IEEE Robotics & Automation Magazine - December 2017 - 69

ground when walking and performing other functions. This
section outlines the details for calculating the desired trajectories, exploiting the described toe-off action.
Design of Swing Leg Trajectory
To increase the flexibility of the walking gait, we designed the
swing-leg trajectory in task space, making it a function of
Cartesian waypoints. We defined four Cartesian waypoints
with corresponding spatial velocities, as illustrated in Figure 3:
the starting and desired ending locations (the red dots) and
two middle waypoints (the blue dots). The two midpoints are
defined at a tuneable percent of the step length, %l s, f , %l s, b,
and a desired swing height, h s, in Figure 3. These parameters
are then selected, for both normal walking and stair ascension, heuristically through testing. We then use inverse kinematics to solve for the necessary hip and knee angles and
velocities at the waypoints that begin each step, and we set
these as the boundary conditions for minimum-jerk joint
trajectories. This allows the step parameters to be changed
online and incorporated at the next step. Stance-leg trajectories are additionally generated to straighten the knee and
rotate at the hip and ankle to move the pilot forward during
the step, as illustrated by the gray leg silhouette in Figure 3.
This approach for calculating swing-leg joint angles was
used for all the tasks in the Cybathlon, from walking on flat
ground to stairs to slopes. By defining the trajectories in this
fashion, changing step lengths and times did not require additional effort beyond changing the final goal position and the
total trajectory time. Not only did this ease the development
effort when the pilot was learning to use the exoskeleton, but
also it accelerated the training process, as all tuning could be
performed online rather than through code changes. Additionally, only one code module was required to calculate joint
trajectories, rather than separate code for each different Cybathlon task.
Design of Transfer Trajectory
In natural, able-bodied walking, ankle plantar flexion is used
to inject energy into the system, starting at the end of the
swing phase and continuing through transfer [15]. To more
closely emulate this, we introduce a toe-off motion during a
short transfer phase at the beginning of every step. This
motion consists of commanding a minimum-jerk trajectory
that ends at a certain angle to the trailing ankle during transfer.
This corresponds to a change in the leading-leg hip flexion as
the body rotates about the leading ankle [see Figure 4(a) and
(b)]. An additional, fast toe-off motion is added at the beginning of the swing phase to impart an additional impulse to the
system, as shown in Figure 4(c).
While the powered ankle does not necessarily enable
dynamic walking equivalent to that of an able-bodied individual, it does provide several benefits. Energy injected by the
powered ankle effectively reduces the amount of additional
"pushing" with the upper body required by the pilot during
walking, potentially decreasing the overall required exertion.
While there are ways to equivalently inject this energy with-

out a powered ankle, such as first bending the leg and then
quickly straightening it, these are undesirable as they move
further away from natural walking gaits. Moreover, a powered
toe-off motion reduces the required crutch force by moving
the pilot kinematically into a more advantageous position to
both begin and to continue walking. We plan to analyze these
effects in more detail in future work.
This toe-off motion worked quite well, helping the pilot
when continuously walking and providing considerable assistance when starting from rest. This is a common situation, as
the lack of hip internal/external rotation requires a "skidsteer" style of ambulation that requires frequent pauses to
reposition. In the Cybathlon, the stepping-stone task, in
particular, was aided by the powered toe-off motion, as the
need for precise foot placement required stopping between
each step, resulting in a long stance length that needed considerable effort on the part of the pilot to resume walking.
Design of Stairs Trajectory
To make stair ascension easier for our pilot, we designed joint
trajectories to capitalize on the powered ankle plantar flexion.
Uniquely, our approach did not take steps one at a time, as
other exoskeletons typically do, instead stepping with only
one foot on each step.
Our approach for stair ascension is outlined in Figure 5.
Between steps, the hips are positioned evenly between the
feet and then moved directly over the leading ankle before
stepping up, as shown in Figure 5(a) and (b). The goal is to
move the center of mass directly over the leading ankle,
making balancing easier for the pilot, and also to have all of
the actuator's work go into raising the center of mass. This

%ls,b

%ls,f

Figure 3. An illustration of the swing trajectory plan. The
calculated midpoints and endpoints are shown by the blue
and red dots, respectively. The stance leg is shown by the light
gray silhouette. The necessary joint positions and velocities are
computed at each of the waypoints.

(a)

(b)

(c)

Figure 4. An illustration of the toe-off motion used during
transfer with a time-lapse shown by (a)-(c).

DECEMBER 2017

IEEE ROBOTICS & AUTOMATION MAGAZINE

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2017