Novel Design of Biped Robot Based on Linear Induction Motors
José-Luis Peralta, Tomi Ylikorpi, Khurram Gulzar, Peter Jakubik and Aarne Halme
Helsinki University of Technology, Finland, [email protected]
Abstract—This work reports the preliminary results on a
new design concept for bipedal walking robots. The concept is
based on the actuators (Linear Induction Motors), and the
prospect that these actuators provide to combine passive
dynamic walking with active walking. Comprehensive
mechanical and dynamic simulations were done to decide the
suitable parameter for the actuators and the mechanical design.
This paper presents results from the early stages of the
actuators simulations until the preliminary result on
equilibrium control tested in the real robot. These results show
promising outcome on the use of these actuators for more
complex equilibrium control and walking algorithms. The
energy consumption is a key factor for further consideration of
this actuators and design approach.
H
I. INTRODUCTION
UMANOIDS and bipedal walking robots have been a
subject of research since early 70s [1]. In addition,
improvements in computer technology in the last fifteen
years have resulted in a huge increase in research and
advances in this area [2], [3]. The applications have varied
from robots for entertainment [4] to knowledge for the
restoration of damaged human locomotion [5]. So far almost
all the solutions for bipedal walking that have actually been
implemented in hardware are mainly ZMP walkers or static
walkers. Static walking is a very old technique that views
the walking as a rigid and defined sequence of events,
meaning that it concentrates on placing the legs in the right
place at the right time according to a predefined algorithm
[6]. Here, however, the dynamics of the robot are neglected
and only static forces are considered. This brings the need
for the projection of the robot’s centre of mass to fall into
the supporting area of the feet, restricting the naturalness and
velocity of the movement.
A better approach to bipedal walking came later with the
idea of the dynamic walking. Here some aspects of the
dynamics of walking are considered but approximated. In
this approach the projection of the robot’s centre of mass can
leave the supporting area of the feet. However the forces and
momentums acting in the robot should be controlled in such
a way that at least one foot always remain flat on the ground.
The previous is commonly called the ZMP (Zero
Momentum Point) approach [7]. Most of the modern robots
[2], [3], [4] use this technique to accomplish walking.
Nonetheless the goal in this technique, as we see it, should
be the total control of the robot’s dynamics, to plan the
correct placing of the ZMP. Most of the robots instead use
predefined patterns for moving each joint, which results in a
dynamic walk, and latter control the resulting ZMP to be in a
restricted area of stability, with adjustment done basically on
the hip movement. The main problems with these previous
mentioned techniques are related to energy and dynamic
locomotion.
An alternative to the previous would be to build robots
that walk more naturally and efficiently in terms of energy
consumption. This leads to a new wave of passive dynamic
walking solutions [8], [9], where a natural gait is obtained
from a simple mechanical design which takes its energy only
from gravity to walk down a slight incline. If the lengths and
masses of the links are correctly adjusted, a simple
pendulum motion is enough to produce very fluid and
human-like walking when the system reaches the limit cycle.
The advantage of this system is that it consumes minimal
energy and requires no controller, however, the plain
mechanical skeleton cannot perform any other task (poor
versatility for robotic usage). So what has been the recent
focus of attention is to try to find the means of reconciling
passive and a controlled dynamic aspect in the same system
[10].
In our project the focus is on the research of a low
consumption and high mobility biped service robot, where
suitable actuators and control techniques must be developed
and merged. In this work a novel electrical actuator is
implemented to bring together both techniques which should
allow passive dynamic walking and active walking to
perform at its optimum when needed. Both, theoretical and
experimental methods are used. Experimental result data
were already gathered from our first robot prototype (Fig.1).
The first results indicate a promising use of these actuators
as well as design approach [17].
Fig. 1. LIM actuated Biped Prototype standing by itself.
