JKA26-103
報告書
平成 26 年度
転倒防止のための歩行補助機能を有する多脚デバイスの
先鋭機能デザイン補助事業補助事業
平成 27 年 3 月
慶應義塾大学 理工学部 システムデザイン工学科
村上俊之
JKA26-103
はじめに
本報告書では，財団法人JKAの補助を受けて実施した「平成26年度（研究補助）転
倒防止のための歩行補助機能を有する多脚デバイスの先鋭機能デザイン補助事業」
の研究成果をまとめたものである．高齢化社会に向けて，歩行動作を支援する機器の
開発が強く望まれている．特に，転倒防止を行なえる機器の開発に多大な関心が寄せら
れている．現状でも歩行補助のための機器は開発されているが，転倒防止機能を中心と
しているものは少ない．そのため，歩行補助器の操作ミスが原因での転倒やそれに伴う
負傷事例が多く見られる．本来歩行補助を行うべき歩行補助器による転倒は絶対に防が
なければならない事項であり，転倒防止は歩行補助器には必須の機能と考えている．こ
の機能は，虚弱高齢者（特に大きな障害ではなく，体力の低下等で歩行が困難となって
いる高齢者）に対する支援に多大に貢献でき，健康寿命の引き上げにもつながるもので
もあり，産業・社会的なインパクトも期待できる．
歩行機能の低下した虚弱高齢者の歩行支援やリハビリ補助を行うに当たっては，装置
自身は軽微であることが好ましい．また，介護者の補助を必要とせずに機器の装脱着が
できることも必要となる．さらに，利用者の歩行のバラツキに対応可能な制御アルゴリ
ズムを適用できることも重要である．こうした点から，開発する歩行補助器では小型軽
量を基本とした機器機構とし，転倒防止制御が実現し易いアクチュエータ配置を検討す
る．また，事前歩行解析による歩行動作モデルの構築により，歩行器利用者の動作推定，
環境の状態推定に基づいた実用的な転倒防止支援アルゴリズムを開発する．
転転倒防止を確実なものとするためには，補助器利用者の不安定な重心変動を適切に
補償する制御の適用が必要となる．また，路面の状態変化（環境変動）も反映できるこ
とが好ましい． こうした点を考慮し，補助器利用者の安定性（安全性）を考慮しつつ
も，環境に対して適応的な制御の行える機構（転倒防止制御が実現できる多脚型デバイ
ス）を開発した．本事業は博士学生（留学生）を中心に実施した研究課題であるため，
主たる研究報告の記載は英語で行っている．また，検証を行った実験結果については学
会誌への論文投稿の関係で報告書には含めていない．事業報告書にて一部の結果を示す
予定である．予めご了解いただきたい．
本研究課題は，研究協力員として村上俊之研究室大学院生 Yang Chuan 君，加賀美直
久君，黄友真平君，蒲谷実千君，小林将大君，長山弘樹君より多大なる協力を得ている．
本報告書は本研究課題の中心テーマを扱っている大学院博士 3 年生 Yang Chuan 君の研
究を中心にまとめたものであり，同君には研究の総まとめもお願いした．最後に，上記
の研究協力員に深く感謝の意を表したい．
[1]
[2]
研究課題の概要（和文）
提案手法の基本概念
高齢化社会の進行により，高齢者人口の
高齢化社会
・高齢者人口の増加
・介護施設の不足
増加が顕著となり，それに伴う高齢者介護
施設の不足が必然の問題となっている．し
かしながら，こうした状況を改善するため
従来の歩行支援器具:
杖, 松葉杖, 歩行器,
歩行ハーネス, 歩行補助
に開発されている様々な器具に関しては，
各種特徴を有するものの，事故（特に転倒
事故）を未然に防ぐことを積極的に考慮し
ている研究開発は少ない．本研究課題では，
高出力，高安定，高利便
性の補助具の需要増加:
こうした状況を踏まえ，転倒防止アルゴリ
歩行補助ロボットへの関心
ズムの導入が容易な多脚型歩行支援デバイ
Fig. A 高齢化社会と歩行補助器
スの概念の提案と初期開発を目的とした．
下図に示すように，提案する多脚デバイス(Fig. 3)は松葉杖，歩行補助器の機能を持ち合
わせつつも，転倒防止支援を行える歩行支援システムを目指したものとなっている．基本
的には人の歩行動作と同期した多脚デバイスの制御と転倒動作検出時の適切な安定化制御
を組み込むことが提案システムの機能実現として重要なポイントとなる．
http://phys.org/news168507367.html
http://www.mrsec.com/2013/09
Fig.4 Wearable assist device
Fig.1 Crutch
http://www.futurity.org/tag/elderly/
Fig.2 Gait harness
