Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:The design of the exoskeleton. Monograph
.pdf
31
In General, the human foot is considered as a structure with seven
degrees of freedom. Three rotational degrees in the thigh, one in the knee
and three in the ankle. Figure 1.14 shows the human anatomical plane and
the kinematic model of the human foot in the sagittal (middle) plane, which
is the main plane of human movement. In figure 1.14 it is indicated:
Coronal plane – frontal plane, Saggital plane – sagittal plane, Transverse
plane – horizontal plane.
Figure 1.14 - A – human anatomical planes; B – kinematic model of the
foot in the middle (sagittal) plane
Thus, the movement in this plane in the positive direction – bending,
and in the negative – extension. The movement of the hip in the coronal
(frontal) plane is referred to as a diversion (from the center of the body)
and bringing. In addition, the movement of the ankle in the coronal plane
is referred to as inversion (from the center of the body) and inversion. The
remaining degrees of freedom of the thigh and ankle are simply called
"rotational".
Figure 1.15 shows biomechanical data for a normal, healthy person
(82kg, 0.99 m – leg length, 28 years old, male) walking at a speed of 1.27
32
m/s and indicates: Joint Angle/Moment/Power – angle/moment/power of
the joints in question (Hip-thigh, Knee – knee, Ankle – ankle).
Figure 1.15 – Angles, moments and strength of leg joints during
flexion/extension
Walking data may be slightly different for different people and
conditions, but the quality of the data remains the same.
33
These data are useful for understanding the amount of power
consumed by each joint of exoskeletons and active corsets. From the gait
data, it can be seen that, in particular at low speeds, the power at the hip
is positive or close to zero, the force at the knee is predominantly negative
(dissipates power), and the force at the ankle is evenly distributed between
positive and negative values.
1.5. Exoskeleton control structure
Consider the overall architecture of the control system. To provide
control tasks, the system has three auxiliary lower-level regulators [3]:
1) high-Performance torque regulator that allows you to take your foot
off the ground while flexing your ankle.
2) resistance Regulator to determine the stiffness (immobility) of the
joints during the support phase)
3) position Controller to control the position of the foot during the shift
phase (swing phase)
In addition, it is necessary to have a high-level control system to
control the transitions between the auxiliary regulators of the lower level,
which will provide the necessary functions in the given conditions. The
complete architecture of the control system is shown in figure 1.16, which
indicates: Final State Machine – finite state machine, Low-level Servo
Controllers – lower level regulators, Impedance Controller – resistance
regulator, Force Controller – force controller, Position Controller – position
controller, Power Amp – power amplifier.
34
Figure 1.16 – control system Architecture
The control system consists of three auxiliary low-level regulators and
a state machine. The state machine consists of two parts: the identification
state and the control state. The first part is used to determine the current
position of the foot, and the second part to perform a predefined control
procedure for this state.
The auxiliary controllers of low-level
The torque control: this controller was designed to provide the offset
torque and facilitate the stiffness modulation. The regulator consists of an
internal power and torque control circuit, and a friction compensation
circuit. The regulator is presented in figure 1.17, where indicated: τd is the
desired torque, τs is the measured torque, Force, Controller, power
regulator, Motor Amp, Ka – amp motor, im is the motor current, Friction
Compensation Feedforward – loop friction compensation.
35
Figure 1.17 – torque Regulator
The main idea of the internal circuit is to use force feedback, taking
into account the deflection of the springs to control the output torque. The
torque/force regulator D(s) is implemented on the basis of the PD
controller in the s-region and is presented in the formula (1.1):
, (1.1)
where e and Vm are the output torque error and the input voltage of
the motor amplifier respectively. KF is the proportional gain, and BF is the
attenuation coefficient of the control law.
Pole filter was included in the controller, since the measured signal
strength s+p has interference in the form of noise and they must be filtered
before using them in the future. The poles p of the regulator are selected
so that the cutoff frequency reaches 30 Hz.
Although an increase in the KF gain can obscure the wave resistance
(such as friction or inertia) in the mechanism, it can cause instability when
the system connects to the environment at a high gain. One way to
increase the torque regulator without violating the stability criteria is to use
the Fr (s) friction compensation model. Friction compensation is defined as:
, (1.2)
36
where and are constant Coulomb's force and a damping factor.