II. ACTUATORS’ SIMULATIONS AND TESTS
The major task to successfully implement efficient
dynamic walking is to overcome the current limitations in
the actuators. There are three basic principles [11] on how to
save energy in a walking machine: by minimizing
dissipative losses (e.g. inefficiency of power transmission),
by minimizing the diversion of energy into unproductive
forms (such as the kinetic energy of limbs), and by
recovering energy whenever possible. Until now mainly
rotational motors have been used to drive the robot’s joints;
however, their gearbox reduction, needed in this case to
reach the desired torque in the active phase, does not allow
the free natural movement of the swinging leg in the passive
stage of walking. Because of that much energy is wasted in
the continuous position control of the leg in both phases.
Our hypothesis is that the correct choice of actuators and
control technique can allow us to significantly reduce the
energy consumption.
In our biped robot, linear induction motors (LIM) are used
as actuators. They do not have gear boxes and for that reason
nothing breaks the natural movement in the passive phase of
the leg’s trajectory. Also, they can be easily controlled by
torque because of its direct force/current relation thus
avoiding the overuse of position control. In addition, a four
quadrant driver will be included so that the motors can be
used as generators to break the acceleration in a downhill
walk (regenerative break), and store energy for later use.
Several other attempts at developing more efficient bipeds
have been made [12], [13], [14]. Some of them rely on linear
actuators too, but only pneumatic and hydraulic linear
actuators have been used for that goal until now. The
problem with both (pneumatic and hydraulic actuators) is
that even though the forces and torques obtained are quite
large, they require the use of compressors or pumps which
do not allow total autonomy of the robot for large
torques/forces. The other drawback is that they cannot work
as efficient generators to restore energy into the system;
LIM do allow this feature. Other approaches make use of a
complex mechanical design based on rotational motors and
elastic elements [12], however they can achieve limited
torque (restrictive heavy load applications) and the
mechanical design is more complex. Our design concept
targets both, portability and direct and simple torque control
for heavy load applications.
A. The Linear Inductive Motor
The motors used in our robot are linear direct drives for
highly dynamic motions. They are from the LinMot vendor,
and fabricated of just two parts, the slider and the stator.
These motors are in essence permanently actuated
synchronous servo motors, with integrated position
measurement (non-contact magnetic field sensors).
Permanent magnets in the slider (like a rotor) and windings
in the stator are used to generate forces, like in a brushless
rotary motor. The slider and the stator are not connected by
brushes or cables and the configuration and different
arrangement of the magnets generate the linear motion
directly, using electromagnetic force, without the wear
associated with mechanical gearboxes, belts, or levers.
The previous design characteristics allow these motors to
achieve highly dynamic values, reaching acceleration of well
over 200 m/s2 and travel adjustable speed within a range of
0.001 m/s to over 4 m/s, allowing cyclical motion sequences
of several Hertz, which are higher than human muscle
bandwidth (~2.2 Hz) [15]. Also one of its main interesting
features, given that our goal is to accomplish a force/torque
driven walking algorithm, is the adjustable force for
programmable press and pulling operations. The motors are
freely positionable with no mechanical end, and they can
play along the entire stroke. However such liberty in the
stroke leads to a non even force constant, given that different
numbers of windings are generating the flow for different
strokes.
B. Motor Model
Initially an approximated dynamic and kinematics model
of the biped robot was developed on MATLAB/Simulink
with SimMechanics and VirtualReality ToolBoxes. This
simulation models the biped with 13 DoF (Fig. 2). The main
purpose of this simulation was to verify the requirements for
the motors’ torque in each joint, which were then compared
with the maximum torque/force that could be obtained with
the LIMs available. This simulation did not include the
kinematics and dynamics of the LIM, instead it just
calculated the torque needed based on reaction forces in the
joints. Different sizes, lengths and weights for the limbs
were tested in this simulator under a ZMP-based trajectory,
generated for each joint [16]. Finally a human size bipedal
robot was developed. Based on it, a corresponding torqueforce transformation was obtained and considered for the
next stage of the design.
Fig. 2. Preliminary kinematics and dynamic simulation in MATLAB.
