robotics Article
Design, Kinematics and Controlling a Novel Soft Robot Arm with Parallel Motion Alaa Al-Ibadi 1,2, * 1 2
*
ID
, Samia Nefti-Meziani 1 and Steve Davis 1
School of Computing, Science & Engineering, University of Salford, Salford M5 4WT, UK;
[email protected] (S.N.-M.);
[email protected] (S.D.) Computer Engineering Department, University of Basrah, Basrah 61004, Iraq Correspondence:
[email protected] or
[email protected]; Tel.: +44-743-846-2585
Received: 19 March 2018; Accepted: 16 May 2018; Published: 17 May 2018
Abstract: This article presents a novel design for a double bend pneumatic muscle actuator (DB-PMA) inspired by snake lateral undulation. The presented actuator has the ability to bend in opposite directions from its two halves. This behavior results in horizontal and vertical movements of the actuator distal ends. The kinematics for the proposed actuator are illustrated and experiments conducted to validate its unique features. Furthermore, a continuum robot arm with the ability to move in parallel (horizontal displacement) is designed with a single DB-PMA and a two-finger soft gripper. The performance of the soft robot arm presented is explained, then another design of the horizontal motion continuum robot arm is proposed, using two self-bending contraction actuators (SBCA) in series to overcome the payload effects on the upper half of the soft arm. Keywords: snake lateral undulation locomotion; double bend pneumatic muscle actuator (DB-PMA); self-bending contraction actuator (SBCA); soft robot arm; horizontal motion
1. Introduction Biological concepts provide significant inspirations for human creation. The robot is one of these inspirations; researchers around the world have converted the fundamentals of biological movements to mechanical forms. Robots resembling humans, dogs, geckos, snakes, and other types of animal, have been designed [1–6]. Several types of actuators used in robotics are also inspired by biology. Since the early 2000s, an alternative form of the rigid robot has been developed by using a soft muscle-like actuator called the pneumatic muscle actuator (PMA). This development has led to the development of soft robotics, which is considered to be a new generation of robotics. The PMA, which was developed by McKibben in the 1950’s, is constructed from an inner rubber tube covered by a braided sleeve and closed from both sides with a small inlet [7]. The PMA has been modelled by numerous researchers. Among these models is the tensile force model [7] and the contractile force model introduced by [8]. Enhancements of these models were presented by [9–13]. The length of the PMA was modelled geometrically by Doumit, M., et al. [14]; the formula length depends on the length of the braided strand, diameter, braided angle, and number of strand turns. Al-Ibadi, A. et al. [12] formulated the length of the contraction actuators as a sigmoidal function depending on the applied pressure and initial length. The PMA is designed to either contract or extend according to the braided angle and the implementation method. The braided angle θ less than 54.7◦ contracts the actuator by a contraction ratio ε to about 30%. The extension behavior occurs when θ is greater than 54.7◦ at an extension ratio of about 50% [12,15,16]. The basic behavior of the PMA involves linearly contracting or extending; however, developments have been proposed to improve the behavior by modifying its structure. A bending performance was presented Robotics 2018, 7, 19; doi:10.3390/robotics7020019
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by numerous researchers, including the PneuNet actuator by Ilievski, F., et al. [17]. The authors presented a bending actuator by changing the wall’s thickness. This actuator is easy to manufacture, but the ratio of the elasticity that was achieved was too limited. To overcome this limitation, Deimel, R., et al. [18] used a PneuFlex actuator that implants polymer fibers to reinforce the rubber substrate. The elasticity of the polyethylene terephthalate (PET) material was three to four times less than silicon. Al-Ibadi, A., et al. [19] designed a self-bending contraction actuator (SBCA) by inserting a reinforced flexible rod to one side of the contraction PMA to achieve bending behavior. Al-Fahaam, H., et al. [20] proposed enabling bending behavior by modifying the structure of the extensor PMA by using a high-tension thread to reinforce one side of the covered sleeve. Faudzi, A.A.M., et al. [21] used the effect of the braided angle on the actuator performance to design a bending behavior by using two different braided sleeves of different braided angles to cover the inner tube of the contractor PMA. Snake propulsion patterns are used to design snake robots to achieve several goals, such as rescue missions after natural and man-made disasters, inspections, investigations, and maintenance for dangerous or narrow areas [22–24]. The multiple links snake robot was designed by Shan, Y., et al. [25] by using direct current (DC) motors to control the angles between the links and solenoids with sharp tip pins to generate a push force to the ground, and provide forward movement by moving the joints in a lateral direction. A wheel snake-like robot, SAM, was presented by Yamakita, M., et al. [26]. The friction between the wheels and the ground was ignored. A series of multi-module snake robots were designed by Wright, C., et al. [27], and the joint angle was