Fig.3 Proposed walking assist robot system
下記に各図において参照したホームページをまとめる．

Fig .1: http://www.mrsec.com/2013/09

Fig .2: http://www.futurity.org/tag/elderly/

Fig .3: http://phys.org/news168507367.html

Fig .4: http://www.danshope.com/news/post/
[3]
http://www.danshope.com/news/post/
Fig.5 Honda walking assist device
通常歩行時の制御
通常歩行時の多脚デバイスと人の歩行動作の関係を示す図を Fig. 6 に示す．提案手法で
は，人の腰部に設置された加速度センサより人の前後左右の加速度情報を取得し，人の見
かけ上の質量𝑚ℎ とヤコビ行列の転置行列𝑱𝑇 を用いて次式により力応答をトルク次元に変換
している．
(1)
式(1)で得られた力情報および多脚デバイスの各関節に設置された反力推定オブザーバ
ℎ𝑢𝑚
(RTOB)の出力𝜏̂ ℎ を用いて，式(2)により人と環境から受ける外力トルク𝜏̂ 𝑒𝑥𝑡
を求める．この
𝑟𝑒𝑓
𝑟𝑒𝑓
外力トルクを用いて，インピーダンス制御器により外力に倣うための角度𝑞ℎ𝑢𝑚 ，角速度𝑞̇ ℎ𝑢𝑚 ，
𝑟𝑒𝑓
角加速度𝑞̈ ℎ𝑢𝑚 の各指令値を求める．ここで，インピーダンス制御器のパラメータ𝑀𝑖 ，𝐷𝑖 ，𝐾𝑖
は任意に決定可能であり，人の状態や環境状況に応じて設定することが望ましい．
(2)
(3)
式(2)で得られた指令値は腰部を基準座標とする関節空間での PD 制御器に用いることで，
最終的な加速度指令が式(3)で求まる．ここで，𝐾𝑝 ，𝐾𝑣 は角度および角速度フィードバック
ゲインである．式(4)の𝑞𝑐𝑚𝑑 および𝑞̇ 𝑐𝑚𝑑 については通常歩行・転倒状態に応じて利用する指
令値である．
(4)
[4]
Fig.6 Normal walking by two encoder
links fixed on legs
転倒防止制御
転倒状態の検出にあたっては，quaternion を用いることによって，Roll，Pitch 方向の倒
れこみ角を求め，これらの角度の総和がある設定値より大きくなった場合，転倒防止制御
を適用する．具体的には，転倒防止を行うために，多脚デバイスのリンク 1 および 3 への
指令値を生成し，制御により多脚デバイスを杖の機能として用いることで，人の転倒を防
ぐための支えの動作を実現する．
Fig.7 Falling down cases and a photo of the proposed device
[5]
各指令値の生成
通常歩行時の指令生成：通常歩行時においては，人の脚に沿って装着されているエンコー
ダ付リンクシステムのエンコーダ情報に基づいて，腰部両脇に装着されている多脚デバイ
スへの角度指令を次のように与える．これにより，式(4)で示される PD 制御器によって多
脚デバイスの動作は人の歩行動作と同期することになる．
(5)
転倒防止のための指令生成：転倒防止制御においては，ジャイロセンサより得られた情報
より，ロール方向動作𝜃⃗ およびピッチ各動作𝜑
⃗⃗の応答を求め，式(6)の動作指令を生成する．
これにより，先述した転倒防止のための多脚デバイスの動作制御を行う．
(6)
上記の制御式に示されるように，人の動作姿勢の状態に応じて，通常歩行制御と転倒防
止制御の切り替えを行うことで，歩行動作の安全性を高めている．提案アルゴリズムの構
造については，Fig. 8 のブロック線図にまとめる．また，多脚デバイスのモデルを含むシス
テム全体のブロック線図を Fig. 9 にまとめる．
Fig.8 Device joint command generation
Fig.9 The whole block diagram of the system
[6]
JKA26-103
まとめ
上述したように，本研究課題では歩行動作時に発生しうる転倒状態の防止を行うため，
多脚デバイスの構造を提案し，加速度・ジャイロセンサ情報に基づいた転倒防止制御アル
ゴリズムの構築を行った．より安全な転倒防止アルゴリズムとするためには，ある程度大
きなパワーを有する多脚デバイスとする必要があり，装着の負担は避けられない状況とな
る．こうした負担の低減を考慮した多脚デバイスの構造設計については今後の課題となる．
アルゴリズムの詳細および実験結果の一部については本報告書後半に英文でまとめられて
いる．
[7]