Force (Newton)
Current (Amps)
Position (mm)
PARAMETERS
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.3
0.35
0.4
0.3
0.35
0.4
0.3
0.35
0.4
Motor Current Input
20
10
0
0
0.05
0.1
0.15
0.2
0.25
Position Silder
100
Velocity (m/s)
TABLE I
MOTORS PARAMETERS
Force Input
0
-200
-400
-600
0
50
0
0
0.05
0.1
0.15
0.2
0.25
Velocity Slider
2
0
-2
0
0.05
0.1
0.15
0.2
Time (s)
0.25
Fig. 3. Motor 1 simulation for a 585 N pull force at 72 [Volts].
Maximum Stroke
Stroke SSa
Peak Force
Force Constant
Maximum Current @ 72 V DC
Maximum Velocity @ 72 V DC
Phase Resist. 25/80 °C
Phase Inductance
Thermal Resistance
Slider Mass
Thermal Time Const.
(mm)
(mm)
(N)
(N/A)
(A)
(m/s)
(Ohm)
(mH)
(°K/W)
(g)
(sec)
a
Shortened Stroke (Constant Region).
The next stage was the electromechanical modelling of
the LIM, done also in MATLAB/Simulink. This model
evaluates the power requirement for the LIM sizing,
checking the current and voltage values needed to obtain a
determined force output. The maximum force output
allowed was set by a linear (approximated) transformation of
the maximum torque obtained in the previous simulator.
Two different motors sizes were selected to be used in
different parts of the robot. Their maximum values of force
output were 585 N and 255 N. For these forces the voltage
and current values were observed to remain under the range
of 72 V and 15 A. Finally, proper parameters were attained
and they are presented in Table 1. Fig. 3 shows the related
simulation for the selected parameters of Motor 1.
C. Biped Motion Profile Simulation
Once the maximum static torques were tested and
approved, a dynamic evaluation of the biped walking motion
profile was done. The motion profile was attained from the
results of the previous 3D ZMP walker simulation. This
motion profile was later tested under different leg and shank
weights. Here the vendor’s sizing simulator was used and as
before a linear approximation was applied to convert the
angular values to linear movement.
Fig. 4 presents the graphical result of a 4 sec. simulation
for the hip movement in a ZMP walking with a velocity of
4.1 km/h. This test presents the measurements of the leg’s
motor (hamstring muscle, Hip-Leg pitch DoF), considering 8
kg of the leg’s own weight (leg) plus 8 kg of load weight
(shank). Numerical results are presented in Table 2. A
similar test was made for the shank’s motor (quadriceps
muscle, Leg-Shank pitch DoF), assuming 5 kg load (security
margin) plus 6 kg of the shank’s own weight. The result can
be seen in Fig. 5 and Table 2. It must be clarified that this
test does not represent an actual walking simulation, instead
is uses the angles trajectory of the walking motion profile to
simulate the motor hanging and lifting a specific weight. The
angles are changed into stroke movement and the simulation
runs as if the stator was hanging from an imaginary grip and
the slider moves up and down lifting the weights according
to the stroke profile.
Fig. 4 Simulation results for thigh motion profile.
Fig. 5 Simulation results for knee motion profile.
Motor 1
Motor 2
180
30
585
39.0
15
1.7
3.1/3.7
3.1
1.1
1460
3000
120
40
255
17
15
3.9
2.35/3.2
1.6
3.2
510
3100
PARAMETERS
Zero Position
Start Position
Load Mass
Mounting Angle
Dry Friction
Min Stroke
Max Stroke
Total Stroke
Peak Velocity
Peak Acceleration
Peak Force
RMS Force
Peak Supply
Mean Supply
Mean Regeneration
Actual Power Dissipation
(mm)
(mm)
(g)
(deg)
(N)
(mm)
(mm)
(mm)
(m/s)
(m/s2)
(N)
(N)
(W)
(W)
(W)
(W)
Motor 1
Hip traj.
65
0.711
8000
-90
5
-33.04
33.04
66.08
0.4
7.33
-217
177
130
83
0.7
81
Motor 1
Knee traj.
65
41.5
6000
-90
5
-41.5
41.5
83
0.92
-21.4
-388
141
460
76
2
64
magnets, the ZP is also the point which the slider finds itself
in steady rest when no current is applied, so this should also
be thought of as the equilibrium position.
