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Hindawi Journal of Robotics Volume 2022, Article ID 7562164, 10 pages https://doi.org/10.1155/2022/7562164 Research Article Compliant Mechanism Soft Robot Design and Peristaltic Movement Optimization Using Random Search 1 1 2 L. A. Pa ´ ramo-Carranza , A. Lopez-Gonza ´ lez , and Juan C. Tejada Universidad Iberoamericana, Mexico City, Mexico Universidad EIA, Medell´ın, Colombia Correspondence should be addressed to A. Lopez-Gonza´lez; email@example.com Received 28 February 2022; Accepted 30 March 2022; Published 12 April 2022 Academic Editor: L. Fortuna Copyright © 2022 L. A. Pa´ramo-Carranza et al. *is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this article, we use the concept of auxetic structures as inspiration for the design of a compliant mechanism that allows the integration of a soft robot whose movement is based on the peristaltic movements of invertebrates. *e TPU mechanism allows for smooth movement of the robot using only two servo motors. To guarantee maximum displacement, a time and angle optimization procedure using photogrammetry and random search was carried out, allowing the advance distance of the soft robot to be maximized. *e capabilities of a soft robot are based on its material 1. Introduction and the morphology of its structure . Hence, materials One of the objectives of robot design is to imitate human and and structure are very relevant for the design and manu- animal behavior in order to create machines capable of facture of new mechanisms. *e variety of materials used in coexisting in our environment and working alongside us . soft robotics is amazing, where structure, sensor, and soft *ere is also a strong motivation to emulate the softness of actuator manufacturing include hydrogels, ionic and con- human and animal tissue to ensure safe interaction between ducting polymers, carbon nanotubes, dielectric elastomers, humans and robots by developing actuators and sensors that shape-memory materials, and so on [10, 13]. allow moving conformable and deformable structures [2, 3]. In robotics, this ﬁeld of study is called soft robotics and promises the safe interaction between living beings and 1.1. Metamaterials and Auxetic Materials. Metamaterials are artiﬁcial compounds that exhibit, by their structure, prop- robots  using soft materials, tensegrity , bending materials , jamming , and other technologies. erties not available in natural materials. Mechanical meta- materials are designed with speciﬁc internal structural Soft robots are biologically inspired machines  be- cause nature uses softness and compliance in many ways to elements that allow special and advantageous behaviors over conventional materials. Speciﬁc geometric pattern structures design biological organisms, which can interact with the environment using body deformations for both object provide metamaterials with desirable properties. For ex- ample, honeycomb cell design generates interesting negative manipulation and locomotion . Venturing into the ﬁeld of Poisson’s ratio behaviors . soft robotics requires the development of new soft structures with more natural behaviors, integrated topology with A material with a negative Poisson’s ratio is called auxetic metamaterial. *e word auxetic comes from the materials, and continuous and conformable bodies. Soft robots have social, biomedical, rehabilitation, exploration Greek “auxetikos” which means “that which tends to grow.” Poisson’s ratio of a material (]) tells us how much a material applications, and many others [10, 11]. 2 Journal of Robotics (a) (b) Figure 1: *e original material depicted in dashed lines is subjected to the longitudinal strain represented by the red arrows. (a) Nonauxetic behavior where the original material contracts in the direction of the blue arrows, while (b) an auxetic behavior where the original material expands in the direction of the blue arrows. (a) (b) (c) (d) (e) Figure 2: Auxetic modules developed in . becomes thinner when it is stretched, formally it is deﬁned as In , the authors use an auxetic mechanism based on a the ratio of the lateral contractile strain to the longitudinal two-dimensional arrangement involving rigid squares tensile strain for a material undergoing tension in the connected to each other at their vertices by hinges, achieving longitudinal direction. Most materials exhibit a positive ], a negative Poisson’s ratio. *ese geometric structures are but auxetic materials have a negative Poisson’s ratio. *at is, extremely useful and important as they can help researchers auxetic materials undergo lateral expansion when stretched better understand how auxetic eﬀects can be achieved and longitudinally and become thinner when compressed how auxetic materials can be manufactured, as well as how [15, 16], as shown in Figure 1, then: their properties can be optimized and predicted. In , ﬁve structures have been developed based on the trans ] � − , (1) auxetic conﬁgurations of rotating squares. *e structure long known as KinetiX presents a novel set of cells that can be arranged in such a way that generates diﬀerent types of where ε is the transverse strain, and ε is the longi- trans long movements. *is type of cell is a square structure to which tudinal strain . As mentioned in , Poisson’s ratio for hinges are placed in diﬀerent positions of each bar, always a stable material is limited between −1 and +0.5 for three- maintaining symmetry in between parallel bars, as shown in dimensional structures and between −1 and 1 for two-di- Figure 2. Hence, a contraction or expansion of the bars mensional structures. generates the desired deformation allowing uniform scaling, shear, bending, and rotation. Jifei Ou and his colleagues  built on the structures 1.2. Previous Work. Many articles have been published on the design of actuators based on the principles of auxetic presented by Evans  and Saxena , rotating square structures to generate a four-bar mechanism shown in mechanisms , conventional robot structural elements , as well as soft robots and structures [20–23]. Re- Figure 3. It is based on four rectangles joined at one of their vertices. *ese joints (h , . . . , h ) are used as hinges and searchers have been exploring metamaterials that exhibit 0 3 auxeticity and their applications [24–26]. compose a two-dimensional movement. Journal of Robotics 3 0 Figure 5: Auxetic cell design. Figure 3: Four bar mechanism. Figure 6: Reinforced section, the force is applied to the corners. However, the one that inspired the present work is hinge-out plane rotation (bending spatial transformation), where the four hinges are angled at (π/2) on the plane of rotation and located in the middle of each bar. Each wall is given an inclination angle β, as shown in Figure 4. *is combination of angles creates a rotation out of the hinge’s plane. *e design of this structure is such that when a tensile force is applied, a bidirectional expansion is generated. 2. Auxetic-Inspired Bending Structure We developed a soft material structure capable of bending out of its geometric plane from a single degree of freedom. *ese characteristics allow the mechanism to be used as a link in a soft robot. We use this mechanism to provide locomotion to a bipedal robot using peristaltic movements with a single degree of freedom for each leg. *is type of mechanisms allows to simplify the redundance diﬀculties of use a cable-driven actuation [31, 32]. *e structure, shown in Figure 5, is based around a 50 mm square cell. By placing a triangular structure at each end of the mechanism, we are allowing the force necessary to bend the Figure 4: Bending conﬁguration cell . mechanism to be applied at each point of the protruding triangle. It was observed that these links, which are made of Using the Chebychev–Grubler–Kutzbach ¨ criterion soft material, did not manage to transmit movement. *is is [29, 30], as shown in equation (2), where the number of rigid why a reinforcement was placed, joining the section with a bodies is N � 4, the number of joints j � 4, and joints with bar of the same dimensions as the designed mechanism. *e only have one degree of freedom f , . . . , f � 1, the four-bar movement is generated by applying force in the corners, 0 3 mechanism in Figure 3 has only one degree of freedom. keeping the central hinge, point P, as the axis of rotation, as depicted in Figure 6. M � 3(N − 1 − j) + f . (2) n�1 2.1. Compliant Hinges. To manufacture the structure using Two types of three-dimensional transformations were only soft material, the use of bolts and rotation axes was developed: hinge-in plane rotation and hinge-out plane avoided by replacing the hinges from the original mecha- rotation, both described in , and ﬁve single units of nisms with compliant hinges. A structural part of a com- planar and spatial transformation are shown in Figure 2. pliant mechanism can be seen as a compliant joint. If two 4 Journal of Robotics (a) (b) Figure 7: Two diﬀerent compliant joints with relative motion. (a) (b) Figure 8: Original hinge (a) and compliant hinge (b). weight. *is allows opening and closing the triangular links are coherently united, then it is known as a compliant coherent joint. *is allows at least one relative motion be- supports of the mechanism with a single motor. tween links, but it is often limited to a localized area [33, 34]. Such union in a compliant mechanism is achieved in two 2.3. Motion Mechanism. *e simple gear transmission ways, as depicted in Figure 7, changing the material and consists of a driving wheel with teeth on its outer periphery, changing the geometry in the area where diﬀerent stiﬀness is which meshes with a similar one, thereby preventing slip- required. page between wheels. *e system also reverses the direction To manufacture the mechanism in a single piece and of rotation of two contiguous axes, which allows the blades completely from soft material, the ﬂexible hinges were made to move in opposite directions for G and G , thereby 1 2 by changing the geometry of the bars and placing them at the stretching the mechanism. Both of these have a diameter of middle point of each link to obtain a symmetrical ﬂexion, as 24 mm. *e gear attached to the motor is a spur gear G with shown in Figure 8. 13 teeth and a base diameter of 12 mm. It is responsible for With this, the mechanism inherits the properties and transmitting the engine torque. advantages that compliant hinges have against classic hinges Each gear, G and G have 24 gear teeth and are 1 2 [33, 34]; a smaller one-piece, one-material design, no rigid mechanically engaged with a 1 :1 ratio. *e driving gear materials, axes, or fasteners, and needless lubrication since attached to the motor has 12 teeth and is in charge of there is no friction between parts. transmitting the movement torque. *is gear has contact only with gear G , with which it has a transmission ratio of 2.2. 