Contents
1
Introduction
2
Robot Modeling
2.1 Kinematics modeling . . .
2.2 Dynamics modeling . . . .
2.3 Normal walking behavior .
2.4 Avoid falling down motion
2.5 ZMP trajectory . . . . . .
3
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Controller Design
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3.1 Command generation . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Impedance controller . . . . . . . . . . . . . . . . . . . . . . . . 13
4
Experiments
4.1 Experiment procedures . . . . . . . . . . . .
4.1.1 Experiment 1 Normal walking motion
4.1.2 Experiment 2 Falling down motion .
4.2 Experiment results . . . . . . . . . . . . . .
4.2.1 Experiment 1 results . . . . . . . . .
4.2.2 Experiment 2 results . . . . . . . . .
5
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Conclusion and Future Works
16
16
16
17
17
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19
20
List of Figures
1
2
3
4
5
6
7
8
9
10
Proposed multi-legged device . . . . . . . . . . . . . . . . . . . .
One device leg model. . . . . . . . . . . . . . . . . . . . . . . .
Schematic model of proposed device. . . . . . . . . . . . . . . .
Frame h rotates from frame w with angle σ around the axis r. . . .
Falling down motion. . . . . . . . . . . . . . . . . . . . . . . . .
Block diagram of proposed controller. . . . . . . . . . . . . . . .
Device joint command generation. . . . . . . . . . . . . . . . . .
A photograph of the proposed device in normal walking motion. .
Machine legs rotate angle and contact force in normal walking
motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ZMP tracking performance in normal walking motion. . . . . . .
1
4
6
10
11
23
24
24
25
26
27
11
12
Machine legs rotate angle and contact force in falling down motion. 28
ZMP tracking performance in falling down motion. . . . . . . . . 29
List of Tables
1
2
Physical parameters of device. . . . . . . . . . . . . . . . . . . .
Parameters of controller. . . . . . . . . . . . . . . . . . . . . . .
2
16
17
1
Introduction
Nowdays, lacking in adequate care for the elders, especially those who are walking with inconvenience is becoming a growing problem for the aging society. It is
very dangerous that the elders walking with inconvenience when they fall down.
It is also necessary for the elders to exercise walking in order to keep normal
social life. While walking, elders with little strength usually use canes to keep
balance. Consequently, they can not balance their own bodies with one leg, making them walk in a very slow pace while having to step forward quite fast in order
to keep balance. For the elders with enough strength in their upper bodies, the
canes do work. However, for those without enough strength, keeping balance is
nearly impossible merely by canes. Therefore, kinds of walking-assisting carts are
proposed. Especially in the rapidly aging Japanese society, elders with walkingassisting carts are quite common.
In order to solve elders’ problem of lacking in strength, many researchers have
invented sorts of machine clothes for elders to put on. H.Herr of MIT Media Lab
classified exoskeletons and orthoses into devices that act in series and in parallel
to a human limb, providing a few examples within each category [1]. In Japan, the
most representative ones are Honda walking assist devices of Honda Motor Co.,
Ltd. and Hybrid Assistive Limb (HAL) robot suits. Honda walking assist device
with bodyweight support system [2] reduced the floor reaction force of the user
was based on biomedical engineering analysis results. Honda prototype stride
management assist device [3] was designed to help lift each leg at the thigh as it
moves forward and backward. It helps lengthen the user’s stride, covering longer
distances at a greater speed. Y.Sankai et al. proposed an estimation algorithm
that infers the intention related to the forward leg-swing in order to support the
gait by HAL [4][5] robot suits. The previously mentioned machines were able to
enhance human walking ability, but they paid little attention to keep elders from
3
falling down motion. D.Matsuura, et al. proposed a motion control algorithm of
walking assist machine using crutches [6]. M.Higuchi et al. developed a walking
assist machine using crutches [7]. But both of them paid little attention to prevent
elders from falling down as well.
