This paper proposes a control structure to resolve the issue of dynamically stepping over large obstacles in the B4LC control system. We reform the local control units LegSwing, LockHip and KneeF lexion respectively. The optimization module with Particle Swarm Optimization (PSO) method is employed to tune the parameters of those controllers by formulating locomotion stability. The optimization process and further validation are conducted on a 3-dimensional simulated bipedal robot. The simulation results reveal that the suggested approach enables robot to dynamically step over a large obstacle with 20cm height by 15cm width in a short time duration

Jie Zhao

Karsten Berns

Q I Liu

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Dynamically stepping over large obstacle utilizing PSO
optimization in the B4LC system
QI LIU, JIE ZHAO, KARSTEN BERNS
Robotics Research Lab, University of Kaiserslautern,
Kaiserslautern, 67655, Germany
This paper proposes a control structure to resolve the issue of dynamically
stepping over large obstacles in the B4LC control system. We reform the lo-
cal control units LegSwing, LockHip and KneeF lexion respectively. The op-
timization module with Particle Swarm Optimization (PSO) method is em-
ployed to tune the parameters of those controllers by formulating locomotion
stability. The optimization process and further validation are conducted on a
3-dimensional simulated bipedal robot. The simulation results reveal that the
suggested approach enables robot to dynamically step over a large obstacle
with 20cm height by 15cm width in a short time duration.
Keywords: Bipedal locomotion, Particle Swarm Optimization
1. Introduction and related work
To achieve human-like stable bipedal locomotion control in rough environ-
ment, Luksch proposed Bio-inspired Behavior-based Bipedal Locomotion
Control (B4LC) system.1 By transferring some of key findings in biome-
chanics and biology of human locomotion control to bipedal robot, it allows
for various bipedal motions, e.g. changing speed locomotion, cyclic walking
on even terrain and uneven terrain with small obstacles, as well as loco-
motion with external pushes.2,3 However, compared to humans superior
mobility in uneven ground, the B4LC system shows limited capability of
large obstacle avoidance.
Accordingly the state-of-the art on this topic is extensive and still grow-
ing. Michel et al. presented an approach that enables robot to navigate to-
ward desired goal position while avoiding obstacles, whereas limited work
is on the capability of traversing a large obstacle.4 Zhou et al. introduced
a control framework by exploiting the redundancy of pelvis rotation and
generating foot trajectory when encountering large obstacles.5 However,
the static stepping over strategies reveal the limitation of redundant time
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and energy consumption. Further researches have been conducted by Koch
et al. that optimization method provides an efficient way to maintain sta-
bility during quasi-static overstepping motion.6 Stasse et al. proposed an
idea that using zero moment point (ZMP) criterion to prevent falling while
dynamically crossing over an obstacle of 15cm.7 The duration of obstacle
stepping is significantly decreased compared to static strategies. Neverthe-
less, the challenge for those model-based approaches is complex dynamical
models.
To exploit the bipedal robot’s potential capability in unstructured ter-
rain, we concentrate on developing a control approach of dynamically step-
ping over large obstacle. We give a detailed introduction of the B4LC system
and the proposed overstepping strategies. Furthermore, the optimization
module in the B4LC system is utilized to find the optimized parameters of
those local control units.
2. The concept of the B4LC system
As described by Luksch, six classes of control units form a hierarchical
B4LC control structure.1 The highest layer locomotion mode evaluates the
locomotion of robot, e.g. standing, cyclic walking and obstacle walking.
Based on corresponding kinematic and kinetic events, five walking phases
are further stimulated by SPG, which are weight acceptance, propulsion,
stabilization, leg swing and heel strike respectively, as shown in Figure 1. The
feed-forward and feedback control units at the local joints, namely motor
pattern and reflex, will be activated to achieve required control behaviors.
Fig. 1. 5 Phases of locomotion for left and right side. Each phase stimulates the corre-
