IEEE Robotics & Automation Magazine - March 2016 - 42

0.8

Simulation Without
Actuator Model
Simulation With
Actuation Model
Experiment

0.7
Height Over Ground (m)

completely autonomous (onboard power and computation) during all these maneuvers.

0.6
0.5
0.4
0.3
0.2
0.1

Gearbox Velocity (rad/s)

0

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Time (s)
(a)

5

1

HFE

0
-5

Gearbox Velocity (rad/s)

-10
10

0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
KFE

8
6
4
Measured (Simulation)
Desired (Simulation)
Measured (Experiment)
Desired (Experiment)

2
0
-2
0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Time From Start Until Take Off (s)
(b)

100
90
80
70
Cost

60
50
40
30
20

Sample
Optimal Sample

10
0
0

50

100
150
200
Number of Iterations
(c)

250

300

Figure 8. The results of a vertical jump. (a) The height trajectories
of torso and foot. (b) The gearbox velocities during the launch phase.
(c) The convergence of the cost.

42

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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march 2016

Periodic Gaits
The sampling-based method successfully tuned 18 control parameters for trotting, bounding, and pronking gaits
in simulation. Due to reasonably good accordance of the
model, the parameters could be directly used on the real
platform. The found gait patterns and some snapshots of
the real robot performing these gaits are shown in Figure 4 (video: http://youtu.be/Tj1wreifYhU). A time series
of snapshots is shown in Figure 5, which captures two cycles of a pronking gait.
The proposed controller is robust enough to deal with
unperceived obstacles up to 10% of the leg length (video:
http://youtu.be/Wuc7mL0hkGo), as well as with external
pushes up to 100 N, as shown in [7].
Furthermore, the terrain estimation together with the
adaption of the control signals to the modeled ground plane
allowed StarlETH to trot on slopes (video: http://youtu.be/
NPuHwxpVUpg) with an angle of up to 21° (38%), as
shown in Figure 6. A 360° turn on the slope verified that the
slope estimation works as intended [16].
We want to particularly highlight here that we were
not able to find control parameters for highly dynamic
gaits by hand despite significant effort and extensive experience (and, hence, intuition) with the machine. However, the optimization approach helped to find a feasible
set for more dynamic gaits, such as a running trot, pronk,
and bound.
High-Dynamic Maneuvers
A sequence of the optimized vertical jump (video: http://
youtu.be/aEsxLN9CnyE) is shown in Figure 7 (video:
http:// youtu.be/aEsxLN9CnyE). The robot's main body
reached the apex height of 0.76 m, which corresponds to
150% of the leg length.
The height trajectories of the torso and the left forefoot are shown in Figure 8(a). The torso height was measured by an external motion capture system (Optitrack),
whereas the foot height measurement is based on the
state estimation.
To generate this high-dynamic jump whereby the motors encounter several saturation effects, it was particularly
important to have an accurate actuator model. As a result,
the trajectory, which was optimized in simulation with the
actuator model, comes close to the trajectory of the real
robot. If the same optimized desired trajectories are applied in simulation without the actuator model, the simulated robot jumps significantly higher than StarlETH.
Good agreement between the measured and predicted
gearbox velocities together with the commands from start
until the takeoff of the jump is shown in Figure 8(b).
The convergence of the optimization is shown in Figure 8(c). After 250 iterations with a population of 15 samples, the best ever seen cost was found.
http://www.youtu.be/Tj1wreifYhU http://www.youtu.be/Wuc7mL0hkGo http://www.youtu.be/ http://http:// http://www.youtu.be/aEsxLN9CnyE http://http:// http://www.youtu.be/aEsxLN9CnyE
Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2016
