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Online Dynamic Tip-Over Analysis for a Wheeled Mobile Dual-Arm Robot with an Improved Tip-Over Moment Stability Criterion
Online Dynamic Tip-Over Analysis for a Wheeled Mobile Dual-Arm Robot with an Improved Tip-Over...
Li, Xianhua;Wu, Liang;Sun, Qing;Song, Tao
Hindawi Journal of Robotics Volume 2021, Article ID 9913335, 11 pages https://doi.org/10.1155/2021/9913335 Research Article Online Dynamic Tip-Over Analysis for a Wheeled Mobile Dual-Arm Robot with an Improved Tip-Over Moment Stability Criterion 1 1 2 2,3 Xianhua Li , Liang Wu , Qing Sun , and Tao Song School of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001, China School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200444, China Shanghai Robot Industry Technology Research Institute Co., Ltd., Shanghai 200063, China Correspondence should be addressed to Xianhua Li; email@example.com Received 29 March 2021; Revised 6 June 2021; Accepted 25 June 2021; Published 12 July 2021 Academic Editor: Weitian Wang Copyright © 2021 Xianhua Li 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. Tip-overstabilityanalysisiscriticalforthesuccessofmobilemanipulationofthedualarm,especiallyinthecasesthatthedualarm or the mobile platform moves rapidly. Due to strong dynamics coupling between the dual arm and mobile platform, online evaluation of dynamic stability of the mobile dual-arm robot still remains challenging. *is paper presents an improved tip-over moment stability criterion dealing with the dual arm and mobile platform interaction and proposes an algorithm for calculating the tip-over stability margin of the arm end in the workspace to analyze the dynamic stability of the wheeled mobile dual-arm robot. *e simulations on a four-wheeled mobile dual-arm robot validate the correctness and feasibility of the proposed method. for the obstacle environment . Kagami et al.  described 1. Introduction afastdynamicallyequilibratedtrajectorygenerationmethod *e wheeled mobile dual-arm robot (WMDAR) is an for a humanoid robot based on the relationship between the emerging class of robots which have capabilities of both robot’scenterofgravityandtheZMP.However,ifthecenter moving and manipulation. *e WMDAR is usually human- of mass of the robot system changes, ZMP is not sensitive to robot collaboration, enabling it to be widely employed in the stabilityof thesystem. *erefore,Papadopoulos andRey home service, restaurant service, and medical treatment deﬁned the tipping stability margin according to the force- [1–3]. However, the WMDAR is a kind of system with angle (FA) margin criterion and described a real-time unstable structure, which may tip-over under the action of rollover prediction and prevention scheme based on static diﬀerent dynamic factors or external interference, especially and dynamic force-angle measure [10, 11]. *is criterion for the mobile service robot with small mobile platform, ignores the reaction force and moment of the manipulator acting on the moving platform. *en, Moosavian and Ali- large variation of system mass distribution, and bearing extraload in work. pour proposed a moment-height stability (MHS) measure Currently, some tip-over stability criteria have been for the wheeled mobile robot considering robot dynamics applied in mobile robots [4–9]. Among the many stability and system gravity center [12–15]. In addition, some other criteria, the zero moment point (ZMP) is the most popular. stability criteria were applied to the stability detection of the Sugano et al. presented concepts of the stability degree and mobile manipulator. Ghassempoor and Sepehri proposed a the valid stable region based on the zero moment point methodtomeasurethestabilityaccordingtotheenergylevel (ZMP) . Korayem et al. proposed an algorithm for de- of the moment acting on the support boundary . A termining the maximum load carrying capacity of a mobile method was presented for tip-over stability analysis of a manipulatorconsideringtip-overstabilitybasedontheZMP wheeled mobile manipulator based on tip-over moment by 2 Journal of Robotics Guo et al.  *e normal bearing force criterion  re- 2. Kinematic and Force Model of the Wheeled quires force sensors to measure the bearing force, which is Mobile Dual-Arm Robot costly. At present, many works have been performed on the tip-over stability criterion of the mobile robot, but, at the 2.1.KinematicModeloftheWheeledMobileDual-ArmRobot. same time, some papers focus on the mobile robot tip-over *eWMDARconsistsofafour-wheelmobileplatform,awaist, avoidance algorithm. and the dual arm mounted on the mobile platform, depicted in Moubarak and Ben-Tzvi  proposed a global optimal Figure 1. *e four-wheel mobile platform is composed of a attitude convergence algorithm for redundant serial robots, platform, two driving wheels, and two driven wheels, in which whichcanpreventtippingwithoutconsideringtheinﬂuence twodrivingwheelsgoforwardorturnthroughdiﬀerentialdrive. of joint velocity and acceleration on tipping stability. Rey TodescribethemotionoftheWMDAR,coordinatesystems and Papadopoulos  used the FA measure method for wereestablished,i.e.,theworldframe O X Y Z ,therobot W W W W initial conﬁguration of the robot to avoid the robot tipping bodyframe O X Y Z ,theleftarmframe O X Y Z ,theend S S S S L L L L over. Based on an adaptive neural fuzzy algorithm, Li and frame of left arm O X Y Z , the right arm O X Y Z , LL LL LL LL R R R R Liu  utilized self-motions of redundant mobile ma- and the end frame of right arm O X Y Z , as shown in RR RR RR RR nipulators to improve a robot’s stability. Ding et al.  Figure 2(a). And, m is the mass of the mobile platform and the proposed a real-time tipping avoidance algorithm to reduce body, and O is the center of mass of the mobile platform and the transmission of tipping torque by adjusting the ma- the body. In the four-wheel mobile platform, points p , p , p , 1 2 3 nipulator posture or changing the robot speed, which can and p are the contact points between the mobile platform and eﬀectively avoid the robot tipping. Many environments and thegroundandthefourblacksolidlinesconnectingtheadjacent scenarios contain rough and irregular terrain and are dif- two points are the four tip-over axes of the robot system, as ﬁcult for robots. Agheli and Nestinger  presented a showninFigure2(b).Meanwhile,therelevantparametersofthe multilegged reactive stability control method for main- robotsystemare showninTable1, andthe positionparameters taining system stability under external perturbations. Feng ofthepointinthetableareexpressedinthereferencecoordinate et al.  introduced a new method for evaluating the frame O X Y Z . S S S S stability of robots in rugged terrain and proposed an al- *en,thetransformationmatricesbetweendiﬀerentframes gorithm for automatically realizing self-balancing of robots. aregivenasfollows,andtheposeoftheendofthearmcouldbe Kashyap and Parhi  utilized the LIPM plus ﬂywheel obtained by the screw theory , as shown in equation (3): model (LIPPFM) for analysis of the complete dynamic cos θ −sin θ 0 d motion of the humanoid robot. It can be seen that the m m xm ⎢ ⎤ ⎥ ⎡ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ previous research on the stability maintenance of the robot ⎢ sin θ cos θ 0 d ⎥ ⎢ ⎥ W ⎢ m m ym ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ � , (1) T ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ S ⎢ ⎥ motionprocessmainlyfocusedontheattitudechangeofthe ⎢ ⎥ ⎢ ⎥ ⎢ 0 0 1 0 ⎥ ⎣ ⎦ manipulator of the single-arm mobile robot through the 0 0 0 1 analysis of the above literature. However, there is no re- search on the attitude change of the two arms and the cos θ 0 sin θ 0 l l overturning compensation caused by the speed and accel- ⎢ ⎥ ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ eration of the two arms. ⎢ L ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 1 0 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ In this paper, an improved tip-over moment stability S ⎢ ⎥ ⎢ ⎥ ⎢ 2 ⎥ ⎢ ⎥ ⎢ ⎥ T �⎢ ⎥, ⎢ ⎥ ⎢ ⎥ L ⎢ ⎥ ⎢ ⎥ criterion is proposed dealing with dual-arm and mobile ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ −sin θ 0 cos θ d ⎥ ⎢ ⎥ ⎢ l l ⎥ ⎢ ⎥ platform interaction. Meanwhile, an algorithm for calcu- ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ lating the tip-over stability margin of manipulator work- 0 0 0 1 space is also presented to analyze the dynamic stability of (2) cos θ 0 sin θ 0 l l WMDAR. *is paper proposes a method to study the sta- ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ bility of WMDAR, and this algorithm is very important for ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ L ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ the follow-up research. *e dynamic stability of the robot ⎢ 0 1 0 − ⎥ ⎢ ⎥ ⎢ ⎥ S ⎢ ⎥ ⎢ 2 ⎥ ⎢ ⎥ ⎢ ⎥ T �⎢ ⎥, ⎢ ⎥ ⎢ ⎥ can be studied by integrating the algorithm into the control r ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ elements,whichlaysafoundationforthetrajectoryplanning ⎢ −sin θ 0 cos θ d ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ l l ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ of the robot to tip-over avoidance. 