sponding motor patterns and reflexes at the local joint when the sensory event for phase
transition is triggered.1
Motor pattern produces uniform patterns of torque for one or more joints
in feed-forward manner. According to target gait and speed, it is capable of
forming the inherent dynamics or swinging upper and lower limb to achieve
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certain body motions. Besides, the B4LC provides feedback control reflex
at the local joints to generate reflexive motor actions based on sensory
information. Some reflexes behave linear and nonlinear relation between
sensor data and control output, in contrast, the others generate the control
signals related to the occurrence of sensor event.
3. Overstepping control approach
By studying on biomechanical behaviors, the hip and knee joints play an
important role in obstacle avoidance during leg swing phase. Humans tend
to bend knee joint when moving leg forward. Thus, the swing-leg is lifted
up to reduce risk of hitting obstacles significantly. Additionally, hip joint
of the swing-leg is locked with a large angle at the end of swing phase.
This leads to a large step length assuring obstacle clearance. Inspired by
those behaviors, we intend to develop the obstacle avoidance strategies in
the leg swing phase of the B4LC system, whereas the control behaviors
in the stance phases weight acceptance, propulsion and stabilization are
kept constant. This enables robot to achieve smooth and fast transition
from even ground locomotion to obstacle locomotion without suspending
for redundant preparations.
3.1. Hip strategy
To actively move swing-leg forward after ground clearance, motor pattern
Leg Swing Obs generates desired torques with different amplitude and du-
ration at hip joints in the sagittal plane, which are modulated as:
τ̂ls = Als ·
{ 1
2 +
1
2 sin( π(
t
T1
− 12 ) ) 0 ≤ t < T1
1 T1 ≤ t < T2
1
2 −
1
2 sin( π(
t−T2
T3−T2 −
1
2 ) ) T2 ≤ t < T3
(1)
where Als, T1, T2 and T3 are the parameters of Leg Swing Obs representing
the maximum torque of torque command, the starting time of maximum
torque, the ending of maximum torque and the total time of torque com-
mand respectively.
Two different behaviors can be observed for the first and second mov-
ing leg during overstepping process. To prevent obstacle collision, biped is
expected to achieve fast leg swinging and large hip flexion for the first step.
Accordingly, intensive torques are generated at the hip joint. Whereas, as
the distance from the second moving foot the obstacle is much less than
the first one, there is limited time for knee-bending if large hip torque is
produced at the second swing-leg. It is required that smaller torques are
given to the rear leg’s hip joint to achieve slow leg movement. Consequently,
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we deploy two motor patterns Leg Swing Obs for the front and rear leg re-
spectively with different parameters Af,ls and Ar,ls, as described in Eq. 1.
At the end of swinging phase, the swing-leg is expected to decelerate
and then lock at a constant angle to prepare for a stable weight acceptance.
Thus, local reflex Lock Hip Obs is designed to control the flexion of the hip
joint at the end of swing phase. When the leg approaches a target angle,
a damping torque which is proportional to the rotational velocity of the
thigh is applied at the hip joint until the swinging phase come to the end.
As soon as the thigh velocity become zero, the hip joint is locked with an
target angle α̂lh. The damping torque τ̂lh and target angle α̂lh are:
τ̂lh = (−α̇leg ·Ktorque) · Pτ,lh (2)
α̂lh = (αlh,max + αpitch ·Kpitch) · Pα,lh (3)
where α̇leg and αpitch stand for the velocity of swing-leg and the angu-
lar position of body pitch respectively. Ktorque and Kpitch represent the
parameters of torque factor and pitch factor, which are defined experimen-
tally in.1 αlh,max is a constant parameter denoting the maximum target hip
joint angle. Pτ,lh and Pα,lh are the scale parameters which are defined as 1
during even ground locomotion. To achieving obstacle avoidance walking,
the derived Pτ,lh and Pα,lh values are optimized in Section 4.
3.2. Knee strategy
By studying on human gait, it is assumed that limited knee muscle behavior
appears during leg swing phase of even ground locomotion. Knee joint tends
to bend passively to guarantee ground clearance. However, to prevent large
obstacle collision during overstepping phase, an active control of knee joint
which can be conducted by reflex Knee Flexion Obs is required.