Motor Force vs. Stroke Profile
600
500
400
Force (N)
TABLE II
MOTION PROFILE SIMULATION RESULTS
300
200
100
0
-20
0
20
40
0
This test is done using PID for positioning control and
with no current limitation apart from the maximum allowed
(no torque/current control applied here). For this reason and
also because the trajectory are generated from a ZMP
walking pattern, this result should be interpreted as the worst
case scenario and not the energy efficient case. Later the
same experiment was performed with the real motors with
the parameters shown in Table 1. The stator was fixed
hanging in -90 degree angle and with the slider lifting a 9.5
kg weight. Fast sinusoidal motions were applied and high
currents were observed, however no overheat or failure of
the system was detected. Based on the earlier results these
motors were selected to build the first prototype.
It is important to observe that much energy is required for
the knee locking and holding, as shown in Fig. 5. Therefore,
an efficient design has been developed for the knee locking
system.
D. Mechanical and Functional Considerations
After deciding to use the previous actuators some
mechanical and functional consideration must be taken into
account to support the design concept. One of the most
important issues is the non even force constant of the LIMs.
Fig. 6 shows the actuators force versus stroke profile and
mechanical configuration of motor 1. In this figure it can be
seen that there is a segment called the Shortened Stroke (SS)
where the force constant is invariable, however, in the
remaining stroke segment, there is a linear decay of this
factor. This linear damping, as mention before, is given so
that different numbers of windings are generating the flow
for different strokes distances. This profile then should be
taken into consideration carefully when designing the
mechanics, trying to match the symmetry of the human
walking with the symmetry present in the torque output of
these actuators. This position around which the stroke is
symmetrically carried out is named the Zero Position point
(ZP). In addition because the sliders are basically permanent
100
120
140
160
ZP=65
50
Numerical results for Motor1 Hip and Knee, with supply voltage of
72V and ambient temperature 25 ºC.
60
80
Stroke (mm)
80
SS Stroke 30
-25
Max. Stroke 180
155
Fig. 6 Motor force vs. stroke profile and mechanical configuration.
Fig. 7. Kinematical sketch of preliminary prototype robot in IDEAS.
III. MECHANICS DESIGN AND SIMULATOR
A preliminary prototype design and simulator were
developed, based on the previous choice of actuators, to
identify the mechanical constraints and physical properties
of each part of the robot. The mechanical design was done in
IDEAS software and later exported to ADAMS, which was
controlled in co-simulation by MATLAB/Simulink for the
kinematics and dynamics analysis.
There are springs and dampers in each ankle sideways
motion joint to allow foot alignment with the floor but there
is no actuator for ankle motion in this direction.
Furthermore, the effect of contact parameters between feet
and floor had a strong effect on model behaviour.
The following simulations and results are based on one of
the first designs which include bigger feet and not much
detail on the upper body weight distribution (Fig. 7). Fig. 7
also shows the CoM of the 3-Link planar approximation of
the robot, which is used to perform passive walking gait
analysis for the future development of energy efficient
algorithms. Several tests were done in this simulator
including some ZMP approaches for energy consumption
comparison. Also important data were obtained for
manufacturing drawings that were changed afterwards.
IV. ENERGY ANALYSIS IN THE SIMULATOR
The latter simulator, in contrast with the first one,
includes the kinematics and dynamics of the LIMs, which
allow us to perform analysis directly in the force interaction
between the motor’s stator and slider. This linear force is the
controlled variable for which was initially developed a PIDtype of algorithm to perform position control. It must be
mentioned that this is not an energy efficient algorithm, and
the goal of this simulation is to evaluate the energy
consumption in the upright equilibrium position and perform
the required adjustment to the prototype.
In the simulation the inputs are the joint angles. All the
angles are constant except the roll angle for the hip joints.