controlled by a servo motor via a proportional–integral–derivative (PID) control system. Wright, C., et al. [28] designed a serial-linkage snake robot that contained several rigid modules with a DC motor and a gear box for each, resulting in an extendable 16 degrees of freedom (DOF). The main contribution in this article is the design of a DB-PMA inspired by the shape of snake lateral undulation locomotion. We present the kinematics for the proposed actuator; hen, a soft arm is designed using the new actuator. A modified version of the continuum arm is presented by using the SBCA. In this article, the motion principle of the snake is explained in Section 2, which is then used to propose a double bend pneumatic muscle actuator (DB-PMA) in Section 3. The kinematics of the proposed actuator are presented and validated experimentally in Sections 4 and 5, respectively. A two-finger soft gripper based on SBCA is designed, implemented, and attached to the end of the DB-PMA to design a soft robot arm for horizontal displacement. Then, another design of the horizontal motion continuum arm is presented by using two SBCA in series. The performance of both the proposed continuum robot arms are illustrated and validated by a control system in Section 6. 2. Snake Motion Snake propulsion can be classified into four patterns: lateral undulation (serpentine), rectilinear locomotion, sidewinding, and concertina progression [23,24,29]. Lateral undulation is the most effective locomotion mode and it is widely perceived in almost all kinds of snakes. For this reason, we chose this pattern for our research. The snake forms its body into several curves, positioning in the X-Y planes during the lateral undulation. Figure 1 shows the lateral undulation locomotion of a snake. Robotics 2018, 7, x FOR PEER REVIEW 3 of 14
Figure 1. The lateral undulation locomotion of a snake.
Figure 1. The lateral undulation locomotion of a snake.
3. Structure of the Double-Bend Actuator The basic structure of the contraction PMA is shown in Figure 2. The length of the braided sleeve was assumed to be similar to the length of the inner rubber tube to ensure that the braided angle θ is less than 54.7°. Figure 1 shows how the snake bends its body several times in two directions. The shape and the performance of this bending pattern were used to design a double
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Figure Figure 1. 1. The The lateral lateral undulation undulation locomotion locomotion of of aa snake. snake.
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3. 3. Structure Structure of of the the Double-Bend Double-Bend Actuator Actuator 3. Structure of the Double-Bend Actuator The The basic basic structure structure of of the the contraction contraction PMA PMA is is shown shown in in Figure Figure 2. 2. The The length length of of the the braided braided The basic structure of the contraction PMA is shown in Figure 2. The length of the braided sleeve sleeve was assumed to be similar to the length of the inner rubber tube to ensure that the braided sleeve was assumed to be similar to the length of the inner rubber tube to ensure that the braided was assumed to be similar to the length of the inner rubber tube to ensure that the braided angle angle 54.7°. angle θθ is is less less than than 54.7°. Figure Figure 11 shows shows how how the the snake snake bends bends its its body body several several times times in in two two ◦ θdirections. is less than 54.7 . Figure 1 shows how theofsnake bends itspattern body several timestoindesign two directions. The shape and the performance this bending were used a double directions. The shape and the performance of this bending pattern were used to design a double The shape and themuscle performance of this bending pattern were used to design a doublerods bend pneumatic bend bend pneumatic pneumatic muscle actuator actuator (DB-PMA) (DB-PMA) by by inserting inserting two two thin thin reinforcement reinforcement rods between between the the muscle actuator (DB-PMA) by inserting two thin reinforcement rods between the rubber tube and rubber rubber tube tube and and the the sleeve. sleeve. Each Each rod rod was was placed placed on on opposite opposite sides sides of of the the two two halves halves of of the the the sleeve. Each rod as was placed oninopposite sides ofrod the two three-dimensional halves of the contractionprinted actuator as contraction contraction actuator actuator as illustrated illustrated in Figure Figure 3. 3. Each Each rod was was three-dimensional (3D) (3D) printed with with illustrated in Figure 3. Each rod was three-dimensional (3D) printed with length of 28 cm, width of length length of of 28 28 cm, cm, width width of of 0.6 0.6 cm, cm, and and height height of of 0.1 0.1 cm. cm. 0.6 cm, and height of 0.1 cm. Braided Braided sleeve sleeve Air Air inlet inlet
Inner Inner rubber rubber tube tube
Figure 2. of the contraction pneumatic muscle actuator (PMA). Figure 2. 2. The The structure structure of of the the contraction contraction pneumatic pneumatic muscle muscleactuator actuator(PMA). (PMA). Figure The structure Air Air inlet inlet Reinforcement Reinforcement rod rod (B) (B)
Braided Braided sleeve sleeve
Reinforcement Reinforcement rod rod (A) (A)
Inner Inner rubber rubber
The The mid mid line line
Figure (DB-PMA). Figure 3. 3. The The structure structure of of the the double double bend bend pneumatic pneumatic muscle muscleactuator actuator(DB-PMA). (DB-PMA).