3D Printed Mechanism. A thermoplastic polyurethane 1 : 2; therefore, the torque increases. *e force exerted on the (TPU) was used to print the mechanism, as shown in corner of the soft mechanism can be calculated from the gear Figure 9. For the structure to function as a soft robot ac- ratio, considering that the torque delivered by the motor is tuator and locomotion mechanism, the application of a force τ � 1.8kg/cm and using the gear transmission ratio, the on the two corners of the mechanism is needed, which cause torque produced in gear two is τ � 3.6kg/cm. a rotation with regard to the axis P. A gripper-like mech- From this torque, the force exerted on the mechanism anism was designed with polylactic acid (PLA) gears, as can be calculated by taking the stem of the gear as a can- shown in Figure 10, actuated by a servo motor as Sg90 Tower tilever beam, with a lever arm of 2 cm, Pro with a maximum torque of 2.5 kg cm and a weight of F � τ · l � (3.6 kg/cm) · (2 cm) � 7.2kg. *erefore, the ap- 14.7 g in order to provide such forces but not add to its plied force at each corner is about 70.63 Newtons. Journal of Robotics 5 Figure 9: CAD design and mechanism 3D printed in TPU. G G 1 2 (a) (b) Figure 10: Movement generated by the gears to bend the mechanism. *e PLA plastic base that supports the gear train is since, properly placed, it can generate a push on the surface shown in Figure 11. *is piece allows the rotation of each . *e bipedal soft robot is displayed in Figure 13. gear. It keeps the gears at the appropriate positions for their *e movement of the robot is biologically inspired, correct operation. *e complete system, assembled with the speciﬁcally from worms, which move from cycles of con- designed mechanism, is shown in Figure 12. tractions and relaxations of certain sections of its body that cause them to periodically expand and contract their length. With this type of movement, the robot is capable of ad- 3. Soft Robot Locomotion and Optimization vancing in each cycle. *is is not properly a worm move- *is actuation mechanism is used in the construction of a ment since the same source of locomotion is not applied as it mobile soft robot. It is considered a limb of the bipedal robot has been developed in many other pieces of research such as 6 Journal of Robotics (a) (b) Figure 11: Gripper-like mechanism. Figure 13: Bipedal soft robot. It was observed from tests with ﬁxed angles (θ and θ ) 1 2 that after the contraction of the link, the link is required to return to its initial position when the servomotor is posi- tioned at zero. Figure 12: Assembled mechanism. 3.1. Random Search Optimization. *e movement of soft robots, as well as their control, depends on the mathematical [9, 36, 37], where the designed robots are themselves robot model that describes their dynamics; however, the modeling worms. However, the use of our soft actuator achieves a of soft robots is quite a complicated aspect due to high similar movement. nonlinearity. *erefore, the application of control meth- By having two limbs, it is possible to combine the odologies is complicated. *is work seeks to maximize the contraction movements of these links sequentially in a cycle movement of the robot, where analyzing from testing, it was of four steps with a period, to allow the robot to pull and observed that this depended directly on the angles of con- push on the movement plane, thus achieving a displacement. traction of the mechanisms and the sequence in which they Figure 14 shows how this cycle of contractions and re- happen. Later, it was detected that to enhance the movement tractions of the links makes the robot advance. At each step, of the robot, we needed to ﬁnd the best values of the angles the robot just moves forward a few millimeters. that maximized the displacement. It was necessary to use *e distance it travels depends largely on the action some optimization techniques; to achieve this, there are sequence of each motor; that is, the independent contraction many methodologies to ﬁnd the most suitable parameters of each link, the time that each motor waits to return to its that allow maximum displacement, such as genetic algo- initial position, and the maximum actuation. *e latter is rithms, simulated annealing, hill climbing, random search, very important. It is a logical assumption that to achieve random forest, particle swarm optimization, and many maximum displacement, it is necessary to contract the others. *e random search algorithm was selected to opti- mechanism as much as possible; however, this is not the case. mize the angle values because it allows us to easily calibrate Journal of Robotics 7 Figure 14: Robot movement: step contractions that generate a displacement of millimeters. Initialize q in the start point q : while q≠ q do Choose a point q � [θ , θ , t , t ] in the sample space as a starting point; 1 2 1 2 Generate a random q set and evaluate the performance metric: maximum distance d if d(q )> d(q) then q � q else search new vector q to be analyzed end end ALGORITHM 1: Random search. diﬀerent robot platform operations . *e random search algorithm  is presented in Algorithm 1. *e servomotor angles θ and θ are sent employing an 1 2 Atmega328 microcontroller and t and t are the times that 1 2 the mechanism remains contracted, then the