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Assembly and implementation of modular quadrupedal architecture/Ensamblaje e implementacion de arquitectura cuadrupeda modular.

1. Introduction

Robotics is designed to support human tasks, perform activities that exceed the people physical capabilities, go where people cannot go and avoid human risks. The robots are divided in countless categories as varied as their applications could be. Mobile robots break the anchoring scheme that is evident in industrial robotics and allow service-oriented applications [1].

Within the ten major fields of research in robotics that are most likely to have an impact in the coming years, it has the tendency to: carry out bioinspired designs and create modular units. The bio-inspired approach looks for use fundamental guidelines of living beings on the robotic field, covering the design and control of these. The modular units are oriented to less expensive and simpler structures with greater adaptability [2]-[4]

This paper demarcates in the field of modular robotics, it is used in the creation of a mobile type architecture of quadrupedal class, for this, the architecture proposal is based on bioinspired mechanisms of quadrupedal and tetrapodal animals. To implement the architecture, the fifth version of modular robots created by the Davinci research group (Military University Nueva Granada) are used.

The modular robotics came up 39 years ago. They can perform an unlimited number of structures which can be divided by divided by morphology: lattice(1D), chain(3D) or hybrid(1 D+3D), or by independence: mobile configuration or full-body. The mobile configuration allows independent modules that can interact by itself with the environment. On the other hand, the full-body configuration needs the other modules to interact and move.[5], [6]

Through the years, many types of modular quadrupedal robots have been developed. Many morphologies have been adopted, the most representatives are: the spider and lizard on the Polybot robot, the mammal-based on the CKBot, the swere drive (wheel-legs) on the SMOREEP and the centaur configuration on the Walbot. [3], [7]-[11]

Inside the modular quadrupedal robots, it stands out the hybrid robots that look for capabilities not limited to terrestrial locomotion. The salamander family has been considered for many designs due to his ability to perform water/land/climb transitions. The salamander phenomenon appears not only in modular robots, there are robots created only to explore this animal movement. Some of the salamander robots are: The Amphibot (modular) and the Pleurobot(non-modular), based on Pleurodeles walt, the Chigon (non-modular), based on Chinese dragon, the bioinspired salamander (modular), based on the crytobranchidae, the AMOS WD02(non- modular) and the StickyBot (non-modular), based on the gecko.[12]-[16] Inside the salamander robots, there is a lot of different approaches in relation with the level of "fidelity". The fidelity determines the similarity between the robot and the animal, more fidelity implies more degrees of freedom and more complex controllers. The Pleurobot, for example, simplifies many column DOFs but it has four DOFs per leg and 11 DOFs in the column, including a tail with a fin and a sophisticated scapula design. On the other hand, the AMOS WD02 has only 2 DOFs per leg and one DOF on the column. The approaches depend off the investigation purpose and the mechanical design. The modular robots are limited by the modules couplings. [15], [18]

The paper is distributed in the following sections: Investigation project, methodology for the architecture approach, methodology for displacement approach, implementation and results, conclusions.

2. Investigation Project

The Mecabot robot is a project that has been developing by the Military University Nueva Granada (Bogota - Colombia) since 2013. The Mecabot modular unit consists of two submodules, each one made up of a body and a pivot.

Between submodules it is possible to realize four types of different couplings, three of them allowing linear union (face-face, pivot-pivot, face-pivot) and one used in perpendicular union (to lateral faces by pivot connection or face connection).

The Mecabot is conceived with the goal of performing tasks of exploration, search and rescue. To expand the robot adaptability capacity, the assembly of different architectures has been studied (snake, caterpillar, wheel and hexapod). The robot in its hexapod configuration has already been tested on unstructured terrain and other topologies with legs are currently under investigation: quadruped and biped [19] [20] [21]. This paper is the result after an exhaustive process of simulation and mathematical analysis.

3. Methodology for the architecture approach

In general, a quadrupedal robot can have three different forms of limb arrangement: perpendicular to the advance direction (frontal), parallel to the advance direction (sagittal) and radial to the robot body (circular). Of these arrangements, the frontal (characteristic of the reptiles) provides the most stable base, in counterpart the sagittal (characteristic of the mammals) requires the greatest stability control, but requests a smaller consumption, reason why, in flat terrains it can reach higher speeds [22]. Looking for good performance on difficult surfaces, the frontal arrangement is chosen to be assembled with the Mecabot and the consumption is reduced using only two degrees of freedom per leg.

