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Abstract Research focuses on robots related to area coverage applications such as cleaning painting demining lawn moving and inspection is gaining significant momentum in recent years The majority of such research platforms faces significant performance issues while accessing narrow and constrained spaces due to their fixed morphology To this end we have developed a novel self reconfigurable robot platform named as hTetran inspired from Polyabolo which can change its morphology to any of the six tetrabolo shapes with an objective of maximizing the area coverage This paper presents the system design reconfiguration theory and locomotion modules of the developed robot including the adaptation of Polyabolo tiling theory as a coverage path planning strategy for autonomous navigation The paper concludes with a set of experiments in a mocked office room setup that validates the efficiency of the proposed robot in terms of area coverage Our experimental trials indicate that the hTetran brings out a higher area coverage performance in all considered experimental cases I INTRODUCTION There has been an upward trend in deploying robots for area coverage task that deals with applications such as cleaning lawnmowers demining cleaning agriculture and painting Majority of such robotic platforms are expected to navigate through all the points in the deployed area without any overlapping paths and obstacle collisions Researchers intensified their efforts in finding solutions to overcome the bottlenecks of coverage robotics and translated them into commercial products such as iRoomba Samsung Hobot Aquabot Honda Miimo and Robot Worx Exploration of coverage robotics was initiated since the 1980s and have studied in depth under various technical aspects including mechanism autonomy and multi robot strategies For instance Miyake et al 1 illustrated the analysis of adsorption and locomotion mechanisms of a window cleaner robot They achieved the locomotion with the help of two motors which gives the freedom of mobility over any axis Adsorption technique is based on the suction cup which holds the robot on vertical surfaces Gao et al 2 studied and demonstrated kinematics and control methods of a floor Research supported by NRPO National Robotics Research Office NRPO Singapore Prabakran Veerajagadheswar is with the Singapore University of Technology and Deisgn Singapore 487372 corresponding author to provide e mail prabakaran sutd edu sg Vinu Sivanantham is with the Singapore University of Technology and Deisgn Singapore 487372 e mail vnu 619 ManojKumar Devarassu is with the Singapore University of Technology and Deisgn Singapore 487372 e mail manojkumar sutd edu sg Prof Mohan Rajesh Elara is an assistant professor working under EPD with the Singapore University of Technology and Deisgn Singapore 487372 email rajeshelara sutd edu sg cleaning robot They studied and developed smooth locomotion capability on the floor cleaning robot using Swedish wheels Baloch et al 3 discussed the design and modeling of an autonomous lawnmower where they studied and discussed on mechanical aspects and electronics to improve the performance of the current prototype Concerning autonomy Liu et al in 4 proposed a novel strategy that deals with the coverage path planning in an autonomous cleaner Here they used a combination of random path planning and local coverage planning to achieve robustness and work efficiently in family environments Shiu et al 5 developed an optimal path planning scheme for autonomous lawnmowers with the help of a global positioning system to realize its real time position in the environment Kim and Ryan 6 reported the use of visual SLAM with an integrated navigation algorithm for robots to achieve area coverage and navigation uncertainty performance to explore the target area efficiently In multi robot area coverage strategies Hazon et al 7 addressed the efficiency and robustness of multi robot coverage algorithms using spanning tree coverage of cell decomposition Fazli et al 8 discuss the problem of repeated area coverage in a polygon space by multi robots Under the effects of the variables like the visual range of robot and environment factors they evaluated the performance of repeated area coverage algorithms Low et al in 9 presented an adaptive multi robot approach to perform novel extensive area coverage with hotspot sampling using non myopic path planning Even though numerous pieces of literature are demonstrating the use of area coverage robots conventional platforms are still facing issues while deployed in constrain workspaces One primary factor that curtails the performance of the robot concerning area coverage is their fixed morphology design Such a model would restrict their navigation while accessing narrow spaces and room corners One viable or an alternative design strategy to overcome these bottlenecks in coverage robotics is to design next generation robotic platforms with self reconfigurable mechanisms Over the past three decades a particular interest has been taken to explore in the domain of reconfigurable robots Such systems were grouped under Intra Inter and nested reconfigurable robots 10 Individual robots that can change their morphology within itself are called intra reconfigurable robots Tan et al 11 presented Scorpio an intra reconfigurable robot that can switch between rolling crawling and wall climbing morphologies Superbot 12 is a reconfigurable robot that can autonomously change its shape to accomplish the specified task Inter reconfigurable robots are when multiple robots that can disassemble and reassemble to form a global morphology Polybot 13 is one such example that can connect with one or more similar modules Nested hTetran A Polyabolo Inspired Self Reconfigurable Tiling Robot Prabakaran Veerajagadheswar Vinu Sivanantham ManojKumar Devarassu and Mohan Rajesh Elara 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE4877 