The contraction occurs on the free sides while the rods prevent it, which leads to bending The contraction contraction occurs occurs on on the the free free sides sides while while the the rods rods prevent prevent it, it, which which leads leads to to aaa bending bending The behavior as shown in Figure 4 behavior as asshown shownin inFigure Figure4.4 behavior
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Reinforcement rod (B)
α1 λ1 β1
γ1
Lv2
Lh1 Lh
γ2
β2 Lh2
Lv1
λ2 α2 Reinforcement rod (A)
β
Lv Figure 4. The bending behavior andand the the geometrical analysis of the DB-PMA. Figure 4. The bending behavior geometrical analysis of the DB-PMA.
4. Kinematics of the DB-PMA 4. Kinematics of the DB-PMA TheThe geometrical analysis of the proposed arm is illustrated in Figures 3 and 4 in4 two conditions geometrical analysis of the proposed arm is illustrated in Figures 3 and in two conditions according to the applied pressure: a relaxed and a pressurized condition. according to the applied pressure: a relaxed and a pressurized condition. 4.1.4.1. Relaxed Condition Relaxed Condition TheThe length of the DB-PMA at zero pressure cancan be be described with Equation (1):(1): length of the DB-PMA at zero pressure described with Equation 𝐿𝑣 = 𝜆 = 𝐿0 L v = λ = L0
(1)
(1)
where: where:
(2) 𝜆 = 𝜆1 + 𝜆2 λ = λ1 + λ2 (2) where Lv is the vertical actuator length and L0 is the actuator length at zero pressure. where Lv is the vertical actuator length and L0 is the actuator length at zero pressure. Hence, the length of the double-bend actuator is divided into two components: the vertical Hence, the length of the double-bend actuator is divided into two components: the vertical length length and the horizontal length. Due to the relaxed condition, the horizontal length of the DB-PMA and the horizontal length. Due to the relaxed condition, the horizontal length of the DB-PMA is zero. is zero. 4.2. Pressurised Condition 4.2. Pressurised Condition Figure 4 shows both the vertical and horizontal lengths of the DB-PMA under pressurised Figure 4 The shows both the vertical and horizontally horizontal lengths of the DB-PMA under pressurised conditions. proposed actuator moves by the summation of the horizontal components conditions. The proposed actuator moves horizontally by the summation of the horizontal of the first and the second halves, as shown in Equation (3). components of the first and the second halves, as shown in Equation (3). h = L h1 + L h2 𝐿L ℎ = 𝐿ℎ1 + 𝐿ℎ2
(3) (3)
where Lh is total horizontal movement with respect to the section area of of thethe actuator, Lh1Lis where Lh the is the total horizontal movement with respect to the section area actuator, is the h1 the horizontal length of the first half, and Lh2Lish2the horizontal length of the second half. horizontal length of the first half, and is the horizontal length of the second half. Both the vertical and horizontal movements can be calculated by using the cosine law as shown in Equation (4):