The development of the frontal quadrupedal topology is based on the four couplings types that the Mecabot can adopt. To achieve that the legs reach the highest possible degree of openness, a coupling to lateral faces by pivot connection is used (see Figure 1) and the spine is designed with a length of two modules, those two aspects allow a movement of [+ or -][pi]/2 in each extremity.

The second degree of freedom of the legs can be assembled using a face-pivot coupling or a face-face coupling. With the first coupling, the robot would reach a height above the ground of 17.4mm, while with the second, this would be 36.4mm. To facilitate the maneuverability that the Mecabot could have on unstructured terrain, it is used the coupling that provides more height: face-face (see Figure 1).

With the structure of the legs determined completely, we continue to address the coupling to be used by the two modules in the spine. The pivot-pivot connection is avoided because it is the structurally weakest, the use of a face-face coupling would implicitly involve this connection, so a face-pivot coupling is chosen. Finally, there are four possible architectures with face-pivot, these are shown in Figure 1.

Of the four architectures, the topology that uses non-inverted couplings would allow the possibility of using an active column, this attracts special interest since the movement of the column would provide step length. Under these conditions, neither the legs nor the spine would have to adopt angles close to the motors mechanical limits and these would not be forced at high speeds. This last topology is finally chosen for the spine.

4. Methodology for displacement approach

The so-called standard gait is the one that provides the best static stability to quadrupedal robots, it is the only one that is evidenced in nature, it is used by some animals in their slow movements [23]. The movement that the robot will execute with active column could be raised based on the numerous locomotion studies on salamanders. Salamanders use the lateral sequence, which corresponds to a standard gait with a high support factor. In this lateral sequence, very specific column-leg coordination aspects must be guaranteed [24] [25] :

[check] The column must reach the maximum contraction after the transition phase of the hindlimb ends.

[check] The beginning of the transition phase of the forelimb must coincide with the maximum retraction of its opposite diagonal hindlimb.

[check] The lifting (transition phase) is carried out only in the protraction.

[check] Protraction is faster than retraction.

These points must be fulfilled to ensure good stability during the steps sequence. When the animal flexes the spine, the center of gravity moves from one side to another and therefore the transition phase and support phase of the legs must be coupled to this change. However, these requirements make that locomotion profiles approach would be complex.

Find the right movement profiles between the legs and the spine means fight against years of evolution, for this case, it is advisable to base the movement on the direct observation of the animal. For this purpose, the complementary material published by the researchers of the Ecole polytechnique federale de Lausanne (Movie S5 Tracking for Pleurodeles waltlii in cineradiographic recordings) are used. This video is taken through innovative X-ray techniques allowing to analyze the bony movement of the salamander [18].

From the video of 15 seconds, a fragment of time (5 s) corresponding to the movement cycle is taken. Due to the robot will only have two degrees of freedom, the legs are analyzed only in the Top View of the video. There are four points of interest indicated in the tracking video, only one of these is chosen for each leg, the angles adopted in these points are extracted over time. The control mechanism that must be programmed in the Mecabot is created using the profiles.

4.1. Simple displacement control mechanism

There are a variety of different strategies for the control of modular robots. From these strategies, the Central Pattern Generators (CPG) allow executing complicated movements with few control parameters and lack of feedback, besides provide a smoother and more harmonious response than traditional methods. However, they demand a high computational cost, they are directly bioinspired mechanisms that tend to be redundant [19] [26] [27].

The sinusoidal generators, as simplified versions of the CPG, have been used in the snake and caterpillar Mecabot configurations giving good results, these demand less calculations and keep the benefits of the CPG. The adopted sinusoidal generators form for the column control is based on [28] [13] and is expressed according to (1).

[[theta].sub.[i]] = ([A.sub.[i]]*Sin([pi]*F*t + [bias.sub.[i]]) + of f [set.sub.[i]]) (1)

Although the legs movement profile is more elaborate than the column profile, it is look for a controller that also allows a variation of frequency, bias and amplitude. For achieve this, a sum of sines interpolation of the video extracted data is proposed, the interpolation allows to create the composite sinusoidal generator shown in (2).