The roll angles of the hip joints are sinusoidal inputs, which
gives as result a sideways movement around the equilibrium
position. The robot starts from the equilibrium position a
few millimetres above the floor, to avoid singularities in the
initial states. This initial position is responsible for the
oscillations in the motors’ forces shown in Fig. 8, given that
the robot basically falls a couple of millimetre before
starting to control its position. It can be observed from Fig. 8
that the robot uses almost no force from the shin (quadriceps
muscle) and thigh (hamstring muscle) to maintain the
upright equilibrium position after the transit period.
However the knee motor does show some enduring constant
force to maintain the robot in the equilibrium state and that
was one of the issues addressed in the new design, where a
proper knee locking system was developed.
Fig. 9 shows the torques applied to achieve position
control for the sinusoidal input on the outer thigh joints.
These torques falls among the limits for the motors’ torque.
V. EXPERIMENTAL RESULTS
The same test was performed in the real robot. Fig. 1
shows our first prototype. This prototype slightly differs
from the simulator in the previous sections. It has smaller
feet and restricted movement in the ankle roll DoF, which
also does not have any springs or dampers. The prototype
has a simple but very proficient design for the knee locking
system, which allows energy efficient use of the knee
motors. The total weight of the robot is about 65 kg and for
now obtains it’s energy from an outside source. In the future
a battery pack will be included with the robot.
The test, similar to before, consists of calculating the
energy consumption around the equilibrium position.
However here, outside oscillatory forces are applied on the
robot (instead of the sinusoidal input in the hip’s angle
reference), which takes the robot out of the equilibrium
position. The analysis is then performed on the energy,
forces and time required to drive it back to the stable
position. The types of movement tested were: font and back
swinging (pitch movement) and sideways sway (roll
movement). There is no further feedback from the robot
apart from the motors’ encoders and current sensors, and
that is why no further equilibrium algorithms and analysis
are presented here. A complete sensor infrastructure
especially designed for this robot is under development.
Position control is used to drive the robot to equilibrium and
current control is then applies to decrease the energy
consumption. Fig. 10 shows the right and left waist’s results
under sideways sway movement and it can be seen how the
position control on the equilibrium point is achieved and that
the energy consumption tends to zero. The same can be
observed in Fig. 11 for the right and left shank’s motors
under front and back swing movement, where again the
position error tends to zero together with the energy
consumption.
VI. CONCLUSIONS AND FUTURE WORKS
It has been shown with simulation and experimental
results that LIMs have promising applications in biped
robots. They can successfully reach the necessary torques
and at the same time are compliant for limit cycle algorithms
applications. They also allow regenerative breaking and
energy harvesting.
Our prototype is still under development, and further
work in walking algorithms should be undertaken based on
additional sensor feedback. Energy efficient method seems
to be suitable with the current prototype but more advanced
equilibrium and walking algorithms should be addressed.
Our initial approaches include dynamic programming and
trajectory optimization to drive the robot into the desired
limit cycle. Changes in the prototype may consider a more
proficient ankle with springs and dampers and lighter motors
to ease the load of the shank and also a different type of feet.
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Demand Pos.
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81
80.5
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41
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39
78
38
77.5
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4
5
6
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8
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10
11
12
37
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200
50
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-50
-100
5
6
7
8
9
10
11
12
-400
13
4
5
6
7
8
Actual Position vs Demand Position
Position (mm)
Position (mm)
77
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76
Actual Pos.
Demand Pos.
42
41
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4
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7
8
9
10
11
12
38
13
4
5
6
7
8
9
10
11
12
13
10
11
12
13
Time (s)
Energy Consumption
200
Energy Consumption
300
150
200
100
100
Power (Watts)
Power (Watts)
13
43
Time (s)
50
0
-50
0
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-200
-100
-300
-150
4
5
6
7
8
9
10
11
12
13
Time (s)
Fig. 10 Right and left waist’s motors results for position control and
energy consumption under sideways sway movement.
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Actual Position vs Demand Position
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75.5
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77.5
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0
Actual Pos.
Demand Pos.
78
[9]
13
-300
4
78.5
-200
12
-100
Time (s)
74.5
11
-200
-150
-200
10
Energy Consumption
300
100
Power (Watts)
Power (Watts)
150
9
Time (s)
Time (s)
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