As long as the first leg begins to swing forward, Knee Flexion Obs re-
ceives a target knee angle signal α̂k,kf . As described in Algorithm 3.1, the
reflex increases the activity with the equilibrium point setting to the target
angle α̂k,kf . The activity ranged from 0 to 1, which means that the higher
value leads to a stronger influence of position control. After the target angle
hip joint α̂h,kf is reached, the activity of Knee Flexion Obs is formulated as
zero. Afterwards, the lower leg moves forward freely to stretching position
until the end of the leg swing.
For the rear swing-leg, the reflex defines activity value autonomously
as 1 with the target angle α̂k,kf until the position of foot is higher than
obstacle. As introduced in Section 3.1, smaller torques are generated at the
hip joint to prevent obstacle collision. Thus, it is hard to achieve passive
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rotation of knee joints for weight acceptance. Consequently, the reflex has
to actively control the knee joint by gradually reducing the knee angle and
activity value until knee is stretched.
Algorithm 3.1 Knee Flexion Obs Algorithm
1: if forward leg swing then
2: if αhip < α̂e,kf then
3: αknee = α̂k,kf
4: activity = 1
5: else
6: activity = 0
7: end if
8: end if
9: if rear leg swing then
10: if swing foot not higher than obstacle then
11: αknee = α̂k,kf
12: activity = 1
13: else
14: for knee stretching do
15: αknee ← αknee − 0.1
16: activity ← activity − 0.1
17: end for
18: end if
19: end if
4. Optimization-based obstacle obstacle locomotion
4.1. Particle swarm optimization algorithm
Particle swarm optimization (PSO) method can be used to search the op-
timal parameters in the B4LC system as already demonstrated in.3 The
position of the particle in the searching space is decided by the value of
the parameters in the B4LC system. The movement of a particle is guided
in the direction of the position of each particle and the entire swarm with
best fitness function values in the past iterations. The velocity of a particle
in one iteration can be derived, as described in Eq. 4.
vp = ωvp + c1 ·Rand1( Bp − xp ) + c2 ·Rand2( Bg − xp ) (4)
where vp and xp represent the velocity and the position of a particle re-
spectively. Bp is the known best position of a particle in the past iterations,
while Bg the known best position of entire swarm in the past iterations.
c1 and c2 mean the parameters of the acceleration constants respectively.
Rand1 and Rand2 are the random values ranged within [0, 1]. The inertia
weight ω controls the impact of the previous velocities on the current ve-
locity. The larger inertia weight tends to favor global searching, while the
smaller one leads to the local searching strategy.
The fitness functions summarizing the distance of a given solution ap-
proaching to the objectives are calculated during each iteration. The best
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position of particles Bp and the best position of the entire swarm Bg are
updated by comparing the fitness values. The position of a particle xp is
updated by summing the calculated particle velocity vp in Eq. 4.
4.2. Parameter optimization of obstacle locomotion
An optimization module termed as Optimization Obstacle is integrated in
the B4LC system by connecting the walking phase leg swing and the cor-
responding motor patterns and reflexes.
A 8-dimensional vector ~Pi,t that consists of the parameters of Af,ls,
Ar,ls, T1, T2, Pτ,lh, Pα,lh, α̂k,kf and α̂h,kf represents the position of a
particle in the searching space. To increase the optimization efficiency, the
searching space is constrained in a range based on the experimental studies
of bipedal locomotion, as depicted in Eq. 5.
Af,ls ∈ [0.0 , 1.0] Ar,ls ∈ [0.0 , 0.6] T1 ∈ [0.0 , 0.4]
T2 ∈ [0.4 , 0.9] Pτ,lh ∈ [1.0 , 2.0] Pα,lh ∈ [0.0 , 1.0]
α̂k,kf ∈ [0.0 , 1.0] α̂h,kf ∈ [1.0 , 1.5]
(5)
The positions of each particles are initialized randomly in the searching
space. The fitness function is formulated by considering optimization goals
including robustness, stability and obstacle avoidance in form of:
F = k1Rd + k2Rf − k3Po (6)
where k1, k2 and k3 are the weightings of the fitness functions. Rd is the
reward for the stable locomotion, which is defined as linear to the walking
distance that the robot achieves. Rf indicates the final reward when the
maximum walking steps reaches after successfully stepping over obstacle.
Po represents the punishment when an obstacle collision is detected.
5. Simulation results
The optimization scenario is set up on the 3D simulated robot with 21