[[theta].sub.[i]] = E1 + E2 + E3 + E4 E1 = [A.sub.[i]]*Sin([pi]*F*t + [bias.sub.[i]]) E2 = [[A.sub.[i]]/2]*Sin(2[pi]*F*t + 2[bias.sub.[i]]) (E3 = [[A.sub.[i]]/3]*Sin(3[pi]*F*t + 3[bias.sub.[i]]) (E4 = [[A.sub.[i]]/8]*Sin(4[pi]*F*t + 4[bias.sub.[i]]) (2)

4.2. Open and closed turns control mechanism

To perform an open turn, the simplest method is to vary the offset in the column sinusoidal generators [24] [24] [13]. When the offset is non-zero, the robot describes a circular path to the left or to the right direction, depending on this variable sign. When this takes place, the time taken by the center of gravity on one side or another is no longer equal, the legs transition phase time must be able to vary depending on this change, otherwise, the robot would lose stability.

The legs located on the direction turn side must increase their transition phase, the legs on the opposite side must decrease it. For do this, the ascending slope (protraction) of the sinusoidal generators must be able to increase or decrease. From the analysis of the proposed interpolation (see (2)), it is observed that such change is possible by varying the number of En terms. For open turn, two other types of composite sinusoidal generators are proposed, these are given by (3) and by (4).

[[theta].sub.[i]] = E1 + E2 + E3 E1 = [A.sub.[i]]*Sin([pi]*F*t + [bias.sub.[i]]) E2 = [[A.sub.[i]]/2]*Sin(2[pi]*F*t + 2[bias.sub.[i]]) (E3 = [[A.sub.[i]]/4]*Sin(3[pi]*F*t + 3[bias.sub.[i]]) (3)

Increase the number of En terms (see (4)) provokes that the slope rises and the legs lifting phase takes less time, decrease them causes the opposite effect. Depending on the offset sign, this change of En terms is made in the corresponding pairs of legs.

[[theta].sub.[i]] = E1 + E2 + E3 + E4 +E5 E1 = [A.sub.[i]]*Sin([pi]*F*t + [bias.sub.[i]]) E2 = [[A.sub.[i]]/2]*Sin(2[pi]*F*t + 2[bias.sub.[i]]) (E3 = [[A.sub.[i]]/3]*Sin(3[pi]*F*t + 3[bias.sub.[i]]) (E4 = [[A.sub.[i]]/4.05]*Sin(4[pi]*F*t + 4[bias.sub.[i]]) (E5 = [[A.sub.[i]]/16]*Sin(5[pi]*F*t + 5[bias.sub.[i]]) (4)

To perform the closed turn or rotation, the robot should adopt a higher offset and the legs located on the rotation side would have to remain completely static at a defined maximum opening. Under these hypothetical conditions the robot is completely unstable, the stability polygon generated by the extremities on the opposite rotation direction side would not cover the center of gravity (see Figure 2).

This phenomenon is compensated by the amphibian flexing his leg below the abdomen, for do that, the robot would need an additional degree of freedom. Increase the number of DOF in the robot leads to an increase in weight, consumption and complexity in programming.

To perform the rotation without losing balance and without increase the cost, the spine should remain motionless during the execution. It is possible to adopt another kind of sequence: a progressive transition, which includes a body movement phase, or a two to two transition. The two to two transition is faster than a progressive sequence, besides it can use few DOFs. To do this transition, two sinusoidal generators are created as shown in (5).

[[theta].sub.[i]] = [A.sub.[i]]*Sin([pi]*F*t + [bias.sub.[i]]) [mathematical expression not reproducible] (5)

5. Implementation and results

The coordination and correct performance of the control algorithms is tested in the Webots simulation environment. Once this is done, the physical modules are programmed. A decentralized control is used.

5.1. Results of simple straight displacement

In simple displacement, six sinusoidal generators are used (four composite generators in the legs and three simple generators in the column). The frequency in all of them is varied, the linear velocity is measured in function of this control parameter change. The tests are performed on three structured areas: varying the level of firmness (the foam is the flat soft surface) and varying the level of friction (the sandpaper is the flat rough surface). Subsequently the tests are carried out on three unstructured terrains: pavement, rocky and grass, of them, the pavement is the least irregular terrain (see Figure 3).

