-phase duration. The desired joint torques result from the sum of a feed-forward torque command, obtained
through a dynamic model of the prosthesis, and a proportional-derivative (PD) closed-loop position control. Finally, the torque references ^Tdes h
are transmitted to the closed-loop, low-level, embedded controller on the prosthesis.

thigh and foot orientation using the prosthetic ankle and knee
angles. Exploiting a simple three-segment planar model of the
leg, we compute the forward velocity of the hip in the sagittal
plane using gyroscope data during the stance phase and by integrating accelerometer outputs during the swing phase. As
the forward velocity profile has an almost sinusoidal trend
with half the duration of the stride [22], we estimate the walking velocity twice during each stride. The first estimate is the
average of the forward velocity during the early and midstance
phases, which accounts for half of the stride duration. The second estimate is the average during the late stance and swing
phase, which accounts for the second half of the stride. The
error of the walking-speed estimate on the treadmill has been
estimated experimentally to be 8%, in agreement with findings
of other researchers using a comparable approach [30]. More
accurate walking-speed measurements could be obtained by
segmenting the gait cycle in multiple parts, as shown in [31].
Walking Controller
The second stage of the controller is responsible for defining
the desired torque profiles to be applied at the ankle and
knee joint, based on current estimates of gait phase and
walking speed.
In the stance phase, the torque reference for the ankle and
knee joint is obtained from intact-leg quasistiffness profiles,
as extrapolated from able-bodied studies [22]. In particular,
we encoded intact-leg torque-angle curves for two different
walking speeds, 0.5 and 1.75 m/s, on bidimensional (2-D)
lookup tables (LUTs). Each joint and subphase of stance has

GRF < 5% BM

Lifting

Standing

GRF > 5% BM
Shank
< 10°/s
Speed

Walking
Late
Stance
(III " IV)

Shank Angle > 5°
Ankle Velocity < 0°/s
III

Midstance
(II " III)
Ankle
Velocity
> 0°/s

GRF
< 5% BM
IV
Swing
(IV " I)

Shank
> 10°/s
Speed

GRF > 5% BM

Early
Stance
(I " II)

Figure 3. The finite-state machine. Able-bodied ankle quasistiffness is
shown in the center of the figure; ideal transitions are indicated with
roman numerals (I, II, III, and IV).

a different 2-D LUT that inputs the current joint angle and
walking-speed estimate and outputs the desired joint torque
normalized by the BM of the patient. A specific torque-angle
curve for any possible value of walking speed and angle is
then obtained by interpolation. Saturation occurs for input
values outside the LUT boundaries. Figure 4 shows the
torque-angle curves embedded in the 2-D LUTs for the
ankle and knee joints; different colors represent subphases of
December 2014

IEEE ROBOTICS & AUTOMATION MAGAZINE

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2014