degrees of freedom. The robot’s height adds up to 1.8m and it weights
76kg. It is designed to start the optimization process with a stable walking
on a flat ground. The obstacle is modeled as a block with dimensions of
20cm height by 15cm width. As long as the distance from stance foot to
obstacle is less than 40cm, the obstacle locomotion is activated.
Table 1. The parameters of controllers in obstacle locomotion
Parameter Af,ls Ar,ls T1 T2 Pτ,lh Pα,lh α̂k,kf α̂h,kf
Value 0.98 0.38 0.24 0.8 0.06 1.24 0.96 1.15
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The parameters generated by Optimization Obstacle known as the po-
sition of searching particles are fed into the motor pattern Leg Swing Obs,
reflexes Lock Hip Obs and Knee Flexion Obs. The parameters are search
in a 8-dimensional space until all searching particles acquire the optimized
fitness function results. The optimized parameters are shown in Table 1.
To validate the performance of the proposed control system, we conduct
the obstacle locomotion transiting from even ground walking to obstacle
avoidance phase. The angular rotation of hip and knee joint as well as foot
height position are shown in Figure 2, which blue and red areas indicate
the swing-phases of the first and second legs respectively. It is revealed that
the first swing-leg generates large hip and knee angular rotation due to the
intensive activation of Leg Swing Obs and Knee Flexion Obs. Thus, the
biped can easily step over the obstacle in a high speed with the bending
knee as shown in Figure 3. At the time of around 1.5s, the hip joint reaches
the maximum angular position. The activity of Knee Flexion Obs is defined
as zero again resulting in the forward passive rotation of the lower leg.
Fig. 2. The hip angle, knee angle and foot height position in the sagittal plane are
shown. The blue and the red area indicate the overstepping phases of the first leg and
the second leg respectively.
A similar behavior is revealed from the second swing-leg. The knee joint
is bended intensively after foot leaves ground. A smaller peek of hip joint
angle can be observed due to less torques defined by parameter of Ar,ls from
Leg Swing Obs. This leads to a smooth transition between two locomotion
modes. The robot is able to regain stable even ground walking after a
successful obstacle avoidance. Besides, the dynamical overstepping duration
is significantly reduced to 1.5s. The snapshots of successful stepping over
obstacle are shown in Figure 3.
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6. Conclusion
In this paper we described novel obstacle avoidance control approach based
on PSO optimization method in the B4LC system. The optimized param-
eters have been used to conduct torque and position control at the hip
and knee joints during overstepping phases. Thus, the simulated biped can
dynamically transit from even ground locomotion to obstacle overstepping
locomotion freely. With optimized parameters, biped can easily step over
large obstacle of 20cm height by 15cm in a short time duration.
Fig. 3. Snapshots of successful stepping over large obstacle in the simulation.
References
1. T. Luksch, “Human-like control of dynamically walking bipedal robots”, Ver-
lag Dr. Hut, 2010.
2. J. Zhao, “Biologically motivated push recovery strategies for a 3D bipedal
robot walking in complex environments”, Robotics and Biomimetics (RO-
BIO), 2013 IEEE International Conference on. IEEE, 2013.
3. Q. Liu, “Adaptive Motor Patterns and Reflexes for Bipedal Locomotion on
Rough Terrain”, IEEE/RSJ International Conference on Intelligent Robots
and Systems (IROS 2015).
4. P. Michel, “Vision-guided humanoid footstep planning for dynamic environ-
ments”, IEEE/RAS International Conference on Humanoid Robots, 2005.
5. C. Zhou, “Exploiting the Redundancy for Humanoid Robots to Dynamically
Step Over a Large Obstacle”, IEEE/RSJ International Conference on Intel-
ligent Robots and Systems (IROS 2015).
6. K. Koch, “Optimization based exploitation of the ankle elasticity of hrp-2
for overstepping large obstacles”, IEEE/RAS International Conference on
Humanoid Robots, 2014.
7. O. Stasse, “strategies for humanoid robots to dynamically walk over large
obstacles”, IEEE Transactions on Robotics, 2006.


Dynamically stepping over large obstacle utilizing PSO optimization in the B4LC system

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Dynamically stepping over large obstacle utilizing PSO optimization in the B4LC system

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