0 0 0 1 *is paper is divided into six sections. *e kinematics and force model of this robot are analyzed in Section 2. An n o a p improvedtip-overmomentstabilitycriterionispresentedin x x x x ⎢ ⎥ ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ Section 3. *en, in Section 4, the workspace pose dis- ⎢ ⎥ ⎢ n o a p ⎥ ⎢ ⎥ ⎢ ⎥ ξ θ ξ θ ⎢ y y y y ⎥ ⎢ ⎥ 1 1 6 6 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ g (θ) � e , . . . , e g (0) � ⎢ ⎥. (3) ⎢ ⎥ cretizationissolvedandanalgorithmforcalculatingthetip- st st ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ n o a p ⎥ ⎢ ⎥ ⎣ ⎦ z z z z over stability margin of the manipulator is proposed. In 0 0 0 1 Section 5, simulation in MATLAB software is carried out in order to validate correctness of this improved tip-over Forthesakeofsimpliﬁcationofanalysisandcomputations stability criterion and an algorithm for calculating the tip- conducted in the paper, the following assumptions are made: over stability margin of workspace to analyze the stability of WMDARisproposed,andinSection6,someconclusionson (1) *e ground is even, and no surface shrinkage is them are drawn. considered Journal of Robotics 3 Figure 1: Model of the wheeled mobile dual-arm robot. Z p r 1 O O R L r θ X L p p 4 2 g Z RR LL RR O LL RR LL X LL RR m p xm Y d W ym (a) (b) Figure 2: Coordinates’ system deﬁnition. (a) Dual-arm robot system. (b) Platform system. Table 1: Related parameters of the robot system. the arm end to joint 1 can be obtained through the iterative relationship between the links based on the Newton Euler Parameters Values method and screw theory. p (m) [0.604, 0, 0] p (m) [0, 0.604, 0] p (m) [−0.604, 0, 0] 2.2.1. .e Speed of Link. *e Jacobian matrix of each link p (m) [0,−0.604, 0] can be obtained by combining the Newton Euler method O (m) [0,−0.399, 1.278] and screw theory, as shown in the following equation: O (m) [0, 0.399, 1.278] O (m) [0, 0, 0.0658] c J � Ad ^ ξ , . . . , Ad ^ ξ , . . . ,0 , i � 1,2, . . . , n. (4) ξ θ ξ θ i 1 1 1 i i i e e m(kg) 60 *erefore, the relationship between the speed of each (2) All wheels are always in point contact with the joint and the speed of the ith link was ground, i.e., no slippage of the wheels occurs V � J θ. (5) i i (3) *e dual arm and body are rigidly connected with the platform, and the links and joints of the ma- nipulator are rigid 2.2.2. .e Acceleration of Link. *e acceleration of each link (4) *e mobile platform and the body were taken as a can be calculated by deriving the following equation: whole because the inﬂuence of the robot’s body € _ _ _ (6) V � J θ + J θ, i i motion is not considered in this paper. where J � [V × Ad ξ , . . . , V × Ad ξ , . . . ,0], i � i 0 1 i−1 i 2.2. Force Model of the Wheeled Mobile Dual-Arm Robot. ξ θ ξ θ 1 1 i i e e In this paper, the dynamic model was mainly aimed at the 1,2, . . . , n, where V is the velocity of the base (body and dynamic model of the manipulator. *e force/moment of mobile platform) in equation (5). d 4 Journal of Robotics 2.2.3. Force/Moment Equation of Link. *e force balance f f z2 z1 equation of ith link can be obtained, as shown in the fol- lowing equation: z2 z1 y2 y1 J J G E ∗ O L1 _ R1 (7) w � w − w + w + w � I V + V × I V, i i i i i i+1 i i m m y2 y1 x1 where w isthegeneralizedjointforce/momentproducedby i x2 x1 the ith joint, w is the generalized joint force/moment f x2 i+1 produced by the joint i +1 exerted on link i, w is the force/ moment of gravity exerted on link i, w is the sum of other ∗ ∗ external forces/moment, I � Ad I (Ad ) , I is the i i0 i ξ θ ξ θ i i i i e e space inertia of the current manipulator conﬁguration, and I is the spatial inertia of the link i in the initial conﬁgu- i0 p i+1 Mobile platform ration of the manipulator. *e above formula was derived from the arm base coordinate frame (for example, coordi- nate frame O X Y Z for left arm). *e force/moment l L L L L i balanceequationofjoint icanbeobtainedbycombiningthe S Newton Euler method and screw theory, as shown in the Z p W Y i following equation: J J G E ∗ Tip-over axis (8) w � w − w − w + I V + V × I V. i i i i i+1 i i W Equation (8) provides a reverse iterative method to calculate the joint constraint force/moment, which can be W calculated from the end eﬀector to the last joint n of the arm Figure 3: Force and moment model of the WMDAR. untiljoint1.*econstraintforce/momentonjoint1andthe force/moment of the arm acting on the body and mobile 2.2, and the force/moment consists of components in three platform are reciprocal from Figure 3. directions, as shown in the following equation: 3. Improved Tip-Over Moment T T (9) −w � f , m , M M Stability Criterion In this section, we have derived a new tip-over moment ⎧ ⎪ f f f f � , 1x 1y 1z stability criterion for WMDAR with consideration of dual (10) m � m m m . arm-mobile platform interactions. Figure 3 depicts the 1x 1y 1z variousforcesandmomentexertingonthebodyandmobile *etip-overmoment(TOM)onthetip-overaxis(TOA) platform. *e reaction wrench from the arm onto the body a can be calculated through the above calculation: ii+1 and mobile platform is expressed as −w based on Section TOM � f × l · a +