All these parameters were determined using experimental data. To obtain
the friction parameters, we set the ankle angle to zero. Friction in the ankle
joint is negligible compared to friction in transmissions. We used a known
linear variation of the motor input power for the system and measured the
spring compression. The Coulomb friction force was derived from the
difference between the known motor input force and the measured spring
compression. We then used different frequencies of sinusoidal motor
power to the system to obtain the system frequency, and then used the
obtained data for the model without taking into account the saturation of
the motor to obtain the attenuation coefficient. The Coulomb force
constant and attenuation coefficient used in the regulator were 0.03 V (23
N) and 1.64 V • s / rad (1240 Н • s / rad), respectively.
Regulator resistance the Regulator resistance was designed to ensure
the output impedance of the SEA (series elastic actuator), especially the
stiffness of the joints. As shown in figure 1.18, an external resistance
adjustment loop [Zd (s)] is introduced to the proposed force regulator to
modulate the output resistance. The external control loop was based on
the "simple resistance control" structure proposed by Hogan. The key idea
was to use feedback from ankle movement to increase the output
resistance of the joints. Figure 1.18 marked with: Zd(s) is the desired value
of the resistance, τ – is the offset torque.
37
Figure 1.18 – resistance Regulator
The external impedance regulator is defined as:
(1.3)
Where , and are the desired values of sea joints for torque,
stiffness and damping respectively.
Due to internal resistance (e.g. friction and inertia), the actual output
resistance consists of: the required output resistance of the regulator plus
what is required by the mechanism. For this reason, the aforementioned
torque controller was incorporated in a controller of the resistance, to
reduce the effects.
Position controller: a standard PD controller H (s ) has been proposed
to control the equilibrium positфion of 1 foot during the leg shift. The
position controller is shown in figure 1.19, which indicates: Desired Position,
d – desired position, Position Controller, H(s) – position controller.
38
Figure 1.19 – position Control
Thus, the input voltage Vm (s) to the motor amplifier
, (1.4)
where K1 and K2 are proportional and differential gain.
Summary
The analysis of open sources showed almost complete absence of
developments in the field of construction of high-precision models of
active exoskeletons, which take into account the relationship of the
dynamics of links, as well as features of modern electric drives.
At the same time, developments in the field of biomechanics of
walking are widely represented in the scientific and technical literature.
39
2. ACTUATORS OF THE EXOSKELETON
2.1. Mechanical design of the five-stage exoskeleton
2.1.1. Subject and methods of research
The applied task of controlling walking robots can be found in many
areas of human activity: robotics, transport, medicine.
A striking example of walking robots is an exoskeleton. Exoskeletons
are one of the most effective devices to compensate, restore or enhance
the motor ability of a person. Their effectiveness is largely determined by
the success of the solution of two scientific and technical problems:
1. Obtaining a detailed mathematical model of the dynamics of the
exoskeleton, taking into account:
• the interrelatedness of the movements on the axes
• interdependence of electromagnetic and mechanical processes in
drives
2. Construction of exoskeleton control taking into account the
peculiarities of its dynamics
This Chapter discusses a model of the dynamics of the five-stage
exoskeleton, which can be used to reproduce the dynamics of human
walking, which, in turn, will make it possible to build an effective
management of exoskeletons.
Figure 2.1 shows the model scheme of the two-legged exoskeleton,
where ψ is the angle between body and vertical; αi - angles between thighs
and vertical; βi – the angles between the shins and the vertical; , control
points that are considered as internal efforts; R1, R2 is the external force
applied to the ends of the legs. This model contains rigid inertia elements:
a body and two identical legs. Each leg has two degrees of mobility – thigh
and Shin.
40
Figure 2.1 – Model and schema bipedal exoskeleton
We introduce the following notations:
, , – weight of the body, thighs, lower legs;
, , – length of the body, thighs, lower legs;
, , – distance from the hip joint, knee joint to the center of mass
of the body, the center of mass of the thigh, the center of mass of the
tibia; , , – the moment of inertia of the body of the femur, tibia; g –
acceleration of gravity;
Let OXYZ be a fixed rectangular coordinate system.
We assume that the exoskeleton moves along the OX axis in the OXY
plane.
The exoskeleton under consideration has five degrees of freedom.
Choose
vector of generalized coordinates q = [ψ, α1, α2, β1, β2] – angles that
form links with the vertical.
Y
X
O
Y
X
O
ψ
α
2
α
1
β 1 β
2 R 1 R 2
u
1 u 2
k 1 k
2
N
B
1
B
2
A
1 A 2
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]