reconfigurable robots are where the concept of intra and inter reconfigurable robots are combined to exhibit global morphology Kee et al presented a nested reconfigurable robot Hinged Tetro 14 that can transform between morphologies as a single unit and can combine with other heterogeneous homogeneous robots to generate global morphologies With the great works of literature on reconfigurable robotics it is clear that most works were limited to mechanism design and lost its connection to an application To this end in our previous efforts we proposed a novel design strategy for robots to improve area coverage performance Wherein we introduce our next generation reconfigurable floor cleaning robot called hTetro 15 which can change its morphology to any of the seven single Tetris pieces which aid the robot to access narrow and impartial spaces to achieve superior area coverage performance than traditional fixed morphology platforms However due to its cubical structure the platform still faces issues in navigating through non parallelogram structured space In another work we investigated the area coverage performance of a robot called hTetrakis 16 wherein we used four equilateral triangles as each block rather than using cubes Although the platform shows a superior area coverage performance in non parallelogram structures there is a considerable coverage degradation when it is deployed in parallel curved and circular spaces To overcome these issues with area coverage in existing polyform robots in this work we explore other polyforms which could mutilate into both parallel and non parallel geometrical structures Such a structure could be achieved while using other trilateral shapes In this paper we are proposing a novel Polyabolo based self reconfigurable robot called hTetran which consist of four isosceles triangles connected with three hinged points The developed robot is capable of changing its morphology to any of the six different Polyabolo shapes to maximize the area coverage This paper presents the challenges that we encountered during the development of our hTetran robot from its reconfigurable mechanism design integration of locomotion modules and translating the abstract design into a physical mechanism Also in this work we discussed the implementation of Polyabolo tiling theorem as a path planning strategy for autonomous navigation The paper concludes with a set of experiments with floor cleaning as a case study in a real world scenario that validates the efficiency of the proposed robot in terms of area coverage II DESIGN PRINCIPLES OF THE HTETRAN ROBOT Polyabolo is the inspiration for the design of our hTetran robot and its reconfiguration strategies Polyaboloes 17 are two dimensional geometric structures consist of two or more right angled isosceles triangle attached in edge to edge under distinct arrangements A Polyabolo with two isosceles triangles is called a diabolo with three triangles is triobolo and with four triangles is tetrabolo shown in Fig 1 Because the tetrabolo accommodates a large number of Polyabolo forms in this work we adopted the tetrabolo geometrical structure as the morphology of our self reconfigurable hTetran robot Our main challenge in designing the hTetran robot is to realize the ability to change between morphologies In order to achieve the transformation in hTetran we implemented the principle of hinged dissection A hinged dissection 18 is a geometric approach that dissects a planar structure into a finite number of pieces and connected with hinged points in such a way that new polygonal structures can be created by just swinging the hinge points without breaking the chain So far there are numerous studies have reported in the literature with the concept of hinged dissection where they study about switching between different polygons 19 3D hinges 20 and pattern generations 21 For the robotics domain we have studied hinged dissection principles by applying it to hTetro 15 and hTetrakis robots 16 In that work we used LLR hinged configuration for the hTetro robot to achieve transformation between all one sided Tetris pieces and worn LL hinge configuration to realize all Tetriamond shapes with the hTetrakis robot Figure 1 Types of Polyabolos Concerning polyabola we separated the polyforms into four individual right angled isosceles triangles Each triangle pi where i 1 2 3 has three vertexes p1 p2 p3 which could hinge to another copy of p Construction of hinged dissection could be achieved by finding the best hinge sequence for the given n forms We identified the hinge sequence for the Tetrabolo by trying different orientation combination of each isosceles triangle In such an approach we could have more than four hindered and ninety hinged sequences for four isosceles triangles Even though we had a lot of hinge sequence the combination that could achieve all possible one sided Tetrabolo forms does not exist The maximum number of tetrabolo forms that we achieved in any hinge combination is six Due to the limitation in attaining maximum configurations we reversed the process of hinged dissection as described in 17 In this work we choose the configuration before identifying the hinge sequence We identified I tetrabolo as our primary form and tried different hinge combinations that benefit the hTetran robot to attain any six tetrabolo forms In an I Tetrabolo form the possible hinge placement is T1 Top Junction Point which connected four triangles B1 B2 and B3 bottom Junction Points connects two triangles respectively shown in Fig 2 In order to achieve all the mentioned tetrabolo forms we must need three hinge points Since T1 connects all four triangles it is critical to fix the top hinge point that allows us to give more hinge combination to achieve the required configurations 4878 Figure 2 Possible morphologies under distinct hinge combination with I Tetrabolo The combination of T1 B1 B2 T1 B2 B3 T1 B1 B3 and their possible transformations are shown in Fig 2 With hinge