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Both the vertical and horizontal movements can be calculated by using the cosine law as shown in Equation (4): λ21 = L2v1 + L2h1 − 2Lv1 Lh1 cosβ 1 (4) where λ1 is the distance between the first end and the mid line of the actuator and β1 is the angle between the direction of the vertical and horizontal distances of the first half. Similarly, the distance between the second end and the mid line (λ2 ) of the actuator under a pressurised condition is described in Equation (5): λ22 = L2v2 + L2h2 − 2Lv2 Lh2 cosβ 2
(5)
From Figure 4, both the vertical and the horizontal lengths of the proposed actuator can be found as follows: 1 1 Lv = (λ21 + L2h1 − 2λ1 Lh1 cosα1 ) 2 + (λ22 + L2h2 − 2λ2 Lh2 cosα2 ) 2 (6) and:
1
1
Lh = (λ21 + L2v1 − 2λ1 Lv1 cosγ1 ) 2 + (λ22 + L2v2 − 2λ2 Lv2 cosγ2 ) 2
(7)
Alternatively, the angles can be calculated in terms of the distances as follows: β i = cos−1
L2vi + L2hi − λ2i , (i ∈ R ) 2Lvi Lhi
(8)
where i is either 1 or 2 according to which half of the angle is being calculated. αi = cos−1
λ2i + L2hi − L2vi , (i ∈ R ) 2λi Lhi
(9)
γi = cos−1
λ2i + L2vi − L2hi , (i ∈ R ) 2λi Lvi
(10)
and:
4.3. Special Condition1 For identical reinforcement rods with similar material and dimensions, the lengths and angles of the presented actuator at pressurised conditions are: Lv1 = Lv2
(11)
Lh1 = Lh2
(12)
λ1 = λ2
(13)
β 1 = β 2 = 90
◦
(14)
α1 = α2
(15)
γ1 = γ2
(16)
4.4. Special Condition2 If the bending angles of the first and the second halves equal 90◦ , then: α1 = α2 = γ1 = γ2 = 45
◦
(17)
and: Lv1 = Lv2 = Lh1 = Lh2
(18)
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or: or:
𝐿𝑣 + 𝐿ℎ = 𝐿0 L0 Lv = Lh = 2
(20)
(19) 5. Experiments and Validations Robotics 2018, 7, x FOR PEER REVIEW 6 of 14 or: Two identical 28 cm reinforcement rods were placed in the two halves of a 60 cm contraction L v + L h = L0 (20) or: actuator to create a DB-PMA. Special case 1 was used to calculate the angles and distances for the (20) 𝐿𝑣 + 𝐿ℎ = 𝐿0 5.DB-PMA. Experiments Validations Two and (HC-SR04) ultrasonic sensors by (ElecFreaks, Shenzhen, China) were used to measure the vertical (Lv) and the horizontal (Lh) distances for the presented actuator. Figure 5 illustrates the Two identical 28 cm rods were placed in the two halves of a 60 cm contraction 5. Experiments andreinforcement Validations presented actuator at two different pressures. actuator to create a DB-PMA. Special case 1 was used to in calculate the angles and distances for the Two identical 28 cm reinforcement rods were placed the two halves of a 60 cm contraction DB-PMA. Two (HC-SR04) sensors (ElecFreaks, Shenzhen, China) were used to measure actuator to create a ultrasonic DB-PMA. Special case by 1 was used to calculate the angles and distances for the Two (HC-SR04) ultrasonic by DB-PMA (ElecFreaks, Shenzhen, were Figure used to measure at 200 kPaChina) the verticalDB-PMA. (Lv ) and the horizontal (Lh ) sensors distances for the presented actuator. 5 illustrates the the vertical (Lv) and the horizontal (Lh) distances for the presented actuator. Figure 5 illustrates the presented actuator at two different pressures. presented actuator at two different pressures.