In this paper, a multi-legged walking assist device which can keep the elders
from falling down and help the them walk is proposed as Fig.1. It can also help the
elders who have poor walking ability walk by themselves and give them simple
walking exercise. In order to measure the human body posture, an IMU sensor
fixed on the waist part of human is applied in this research. The IMU sensor
Figure 1: Proposed multi-legged device
4
can not only measure posture but also measure human walking motion. O.H.
Madgwick et al.[8] presented a novel orientation algorithm by a wearable inertial
human motion tracking system. The results indicated the algorithm achieving
levels of accuracy matching. Y.Hirata et al.[9] focused on the support of walking
on slope, and estimated slope angle based on accelerometer and force sensors.
The method was able to apply to Wearable Walking Helper but it was a little
complicated. Since the IMU sensor contains a triaxial accelerometer, a triaxial
gyro and a triaxial magnetometer. Only one IMU sensor can offer Euler angles to
obtain posture angles. Based on this IMU sensor and a mobile manipulator, the
authors have already proposed a novel walking assist device [10] to help elders
walk. It is possible to apply two IMU sensors to tracking human walking motions.
In order to improve the reliability of the system, however, this paper introduces
links with two encoders to measure human normal walking motion. To analyse
the stability of the proposed multi-legged system, ZMP concept is used. C.Zhu et
al.[11] analysed walking principle of biped robot was clarified by means of ZMP
concept, friction constraint, and inverted pendulum model. A.Suzumura et al.[12]
proposed a four-wheel-legged mobile robot, and the ZMP was introduced as a
stability index. In this paper, the ZMP is also introduced as a stability index for
the multi-legged system.
The authors summarize the primary contributions of the paper as follows: 1)
the kinematics modeling and dynamics modeling are introduced for this novel
multi-legged system; 2) keeping the elders from falling down and help the them
walk is proposed; 3) ZMP is introduced as a stability index for the system. This
paper is organized as follows. Section 2 presents the system modelings, section
3 presents the controller design, section 4 introduces the experiments and results,
and section 5 provides our conclusion and future works.
5
Figure 2: One device leg model.
2
Robot Modeling
The model of 2 DOF manipulator used as a leg of the proposed device is described.
There are two machine legs for the device. Because the two legs are basically the
same, for simplicity, only one leg is modelled in this section. Left device leg
consists of link 1 and link 2, right device leg consists of link 3 and link 4. The
architecture of a single device leg is shown in Fig.2.
2.1
Kinematics modeling
In this subsection, kinematics of the device leg is described. The joint space coordinates can be written as qr = [q1 q2 ]T . The end position of the device leg
in work space is represented as 2-dimensional vector xr = [xr yr ]T . Since the
device leg base is not fixed but moved by human waist, the 2-dimensional vector xb = [xh yh ]T represents the human waist position that measured by the IMU
6
sensor. Forward and inverse kinematics can be derived as follows.
ẋr = J q̇r + ẋb
(1)
q̇r = J −1 ( ẋr − ẋb )
(2)
where J denotes the Jacobian matrix of the device leg. The Jacobian matrix is
used to perform mapping from work space to joint space, and it can be written as
the following equation.
[
J=
J11 J12
J21 J22
]
(3)
J11 = L1 cosq1 + L2 cos(q1 + q2 )
J12 = L2 cos(q1 + q2 )
J21 = −L1 sinq1 − L2 sin(q1 + q2 )
J22 = −L2 sin(q1 + q2 )
where L1 , L2 represent the length of each device leg link.