combination T1 B2 B3 we could achieve all the mentioned configurations To the orientation and vertex links of each triangle p the triangle vertex p11 is attached to p23 of triangle 2 The triangle 2 and 3 were connected in the vertex of p21 and p33 Similarly with triangle 3 and 4 the vertex connection was implemented in p32 and p42 shown in Fig 3 For the work presented in this paper we adopted the T1 B2 B3 hinged dissection as shown in Table 1 to enable its shape shifting capabilities Figure 3 Hinged link between each Right Triangle for the hinged combination Table 1 Hinged points and its six achievable configurations of htetran robot III HTETRAN SYSTEM ARCHITECTURE hTetran is a self reconfigurable robot that is constructed under the principle of Polyabolo which consists of four isosceles triangular blocks connected three active hinges Each triangular block being a right angled isosceles triangle the robot plays a critical role in achieving maximum area coverage specifically in convex boundary regions by reconfiguring itself to different morphologies The structural design locomotion mechanism hinge dissection and control modules play an essential role for the robot to adapt to the environment according to the boundary of the environment as well as the obstacle present A Structural and Electronics Design The dimensions of the adjacent and opposite side of each triangular block are 210 mm whereas Hypotenuse is 294 mm The vertices of each block around the hinge position are chamfered to avoid edge to edge collision while reconfiguring The base and walls of the robot are fabricated with acrylic sheets of 2 mm thickness Each block is equipped with a Herkulex servo motor mounted on top of a Pololu DC Gearmotor as in Fig 4 Left This Servo motor controls the direction of locomotion by turning the locomotion module with a maximum of 180 degree freedom of rotation while the DC motor is responsible for the locomotion of each block Altogether allowing locomotion in any direction along the X Y plane The mobility part of the robot is handled by a set of 4 Pololu dc gear motors and four herkulex servo motors one in each block Each Pololu dc motor has a voltage rating of 7 4 12 v and stall torque 3 kg cm The transformation of the robot is attained by actuating the active hinge motors Three herkulex servo motors are used on each joint connecting all four blocks to achieve reconfigurability Each servo motor has an operating angle of 320 degrees stall torque of 24 kg cm and operates at a voltage of 7 4v The servo SM1 attached with block 1 and 2 at right angles has maximum freedom of 180 degree rotation While SM2 and SM3 placed at the 45 degree angles of each triangle has maximum freedom of 270 degree rotation The system locks the hinged motors to maintain the robot morphology throughout the locomotion Concerning the electronics shown in Fig 4 Right each block is equipped with a motor controller that has a maximum current rating of 7A So four motor controllers are used in total where each one is defined with a specific address and communicates with Arduino serially TX1 RX1 The serial communication between Arduino Atmega 2560 16 bit microcontroller and motor controller is full duplex which enables the motor controller to send encoder feedback from the motors to Arduino and receive the control signals from Arduino to drive the dc motors simultaneously Herkulex servo motors directly communicate with the Arduino board through full duplex serial TX2 RX2 communication Specific address id is defined for all the servo motors so that the TX and RX channels of each servo can be connected like daisy chain connection Power supply to the servo motors is given parallelly from the battery so all the motors get sufficient current for operation A Lidar is mounted on top of the robot to achieve autonomous navigation Intel computes stick is used as a microprocessor to map the environment based on the Lidar output Arduino is connected to compute stick using USB serial compute stick uses ROS platform to establish a proper communication interface with Lidar and Arduino In this system Arduino works in slave mode and Compute stick as a master Based on the Lidar values compute stick sends navigation commands to the Arduino to achieve area coverage for the given space 4879 Figure 4 System Architecture and Locomotion module of hTetran IV COVERAGE PATH PLANNING OF HTETRAN In the process of developing an area coverage robot it is critical to address its ability to demonstrate autonomous navigation and coverage planning So far numerous coverage path planning techniques have been proposed and implemented successfully in various robotic systems However such an algorithm was mostly realized in the fixed morphological platforms When it comes to reconfigurable robotic systems due to their ability to assume morphologies we required novel coverage path planning approaches which could account the different morphological forms of the robot To this end we are proposing a novel area coverage technique for our hTetran robot based on Polyabolo tiling theory By utilizing this approach the hTetran robot could generate a global tileset for the deployed region and perform coverage by navigating on the generated tiles while assuming its morphology on each tile pieces A Polyabolo Tiling Polyabolo tiling is a mathematical study wherein theories were developed based on the tiling a region using the same polyform or a set of distinct polyforms Tiling theories were studied with various polyforms and applied in the graphics 22 and gaming 23 applications However there is not much work that has been recorded in the literature were they study the application of Polyabolo tiling in the robotics field The presented work is our initial attempt to implement Polyabolo tiling as a coverage path planning technique in a reconfigurable robot Specifically we evaluated the tiling theorems that was proved in 24 where they tiled a
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