DB-PMA at 200 kPa
Lower-half
Air inlet Upper-half Air inlet
Lower-half
Upper-half
DB-PMA at 400 kPa DB-PMA at 400 kPa
FigureFigure 5. The presented two different air pressures. 5. The presentedDB-PMA DB-PMA atattwo different air pressures. Figure 5. The presented DB-PMA at two different air pressures. The pressure was applied by using a Matrix 3/3 solenoid valve in 50 kPa steps. At each pressure The pressure was applied by using a Matrix 3/3 solenoid valve in 50 kPa steps. At each pressure step, both the vertical and horizontal distances were measured by sensors and the angles were step,The both the vertical and horizontal were measured sensors and At theeach angles were pressure was applied by using adistances Matrix 3/3 solenoid valve by in 50 kPa steps. pressure manually measured for several repeats and the average was recorded. manually measured for several repeats and the average was recorded. step, both the vertical andshow horizontal distances measured and the were Figure 6a–f the experiment andwere validation resultsby forsensors the distances andangles angles of the manually presented actuator. Figure 6a–f show the experiment and was validation results for the distances and angles of the measured for several repeats and the average recorded. presented actuator. Figure 6a–f show the experiment and validation results for the distances and angles of the presented actuator.
Figure 6. Cont.
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Figure 6. Cont.
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Figure 6. 6. The The parameters βc Figure parameters of of the the DB-PMA DB-PMA as as aa function function of of air airpressure: pressure:(a) (a)βmβmand andthe thecalculated calculated (b) αm and the calculated αc angle, (c) γm and the calculated γc angle, (d) λm and the calculated βangle, c angle, (b) αm and the calculated αc angle, (c) γm and the calculated γc angle, (d) λm and the calculated λ c distance between the two ends, (e) Lhm and the calculated Lhc horizontal distance, and (f) Lvm and λc distance between the two ends, (e) Lhm and the calculated Lhc horizontal distance, and (f) Lvm and the calculated calculatedLLvc vertical vertical distance. distance. the vc
Figure 6a shows the calculation and the measurement value of β. Since the actuator is designed Figure 6a shows the calculation and the measurement value of β. Since the actuator is designed under under special case 1, β has ◦to be 90°. The measured angle is similar to the designed angle, with a special case 1, β has to be 90 . The measured angle is similar to the designed angle, with a maximum maximum error of 0.6°. Because β is constant, α decreases from 90° to 10° (Figure 6b), whereas γ error of 0.6◦ . Because β is constant, α decreases from 90◦ to 10◦ (Figure 6b), whereas γ increases from 0◦ to increases from 0° to 80°, as shown in Figure 6c, so that the summation of the triangle angles is 180° at 80◦ , as shown in Figure 6c, so that the summation of the triangle angles is 180◦ at each pressure step. each pressure step. Figure 6d illustrates the performance of λ with the increase in the applied air pressure. This distance Figure 6d illustrates the performance of λ with the increase in the applied air pressure. This decreases when the pressure increases from the original length of the actuator to about 25 cm at 400 kPa. distance decreases when the pressure increases from the original length of the actuator to about 25 cm When the horizontal distance in Figure 6e was changed from 0 to 24.3 cm, through to its maximum value at 400 kPa. When the horizontal distance in Figure 6e was changed from 0 to 24.3 cm, through to its of 30 cm, the maximum change in horizontal direction occurred with special case 2 when both α and γ maximum value of 30 cm, the maximum change in horizontal direction occurred with special case 2 were about 45◦ . Figure 6f shows that Lv decreases continuously with pressure increase. when both α and γ were about 45°. Figure 6f shows that Lv decreases continuously with The maximum variation ratio in the horizontal (εh) and vertical (εv) distances are defined in pressure increase. Equations (21) and (22) as follows: The maximum variation ratio in the horizontal L0 − (εh) Lh and vertical (εv) distances are defined in εh = (21) Equations (21) and (22) as follows: L0 𝐿0 − 𝐿ℎ 𝜀ℎ = (21) 𝐿0 and:
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and: Robotics 2018, 7, x FOR PEER REVIEW
εv =
L0 − L v L0
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(22)
− 𝐿𝑣 where LRobotics the 7,initial length of the actuator at𝐿0relaxed conditions according to the 0 is 2018, x FOR PEER REVIEW 9 ofdesigned 14 𝜀𝑣 = (22) 𝐿 dimensions. The maximum ratios for the horizontal and0 vertical distances are 0.5 and 0.83, respectively. − 𝐿𝑣 conditions where Lwith 0 is the of the actuator at𝐿DB-PMA according an to efficient the designed In comparison the initial simplelength contraction PMA, the can be considered alternative 0relaxed 𝜀𝑣 = (22) 𝐿 dimensions. The maximum ratios for the horizontal and vertical distances are 0.5 and 0.83, in terms of the contraction ratio between the two ends 0of the actuator. respectively. In comparison with the simple contraction PMA, the DB-PMA can be considered an where L0 is the initial length of the actuator at relaxed conditions according to the designed
efficientMoving alternative in terms of the contraction ratio between the two ends of the actuator. 6. Horizontal Robot Arm dimensions. The Soft maximum ratios for the horizontal and vertical distances are 0.5 and 0.83,
respectively. In comparison with the simple contraction PMA, the DB-PMA can be considered an
Horizontal DB-PMA Moving Soft Robot Arm as a soft robot arm for moving an object horizontally and The6. proposed can be used efficient alternative in terms of the contraction ratio between the two ends of the actuator. vertically byThe a distance depends the of the object. A soft gripper was proposed that DB-PMA can beon used as pressure a soft robotand armweight for moving an object horizontally and mounted at the end of the DB-PMA toArm grasp anpressure object and move it to another position. 6. Horizontal Soft vertically by aMoving distance thatRobot depends on the and weight of horizontally the object. A soft gripper was at the was end of the DB-PMA to two grasp15-cm an object and move itcontraction horizontally actuators to another position. Themounted softThe gripper made by using self-bending (SBCA), proposed DB-PMA can be used as a soft robot arm for moving an object horizontally and as seen The soft gripper was made by using two 15-cm self-bending contraction actuators (SBCA), as seen in Figure 7. To maximize thethat range of motion the fingers, a thinofribbon of elastomeric material was vertically by a distance depends on theofpressure and weight the object. A soft gripper was in Figure 7. To maximize the range of motion of the fingers, a thin ribbon of elastomeric material was mounted at the end offinger the DB-PMA to grasp an object movewhen it horizontally to another position. placed on the rear of each to cause the fingers toand spread the actuator is unpressurised. placed on the rear of each finger to cause the fingers to spread when the actuator is unpressurised The soft gripper was made by using two 15-cm self-bending contraction actuators (SBCA), as seen in Figure 7. To maximize the range of motion of the fingers, a thin ribbon of elastomeric material was placed on the rear of each finger to cause the fingers to spread when the actuator is unpressurised
The elastomeric ribbon
The elastomeric ribbon The reinforcement rod
(b) reinforcement rod The
(b)
(a)
Figure 7. The two-finger soft gripper based on self-bending contraction actuators (SBCA). (a) The soft Figure 7.gripper The two-finger soft gripper(b) based on self-bending actuators (SBCA). (a) The soft at different air pressures. The schematic design ofcontraction the soft finger. (a)
gripper at different air pressures. (b) The schematic design of the soft finger.
Figure 7. The two-finger soft gripper based on self-bending contraction actuators (SBCA). (a) The soft Figure 8 shows the DB-PMA and the two-finger soft gripper as a continuum arm at different gripper at different air pressures. (b) The schematic design of the soft finger.
pressurized conditions.
Figure 8 shows the DB-PMA and the two-finger soft gripper as a continuum arm at different 8 shows the DB-PMA and the two-finger soft gripper as a continuum arm at different pressurized Figure conditions. pressurized conditions.
Figure 8. The presented continuum robot arm at different pressurised conditions.
Figure 8. The presented continuum robot arm at different pressurised conditions.
Figure 8. The presented continuum robot arm at different pressurised conditions.