2.2
Dynamics modeling
By using the IMU sensor, the 3-D accelerometer, velocity and position of human
waist can be measured. Therefore the kinetic energy of human is given by,
1
Kh = mh ( ẋh2 + ẏ2h )
2
(4)
Kinetic energy of link 1 can be calculated as,
1
1
K1 = m1 [( ẋh + l1 q̇1 cosq1 )2 + (ẏh + l1 q̇1 sinq1 )2 ] + I1 q̇21
2
2
(5)
where I1 is the inertia moment of link 1. l1 and m1 represent the CoG length and
mass of link 1 respectively. Note the absolute angle of link 2 is qa2 = q1 + q2 ，then
the kinetic energy of link 2 can be calculated as,
K2 = 21 m2 [( ẋh + L1 q̇1 cosq1 + l2 q̇a2 cosqa2 )2
2
+ (ẏh + L1 q̇1 sinq1 + l2 q̇a2 sinqa2 )2 ] + 12 I2 q˙a2
7
(6)
where I2 is the inertia moment of link 2. l2 and m2 represent the CoG length and
mass of link 2 respectively. Potential energy of human is given by,
Ph = mh gyh
(7)
Potential energy of link 1 can be calculated as,
P1 = m1 g(yh − l1 cosq1 )
(8)
And the potential energy of link 2 can be calculated as,
P2 = m2 g(yh − L1 cosq1 − l2 cosqa2 )
(9)
Thus the Lagrangian of the device leg is given by,
L = Kh + K1 + K2 − Ph − P1 − P2
(10)
Applying the Lagrangian-Euler formulation for the torque τ = [τ1 τ2 ]T at joint 1
and 2 is,
τ=
d ∂L ∂L
−
dt ∂ q̇ ∂q
(11)
where q = [xh yh q1 q2 ]T . Dynamics equation of the device is derived from the
Euler-Lagrange formulation. It can be expressed in the joint space as equation
(12).
τ = M(q) q̈ + C(q, q̇) q̇ + G(q)
(12)
where M(q) is the inertia matrix, C(q, q̇) represents the Coriolis and centrifugal
force, and G(q) represents the gravity terms.
]
[
d1 cosq1 d1 sinq1
d2
d3 cosq2
M(q) =
d4 cosqa2 d4 sinqa2 d5 cosq2
d6
8
(13)
[
C(q, q̇) =
0 0
0
−d3 q̇a2 sinq2
0 0 d5 q̇1 sinq2
0
[
G(q) =
d1 gsinq1
d4 gsinqa2
]
(14)
]
(15)
where,
d1 = m1 l1 + m2 L1
d2 = m1 l12 + m2 L12 + I1
d3 = m2 L1 l1
d4 = m2 l2
d5 = m2 L1 l2
d6 = m2 l12 + I2
2.3
Normal walking behavior
Fig.3 shows how the proposed device cooperates with human walking. In order to
measure the human gait motion, two tiny encoder links are fixed on the each leg
of human. They only measure the rotate angles between posterior and thigh. If
human raise his left leg firstly, the right leg of the device will be raised. Similarly,
if human raise his right leg firstly, the left leg of device will be raised. Both of the
second links of device leg are maintaining an initial angle. Because the impedance
control is employed in all of the device links, the joints are flexible.
2.4
Avoid falling down motion
The IMU sensor fixed on the waist can also generate 3-D posture information. A
quaternion (a, b, c, d) is a four-dimensional complex number that can be used to
9
Figure 3: Schematic model of proposed device.
represent the orientation of a rigid body or coordinate frame in three dimensional
space. Fig.4 shows an arbitrary orientation of frame h relative to frame w. qwh
describes the arbitrary orientation and r is a unit vector described in frame w.
qwh = [a b c d]
σ
σ
σ
σ
= [cos − r x sin − ry sin − rz sin ]
2
2
2
2
(16)
where r x , ry and rz define the components of the unit vector r in the x, y and z axes
of frame w respectively.
Applying the quaternion, the Euler angle representation roll θ and pitch φ can
10
Figure 4: Frame h rotates from frame w with angle σ around the axis r.
be defined by,
θ = −sin−1 (2bd + 2ac)
(17)
φ = Atan2(2cd − 2ab, 2a2 + 2d2 − 1)
(18)
To avoid the singular point of the pitch angle, the angles are limited by,
−90o ≤ θ ≤ 90o
(19)
−180o < φ < 180o
(20)
In normal walking motion, pitch and roll are almost zero. But in emergency
conditions, pitch and roll are not zero absolutely. By applying the vectors of pitch
and roll angles, the angle of summation is,
e
⃗)
θ1,3
= ∠(⃗θ + φ
(21)
e
where θ1,3
indicates the emergency command angle of link 1 or link 3 in Fig.5.
e
e
Emergency situations are defined as a limitation of θ1,3
. When θ1,3
bigger than
the limitation, this avoiding falling down motion starts working. Otherwise, the
11
multi-legged system works in the normal walking assist motion. Fig.5 explains
the falling down motion in the world coordinate as well.