In the tests it is evident that the increase in the frequency of the six generators causes the increase in the linear speed of the robot. The maximum reached speed is 0.25m/s. As the difficulty and irregularity of the terrain increase, the speed decreases. In grass the robot reaches 19.74% of the Lab Floor maximum speed.

5.2. Results of open turn

In open turn, six sinusoidal generators are used (four composite generators with variation in protraction time), the offset of the three generators of the column is varied and the radius of the described circumference is measured in function of this control parameter change. The tests are performed on a structured terrain and two unstructured terrains (pavement and rocky). During the tests it is evident that the increase in the offset causes the decrease in the described circumference radius (see Figure 4).

With an offset higher than [+ or -][pi]/18, conditions close to instability, similar when the robot perform a rotation with an active column, are present. For this reason, the minimum reached turning radius is 0.4225m. This radius increases as the irregularity of the terrain, the ups and downs of the surface tend to divert the robot from its path. The minimum reached turning radius in the pavement is 0.58 m and in rocky terrain is 0.765 m.

5.3. Results of closed turn

The rotation tests are carried out in the same terrains of the simple locomotion tests. The frequency is varied in the two simple sinusoidal generators (one per diagonal pair of legs) and the angular velocity is measured. It is evident that the increase in the frequency causes the increase of the robot angular velocity (see Figure 5).

The maximum reached angular speed is 0.2443rad/s. The level of firmness or friction in the structured terrains does not affect in high way the development with intermediate frequencies (less than 0.8 Hz). However, the irregularity of the terrain does, on these surfaces the central rotation axis could be move, product of the ups and downs in the terrain, this affects the time it takes to the robot to turn. In grass the robot reaches 19.74% of the Lab Floor maximum angular speed.

6. Conclusions

The use of composite sinusoidal generators proved to be beneficial in the control of modular robotic units in absence of feedback, since it still retains the low computational cost of a simple sinusoidal generator and allows performing elaborate movements, varying the same control parameters: bias, frequency, amplitude and additionally changing the protraction time of the legs.

The open turn is useful to surround intermediate size obstacles in structured terrains and obstacles of greater size in all kinds of surfaces, for turns that demand a radius less than 0.4225m it is necessary to use a combination of successive closed turns and simple displacements. To change the direction of locomotion, rotation is the most indicated method. A gait for simple displacement and open rotation is successfully created through a bioinspired control approach. The use of this approach is limited by the processing, consumption and torque capacity of the Mecabot modular unit, it is necessary always weigh the cost / benefit of this strategy.

The integration of different types of sinusoidal generators programmed in a decentralized way allowed the correct coordination and execution of the gaits for simple displacement, open and closed turns in different terrains, thus complementing the research works carried out for apodal configurations (snake, caterpillar wheel) and the hexapod, improving the robot adaptability. Considering the decrease in angular/linear velocity and the increase in the described radius because of the deviation caused by the ups and downs of the terrain, future coordination work with feedback of the surface condition should be carried out to improve the performance of the robot.

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Vanessa Cruz-Carbonell (1); Ricardo Andres Castillo-Estepa (2)

(1) BSc. In Mechatronic Engineering, Universidad Militar Nueva Granada, Colombia. E-mail: u1802306@unimilitar.edu.co ORCID: https://orcid.org/0000-0002-1422-7308

(2) BSc. In Mechatronic Engineering, Universidad Militar Nueva Granada, Colombia. MSc. In Mechanic Engineering, PhD. In Mechanic Engineering, State University of Campinas, Brazil. Current position: Professor at Universidad Militar Nueva Granada, Colombia. E-mail: ricardo.castillo@unimilitar.edu.co ORCID: https://orcid.org/0000-0001-6070-2184

Cite this article as: V. Cruz-Carbonell and R. A. Castillo-Estepa, "Assembly and implementation of modular quadrupedal architecture", Vision electronica, algo mas que un estado solido, vol. 13, no. 2, july-december 2019, pp. xx, DOI: XX

Fecha de envio: 4 de abril de 2019

Fecha de recepcion: 15 de abril de 2019

Fecha de aceptacion: 11 de mayo de 2019
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