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To the object objectwill willmove movetotothe the specified position, a neural network (NN) controller To ensure the specified position, a neural network (NN) controller was was designed to control horizontal distance continuumarm armvia viaan an ultrasound ultrasound sensor sensor by designed to control the the horizontal distance of of thethe continuum controlling andand venting of the via a 3/3 (Matrix)(Matrix) valve and an Arduino controlling the theair airfilling filling venting of actuator the actuator via solenoid a 3/3 solenoid valve and an Mega 2560. Figure 9 shows flowchart the control and the DB-PMA. The NARMA-L2 Arduino Mega 2560. Figurethe 9 shows the of flowchart of system the control system and the DB-PMA. The NN-controller included nine neurons in one hidden layer, three-delayed plant inputs, and two-delayed NARMA-L2 NN-controller included nine neurons in one hidden layer, three-delayed plant inputs, plants outputs, which was trainedwhich by (trainlm) for 100by Epochs. Thefor mean the and two-delayed plants outputs, was trained (trainlm) 100 square Epochs.error The (MSE) mean for square −7 . data training, testing, andtraining, validating of theand datavalidating was aboutof10the The controller wascontroller the pulseoutput width error (MSE) for the testing, was aboutoutput 10−7. The modulation (PWM) signal that controls the air flow that for both the filling andflow venting processes to achieve was the pulse width modulation (PWM) signal controls the air for both the filling and the desired horizontal position. venting processes to achieve the desired horizontal position.
Figure 9. 9. The The flowchart flowchart of of the the control control system system and and the the DB-PMA. DB-PMA. Figure
An approximate model was used to train the neural controller and the actuator length as a An approximate model was used to train the neural controller and the actuator length as a function function of the duty cycle of the controlled input, which is given by Equation (23): of the duty cycle of the controlled input, which is given by Equation (23): 0.5𝐿0 × 𝑢 (23) 𝐿ℎ =0.5L × u 098 Lh = (23) 98 where Lh is the horizontal distance between the initial position (relaxed condition) and the new position condition), is the controlled cycle(relaxed of the pulse widthand modulation (PWM) where Lh (pressurised is the horizontal distanceubetween the initialduty position condition) the new position signal, L0 represents the uinitial the number 98 of refers to thewidth 98% ofmodulation the maximum dutysignal, cycle (pressurised condition), is thelength, controlled duty cycle the pulse (PWM) the control signal to avoid continuous supply to the air valve, and 0.5 is the maximum horizontal Lfor represents the initial length, the number 98 refers to the 98% of the maximum duty cycle for the 0 distance L hmax (50%) for special case 2. control signal to avoid continuous supply to the air valve, and 0.5 is the maximum horizontal distance and signals were applied to the controller system at 0.5 Hz, and the response for LhmaxStep (50%) forsinusoidal special case 2. the horizontal moving process illustrated into Figure 10a,b. system at 0.5 Hz, and the response for Step and sinusoidal signalsiswere applied the controller the horizontal moving process is illustrated in Figure 10a,b.
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(a)
(b) Figure 10. (a) The step response of the horizontal distance at 0.5 Hz. (b) The sinusoidal response of Figure 10. (a) The step response of the horizontal distance at 0.5 Hz. (b) The sinusoidal response of the the horizontal distance at 0.5 Hz. horizontal distance at 0.5 Hz.
Figure 10a shows that the contraction time was more than the elongation time due to the Figureof10a thatmaterial the contraction was more than the elongation due to thethe hysteresis hysteresis theshows actuator and thetime pressure difference between the time actuator and outside of the actuator material and the pressure difference between the actuator and the outside pressure. The sinusoidal response shows that the Lh is tracking the input signal with low errorpressure. values. The sinusoidal response shows the Lto tracking the soft inputactuator signal with low error values. h isuse This process illustrates thethat ability a single as an effective robot arm for This process illustrates the ability to use a single soft actuator as an effective robotand arm for specific applications at zero or minimum loads. The second half, the gripper the specific object, applications zero minimum The second the gripper andreduces the object, a load represents a at load onorthe first halfloads. (upper-half). Thishalf, accumulative load the represents bending angle of on the first half (upper-half). This accumulative load reduces the bending angle of the upper-half and the upper-half and places the end of the DB-PMA not in the vertical direction. Two options were places thetoend of the DB-PMA notof in the the vertical direction.either Two options wereofpossible to overcome rod the possible overcome the effect load condition: the length the reinforcement effect of the condition: either the length of the reinforcement increases to increase the in bending increases toload increase the bending angle of the upper-half (Tablerod 1) or two identical SBCAs series angle of the upper-half (Table 1) or two identical SBCAs in series are used instead of a single DB-PMA. are used instead of a single DB-PMA. Table bending angle for the different self-bending contraction actuatorsactuators (SBCAs) Table1.1.The Themaximum maximum bending angle forthree the three different self-bending contraction at 500 kPa. (SBCAs) at 500 kPa.