2.5
ZMP trajectory
The ZMP stability criterion that means it is necessary to keep the ZMP within
the support polygon. In this paper, in order to prevent the human from falling
down, the ZMP stability of the device needs to be analyzed. Since the diameter
of the proposed device legs are small, the ground support polygon is assumed as a
point. The IMU sensor that fixed on the human waist part can measure the triaxial
acceleration. The position of the IMU sensor can also be assumed as the center
of gravity (CoG) of the whole system with human. From D’Alembert’s principle,
ZMP of the proposed two legs device in Fig.5 can be expressed as,
ZMP x = CoG x −
ẍy
ÿ + g
(22)
ZMPz = CoGz −
z̈y
ÿ + g
(23)
where ẍ and z̈ are sagittal and frontal acceleration of CoG respectively. y is the
vertical position of CoG. CoG x and CoGz are sagittal and frontal position of CoG
respectively. And ZMP x and Z MPz are the sagittal and frontal position of the zero
support torque respectively.
12
3
Controller Design
The device motors are based on acceleration control with disturbance observer
(DOB) [13]. In addition, by utilizing reaction torque observer (RTOB), forcesensorless control was realized [14]. In this section, in order to make the user
feeling comfortable, impedence control is considered. Firstly, command generation of the proposed controller is described.
3.1
Command generation
During the normal walking motion, the two encoder links fixed on human legs
supply the rotate commands to the device.
qcmd = [qcmd
1e
0 qcmd
2e
0]T
(24)
cmd
where qcmd
1e and q2e are encoder link 1 command and encoder link 2 command
respectively. But if the pitch or roll angle is bigger than a certain value which
means the emergency occuring, the commands are only supplied by IMU sensor.
Also, in order to ensure a successful action to stop the falling down motion, the
upper limit of rotation angle should be set as well. The command of emergency
can be derived as,
qcmd = qcmd
s

 Kr ∠(⃗θ + φ
⃗ ) − qcmd
1b

0

= H(⃗θ, φ
⃗ ) = 
 Kl ∠(⃗θ + φ
⃗ ) − qcmd
2b

0






(25)
cmd
where qcmd
1b and q2b are initial angle of the device right leg and left leg before the
emergency occuring respectively. The details are showed in Fig.7.
13
3.2
Impedance controller
When the device legs touch the ground, the reacting force and the force pushing
by human are needed to be considered in Fig.6. During the device leg touching the
ground, assuming the end of device leg dose not slid. The acceleration of human
waist is measured by the IMU sensor, then the extend force for each link motor is,
τh = J T mh ẍb
(26)
where mh is the mass of testing object. The total extend force for each link motor
is,
r
τ̂hum
ext = Kh τh + Ke τ̂m
(27)
where Kh and Ke are the gains of human force and ground reaction force respectively. τ̂rm is the estimated force of RTOB. By applying the impedance control, the
human force accelertion reference is given by,
f
q̈re
hum =
1 hum
f
re f
(τ̂ − Di q̇re
hum − Ki qhum )
Mi ext
(28)
To make a big enough force and hold on the human when they falling down,
impedance control gains Mi , Di , Ki are studied. The transfer function of impedance
control is,
f
qre
hum
τ̂hum
ext
=
Mi
s2
1
+ Di s + Ki
The natural frequency ωi and damping ratio ζi are derived as follows.
√
Ki
ωi =
Mi
Di
ζi =
√
2 Mi Ki
14
(29)
(30)
(31)
To adjust a suitable value for the natural frequency and damping ratio, the impedance
control gains Di , Ki are be determined as follows.
Di = 2ζi ωi Mi
(32)
Ki = ωi 2 Mi
(33)
By applying the RTOB and IMU sensor to get the enviroment force, the device
motor rotate accelertion reference is given by,
f
re f
f
cmd
res
q̈re
− qre
m = − q̈hum + K1 (q
hum − qm )
f
res
+ K2 ( q̇cmd − q̇re
hum − q̇m )
(34)
Fig.7 shows the command generation. For the normal walking cases, the system
cmd
command qcmd = qcmd
= q̇cmd
e , q̇
e . For the emergency cases, the system comcmd
mand qcmd = qcmd
= q̇cmd
= u pitch .
s , q̇
s
15
4
Experiments
In this section, experiment procedures and results are explained. In these experiments, normal walking motion and falling down motion were conducted with the
proposed controller. Fig.8 shows the real device in the world coordinate. The
testing subject of this experiment was a 28 years old man. His height was 175cm
and weight was about 60 kg. An iBIS system that is a PC based DSP was used as
a processor in this device. A 24V battery was used to supply power for the whole
system. The total mass of this device was about 15 kg. The parameters of device
and controller are shown in Table.1 and Table.2.