mechanism returns to its original position. To know how much the robot has moved, it is necessary to know the new position of the robot in the work area. *e photogrammetry procedure is used to measure the robot’s displacement by documenting images sequentially through a Figure 15: Display of the distance traveled from an initial point. camera . A green circle was placed on the robot as shown in Figure 15, which is used as the reference position of the robot and is detected in the image through an algorithm With the data obtained by the random search optimi- written on MATLAB zation, the vector of parameters that achieves the greatest *e algorithm begins by taking a capture of the distance traveled is selected and used for a veriﬁcation stage mechanism through the camera by calculating and marking contrasting performance with ﬁxed maximum angles. its initial position on the screen with a yellow cross, as shown in Figure 15. In one cycle, the algorithm sends values of position angles to each motor, as well as the time that each 3.2. Optimization Results. *e values presented in the fol- motor must wait to return to its initial position. Once the lowing graphs correspond to the vector q in random search. robot has moved, the algorithm calculates the new position *e ﬁrst graphs are focused on showing the random vari- of the robot and computes the robot’s displacement. Sub- ation of the angles θ , θ that were used in the random 1 2 sequently, it compares the distance traveled with the pre- search. vious one and decides whether to calculate new random *e displacement achieved for θ , θ , t , and t through 1 2 1 2 values or to use the same ones. *is process continues for the random search algorithm is considerably greater than one hundred cycles. that achieved when the ﬁxed angles and waiting times are 8 Journal of Robotics Degrees for motor L Degrees for motor R 160 160 θ θ 1 2 0 10 20 30 40 0 10 20 30 40 Wait time L Wait time R 1 0.2 0.15 t t 0.5 0.1 1 2 0.05 0 0 0 10 20 30 40 0 10 20 30 40 Figure 16: Maximum actuator values for (θ , θ ) and (t , t ). 1 2 1 2 Table 2: Maximum contraction and extension times. Maximum Distances Parameter Contracted Extended Time t t t t 1 2 1 2 0.82 0.03 0.90 0.62 Position 1 2 3 4 5 6 7 8 9 10 246.0252 43.2105 0 5 10 15 20 25 30 35 40 Samples Distance Figure 17: Maximum values of reached distances. Table 1: Motor angles to generate link shrinkage. Parameter θ θ 1 2 Optimal degrees 149 146 1 2 3 4 5 6 7 8 9 10 Fixed degrees 160 160 Optimum Fixed Figure 18: Comparative graph, ﬁxed values (blue) versus optimal chosen. Figure 16 shows the angle variation and times found parameters (black). by random search throughout ﬁfty iterations of the search cycle. Since the random search algorithm requires a consid- parameters were carried out. Each of these tests consisted of erable number of tests to search for the optimal values of 100 iterations. Once we had all the statistical data of the 40 angles and times in the robot’s movement, 40 search tests for maximums of each test, the maximum value of this new set d (mm) x (mm) d (mm) Journal of Robotics 9 Table 3: Comparison between distance traveled with optimal system with these manufacturing restrictions, a scheme that values and ﬁxed values. we would like to explore in future developments of the proposed mechanism. Test d d max avg Finally, the proposed compliant structure and actuator Optimal values 21.94 21.24 could be used to design diﬀerent kinds of legged robots. It is Fixed values 1.4 0.6 possible to consider several conﬁgurations for the actuator to construct diﬀerent types of mobile soft robots by exchanging both the horizontal or vertical disposition of the limbs or was obtained, and the average value of the distances was adding more links that the type of robot requires, such as calculated, as shown in Figure 17. bipedal robot, quadruped robot, and so on. *e maximum distance that the robot traveled from among all cycles was d � 25.64 for which the maximum Data Availability values are depicted in Table 1, which shows the angles at which the motors must move, remembering that they return *e data that support the ﬁndings of this study are available to the zero initial position at time t. Table 2 displays the from the corresponding author, A. Lopez-Gonzalez ´ (alex- contraction and extension times for each motor. firstname.lastname@example.org), upon reasonable request. Once the maximum parameters were obtained, they were applied to the robot, and the photogrammetry process Conflicts of Interest was carried out to verify the distances obtained at each step *e authors declare that they have no conﬂicts of interest. of the robot. *e results were compared with those obtained when ﬁxed values are chosen for the parameters of the vector Acknowledgments q. *e total path was observed during ten iterations or ten steps of the robot in the photogrammetry, also measuring *is research was supported by the Universidad Iber- the distance in each step. *e graph in Figure 18 exhibits the oamericana (Ibero DCI-002847 and Convocatoria 14 DINV) comparison between both experiments from a starting point and the Universidad EIA (CO12021002). as well as the advance distances at each step. Table 3 also shows the values obtained for each of the experiments. References  C. Majidi, “Soft-matter engineering for soft robotics,” Ad- 4. 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