Length ofthe theActuator Actuator and Reinforcement Length of and Reinforcement Rod Rod (cm) (cm) 10 10 20 20 30 30
MaximumBending Bending Angle Maximum Angle ◦ 2525° ◦ 125 125° ◦ 213 213°
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Figure 11 shows the new horizontal moving continuum using the SBCA. modification Figure 11 shows the new horizontal moving continuum armarm using the SBCA. ThisThis modification ensures the horizontal motion of the continuum robot arm by applying different air pressure. ensures the horizontal motion of the continuum robot arm by applying different air pressure. Using SBCAs insteadofofthe the DB-PMA DB-PMA increased variables; however, the features Using twotwo SBCAs instead increasedthe thecontrolled controlled variables; however, the were improved. Since each bending actuator is controlled individually, the soft robot armarm shows features were improved. Since each bending actuator is controlled individually, the soft robot different shapes and performances. shows different shapes and performances.
Upper SBCA
Upper SBCA
Lower SBCA
Upper SBCA
Lower SBCA
Lower SBCA
Upper SBCA
Upper SBCA Two-fingers gripper
Lower SBCA Lower SBCA
Figure 11. The horizontal moving arm of two SBCAs at different pressurising conditions. Figure 11. The horizontal moving arm of two SBCAs at different pressurising conditions.
7. Conclusions 7. Conclusions We presented a novel double bend pneumatic muscle actuator (DB-PMA) inspired by the We presented novel The double bend pneumatic muscle actuator (DB-PMA) inspired byunique the lateral lateral undulation of aasnake. kinematics and experiments explained and validated the undulation of a snake. The kinematics and experiments explained and validated the unique features of the actuator presented. The DB-PMA was used to design a continuum robot arm withfeatures the of the actuator presented. The DB-PMA was used to design a continuum robot arm with the ability ability of both ends of the actuator to maintain horizontal position so that objects can be moved of both ends of the actuator to maintain horizontal position so that objects can be moved parallel parallel to the ground. A soft gripper was designed by two SBCAs and attached to the end of the to the ground. A soft gripper was designed by two SBCAs attached to the end of gripper, the DB-PMA DB-PMA to validate the performance of the soft robot arm. and Because the weight of the the to validate performance of the softaffects robotthe arm. Becausebending the weight of the gripper, the presented load, and the load, and thethe weight of the lower half resulting of the upper half, the weight of the lower half affects the resulting bending of the upper half, the presented arm is suitable arm is suitable for working with light loads. To increase the efficiency of the presented arm, two for working with light loads. To increase the efficiency of the presented arm, two SBCAs were used in SBCAs were used in series instead of a single DB-PMA to ensure that the distal end of the soft arm series instead of by a single DB-PMA to ensure that the distal end of themodification soft arm moved horizontally moved horizontally applying a different pressure at each SBCA. The increased the by applying a different pressure at each SBCA. The modification increased the complexity of the complexity of the system. However, the efficiency and the resulting performance and forms of the system. However, efficiencyThe and displacement the resulting performance and forms of the continuum armofwere continuum arm were the improved. amount depends on the design and size improved. The displacement amount depends on the design and size of the actuators. the actuators. As future work, a modification be applied to the presented to enable horizontal As future work, a modification can can be applied to the presented armarm to enable the the horizontal movement on both sides by adding DB-PMAs in parallel inopposite an opposite layout. movement on both sides by adding twotwo DB-PMAs in parallel but but in an layout. Author Contributions: A.A.-I. designed and performed the experiments; A.A.-I. and S.D. analysed the data; Author Contributions: A.A.-I. and performed A.A.-I. wrote the paper; anddesigned S.N.-M. edited the paper. the experiments; A.A.-I. and S.D. analysed the data; A.A.-I. wrote the paper; and S.N.-M. edited the paper.
Acknowledgments: The authors would like to thank the Ministry of Higher Education (Iraq), University of Basrah, Computer-Engineering Department for providing scholarship support to the first author of this paper.
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Acknowledgments: The authors would like to thank the Ministry of Higher Education (Iraq), University of Basrah, Computer-Engineering Department for providing scholarship support to the first author of this paper. Conflicts of Interest: The authors declare no conflict of interest.
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