Table 1: Physical parameters of device.
Name
Width of the machine W
Length of links (the first link of each leg) L1 , L3 [m]
Length of links (the second link of each leg) L2 , L4 [m]
CoG length of links l1 , l3 [m]
CoG length of links l2 , l4 [m]
Length of encoder links [m]
Mass of link 1 and 3 m1 , m3 [kg]
Mass of link 2 and 4 m2 , m4 [kg]
Mass of testing object mh [kg]
Rotary encoder resolution Re [PPR]
Gear reduction of motors Gr
4.1
4.1.1
Value
0.420
0.435
0.543
0.210
0.270
0.310
0.610
0.347
60
400000
100
Experiment procedures
Experiment 1 Normal walking motion
The device legs can touch the ground like the human using two crutches while
walking. Therefore, adding the human two legs, there are four legs in total. Four
16
Table 2: Parameters of controller.
Name
Position gain K1
Velocity gain K2
Human force gain Kh
Ground reaction force gain Ke
Virtual mass gain Mi
Virtual viscosity gain Di
Virtual spring gain Ki
Cut off frequency of DOB
Cut off frequency of RTOB
Sampling time dt [ms]
Value
200
10
0.3
0.7
5.0
14.0
40.0
50
20
0.5
legs walking can make elders feel there is something to rely. This experiment goal
is to know whether the device enables to coordinate with human walking motion.
4.1.2
Experiment 2 Falling down motion
Makes the device inclined at a small angle for a test firstly. This test guarantees
the system command following the encoder links but not the IMU sensor. Then
tests are done for the subject falling forward which means the emergency occurs.
After the device legs stop the falling down motion, the testing subject returned to
a normal posture by himself. This experiment’s goal is to enable the two machine
legs to prevent elders from falling down. Fig.5 also describes this falling down
motion.
4.2
Experiment results
4.2.1
Experiment 1 results
Fig.9 shows the results of experiment 1. There are four normal walking steps in
the experiment. In Fig.9 (a), the machine leg link 1 motor tracks the encoder link
17
1 command. The tracking error depends on the gains K1 , K2 . If the position gain is
larger, the tracking error is smaller. But it does not mean that the smaller the error
is, a better system response is achieved. In order to reduce the sensitivity of the
system, the gains should not be very large. Since the velocity command is noisy,
the velocity gain should be reduced accordingly as well. In this paper, for link 1
and link 3, the position and velocity gains were chosen as 400 and 40 respectively.
The bound of position gain is recommended between 100 to 625. In accordingly,
the bound of velocity gain is recommended between 20 to 50. For link 2 and
link 4, the position and velocity gains were chosen as 100 and 20 respectively.
The bound of position gain is recommended between 81 to 225, and the bound of
velocity gain is recommended between 18 to 30. The tracking command of the
machine leg link 2 is zero. But because of impedance control, the rotation result
is not always zero. The RTOB results indicate that there is an obvious reaction
force when the machine leg has contacted with the ground.
To analyse the stability of the device with human walking, ZMP tracking performance is introduced in Fig.10. Measuring CoG x and measuring CoGz are obtained by the IMU sensor. Z MP x and Z MPz are obtained by equations (22) and
(23) respectively. Because this device is not similar to the biped robot, there is
no desired ZMP trajectory in advance. In this paper, reference ZMP x is a point
connection from the experiment data. It is only a reference for the system stability. The flex points are decided by the moments of device contacting or leaving
the ground. Denotes the rotate postion is 0 m in 0 second as (0, 0), the other flex
points are (0, 0.58), (0, 1.33), (0.4, 2.77), (0.4, 3.55), (0.74, 4.67), (0.74, 5.72),
(1.1, 6.84), (1.1, 7.47) and (1.35, 8.40). T r and T l are the period of single support
phase of right and left device leg respectively. T d is double support phase period,
S is the device stride of one step. Reference Z MPz is obtained by the similar way
as ZMP x . -0.21 m or 0.21 m is a half of the device width W. -0.1 m or 0.1 m is
18
a half of the distance between the two feet fo human. The results show the whole
system is very stable during the human walking in a normal slow speed motion.
4.2.2
Experiment 2 results
There are many kinds of falling down motion for the elders. For simplicity, only
falling forward motion was considered. Also, the device two legs did the same
motion in this emergency case. Fig.11 and Fig.12 show the results of experiment
2. In the experiment, the current device motors did not have enough power to hold
on the human body when he falls down. In the future work, we need to change
bigger motors for the device links. Therefore in this experiment, for the safety,
the testing subject fell forward and used his hands to support on a wall. That is
why the RTOB force is not very big in Fig.11.
In Fig.12 (a), reference Z MP x is obtained in the same way as the normal walking motion. Because human feet did not move on the ground in this experiment,
there is no reference Z MP x data for the human. T f and T r are the period of falling
down and recovery respectively. T h is device holding period. Maybe this case
can not represent all of falling down motions, but at least it can make it possible
to prevent elders from falling down. In Fig.12 (b), machine reference ZMPz and
human reference ZMPz are obtained by the similar way as reference ZMP x . The
time of flex points are 0 s, 2.95 s, 3.94 s, 5.6 s, 6.79 s and 8.3 s. During the period
of T f and T r , because both of the device two legs are leaving the ground, there is
no data for the machine reference ZMPz . The results show the whole system is
stable even in this falling forward down motion. Finally, if this system is applied
to various users, the initial joint angle device of two legs should be adjusted according to the height of the user. Also, the impedance control gains are need to be
adjusted according to different weight users.
19
5
Conclusion and Future Works
In this paper, a novel multi-legged system device is proposed. The purpose of this
research is to hold and help elders walk using two robotic crutches and prevent
them from falling down when an emergency occurs. Since the device legs are
2 DOF manipulators, only forward falling down motions were discussed. ZMP
tracking results was introduced as a stability index for the whole system. The
results also indicated that the proposed device can stop human from falling down
when the emergency occurs. After this falling forward down motion, human can
return to the normal safe posture by themselves and keep on normal walking. As
a future work, two 3 DOF manipulators need to be considered. Then it is possible
to consider about the other kinds of falling down motions. In addition, variable
impedance should be designed to increase the performance, based on different
cases.
Acknowledgement
This report was subsidized in part by JKA(26-103) through its promotion
funds from KEIRIN RACE.
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22
Figure 5: Falling down motion.
23
Figure 6: Block diagram of proposed controller.
Figure 7: Device joint command generation.
24
Figure 8: A photograph of the proposed device in normal walking motion.
25
電気学会産業応用部門論文誌投稿中のため省略します．
Figure 9: Machine legs rotate angle and contact force in normal walking motion.
26
電気学会産業応用部門論文誌投稿中のため省略します．
Figure 10: ZMP tracking performance in normal walking motion.
27
電気学会産業応用部門論文誌投稿中のため省略します．
Figure 11: Machine legs rotate angle and contact force in falling down motion.
28
電気学会産業応用部門論文誌投稿中のため省略します．
Figure 12: ZMP tracking performance in falling down motion.
29
JKA26-103
学会等への発表
1. Nobuhiro Kobayashi and Toshiyuki Murakami, "Workspace Acceleration Based MDOF Motion
Control in Redundant Manipulators", 2014 IEEE International Symposium on Industrial
Electronics, pp293-298, Istanbul, Turkey, 2014
2. Miyuki Kamatani and Toshiyuki Murakami, ＂Traveling Control of Two-wheel Wheelchair
Using Variable Command″, IEEE IECON2014, pp5278-5282, 2014
3. Ynag Chuan and Toshiyuki Murakami, ＂An Approach to Walking Assist Control by a
Multi-Legged System in Human Gait Motion″, IEEE IECON2014, pp5236-5241, 2014
JKA26-103
事業内容についての問い合わせ先
慶應義塾大学 理工学部 システムデザイン工学科
〒２２３－８５２２
横浜市港北区日吉３－１４－１
教授 村上俊之
E-mail: [email protected]
URL: www.fha.sd.keio.ac.jp
村上俊之研究室