外文翻譯---機(jī)械臂動(dòng)力學(xué)與控制的研究（英文）

1、Control of Mobile Manipulator using the Dynamical Systems ApproachLars-Peter Ellekilde Henrik I. ChristensenAbstract— The combination of a mobile platform and a manipulator, known as a mobile manipulator, provides a high

2、ly flexible system, which can be used in a wide range of appli- cations, especially within the field of service robotics. One of the challenges with mobile manipulators is the construction of control systems, enabling th

3、e robot to operate safely in potentially dynamic environments. In this paper we will present work in which a mobile manipulator is controlled using the dynamical systems approach. The method presented is a two level appr

4、oach in which competitive dynamics are used both for the overall coordination of the mobile platform and the manipulator as well as the lower level fusion of obstacle avoidance and target acquisition behaviors.I. INTRODU

5、CTIONThe majority of robotic research has in the last decades focused on either mobile platforms or manipulators, and there have been many impressive results within both areas. Today one of the new challenges is to combi

6、ne the two areas, into systems, which are both highly mobile and have the ability to manipulate the environment. Especially within service robotics there will be an increased need for such systems. The demography of most

7、 western countries causes the number of old people in need of care to increase, while there will be less working to actually support them. This requires an increased automation of the service sector, for which robots abl

8、e to operate safely in indoor and dynamic environments are essential. The platform used in this work is shown in Figure 1, and consist of a Segway RMP200 with a Kuka Light Weight Robot. The result is a platform that has

9、a relative small footprint and is highly maneuverable, making it well suited for moving around in an indoor environment. The Kuka Light Weight Robot has a fairly long reach and high payload compared to its own weight, ma

10、king it ideal for mobile manipulation. When controlling a mobile manipulator, there is a choice of whether to consider the system as one or two entities. In [1] and [2] they derive Jacobians for both the mobile platform

11、and the manipulator and combine them into a single control system. The research reported in [3] and [4], on the other hand, considers them as separate entities when planning, but do include constraints, such as reachabil

12、ity and stability, between the two. The control system we propose is based on the dynamical systems approach [5], [6]. It is divided into two levels,L.-P. Ellekilde is with The Maersk Mc-Kinney Moller Institute, Faculty

13、of Engineering, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark, lpe@mmmi.sdu.dk H. I. Christensen is with Center for Robotics and Intelligent Machines, Interactive Computing / College of Computing,

14、Georgia Institute of Tech- nology, 85 5th Street, Atlanta, GA, USA, hic@cc.gatech.eduFig. 1. Platform consisting of a Segway RMP200 and a Kuka Light Weight Robot.where we at the lower level consider the mobile platform a

15、nd the manipulator as two separate entities, which are then combined in a safe manner at the upper level. The main reesarch objective in this paper is to demonstrate how the dynamical systems approach can be applied to a

16、 mobile manipulator and used to coordinate behaviours at various levels of control. The remaining of this paper is organized as follows. The overall architecture is described in Section II, followed by the control of the

17、 mobile platform and the manipulator in Sections III and IV. In Section V we will show some experiments before concluding the paper in Section VI. However, first a summary of work related to the dynamical systems approac

18、h will be provided in Section I-A.A. Related WorkThe dynamical systems approach [5], [6] provides a frame- work for controlling a robot through a set of behaviors, such as obstacle avoidance and target acquisition. Each

19、behavior2009 IEEE International Conference on Robotics and Automation Kobe International Conference Center Kobe, Japan, May 12-17, 2009978-1-4244-2789-5/09/$25.00 ©2009 IEEE 1370dmobile threshold specifies a minimum

20、 distance to the target required before the mobile platform should move. The mobile behavior has no ability to interact and suppress other behaviors, thus its competitive interactions are set to 0. 2) Manipulator Acquisi

21、tion: This behavior should be strengthened when the mobile platform gets close to its target. The competitive advantage will thus be defined asαmanip acquisition = ? tanh(kmanip α (dtar ? dmanip threshold)) (5)The activa

22、tion distance dmanip threshold must be greater than dmobile threshold to make sure the behavior is activated. This behavior has no direct interaction with the others, thus its interactions are set to 0. 3) Manipulator Re

23、tract: The retract behavior should be activated opposite the goal behavior, henceαmanip retract = ?αmanip acquisition= tanh(kmanip α (dtar ? dmanip threshold)) (6)Except for a very small transition time this prevents the

24、 manipulators acquisition and retract behaviors from being active at the same time, thus we can set γretract,acquisition = 0. For the interaction between the retract and the mobile behaviors we wish retract to deactivate

25、 mobile when the manipulator is far away from its home configuration. The interaction is therefore defined asγretract,mobile =12(1 + tanh(kretract γ (?qcurrent ? qhome? ? ?q))) (7)in which qcur and qhome are the manipula

26、tors current and home configurations, ?q specifies a proximity distance around qhome and kretract γ specifies how quickly the interaction changes.III. CONTROL OF THE MOBILE PLATFORMThe control of the mobile platform is c

27、onstructed very similar to what is presented in [14], but with a few differ- ences. First of all only the target acquisition and obstacle avoidance behaviors are used. The corridor following and wall avoidance are not in

28、cluded, but would be straight forward extensions. The second area in which this work differs is in how the density of obstacles is calculated. Details of this will be explained in section III-D. For the control to actual

29、ly be able to navigate through the environment, it is necessary with a method for localiza- tion. The approach we have used is based on the method described in [20], which combines odometry and laser range measurements m

30、atched against a map of dominating lines in the environment. The control of the platform is encoded using the orien- tation, φ, and the velocity, v, which results in a system with control inputs f mobile = { ˙ φ, ˙ v}. T

31、he values of f mobileare made up of two parts, f mobile tar and f mobile obs , which are combined asf mobile = wmobile tar f mobile tar + wmobile obs f mobile obs (8)where the weights wmobile tar and wmobile obs are cont

32、rolled using Eq. (3) with the competitive advantage and interactions described in section III-C. As control input we need expressions for the left and right wheels of the mobile platform, denoted uleft and uright, respec

33、tively. To obtain these ˙ v is integrated to get v, which together with the desired rotational velocity ˙ φ, the wheel diameter dwheel and the distance between the wheels dwheelbase can be used to calculate the control i

34、nputs asuleft( ˙ φ, v) = vπdwheel ? ?2 (9)uright( ˙ φ, v) = vπdwheel + ?2 (10)(11)where ? is the needed difference in wheel speed given by? = ˙ φdwheelbasedwheelπ (12)A. Target DynamicsThe basic dynamics of this target b

35、ehavior isf mobile,φ tar (φ) = λmobile,φ tar sin(ψtar ? φ) (13)f mobile,v tar (v) = λmobile,v tar (min(kmobile tar dtar, vmax) ? v) (14)in which λmobile,φ tar and λmobile,v tar are the strengths of the attractors and ψta

36、r is the direction to the target. The con- stant kmobile tar gives the relation between the distance to the target and the desired velocity. Finally vmax is the maximal velocity allowed for the mobile platform.B. Obstacl

37、e DynamicsGiven a distance dobs,i and a direction ψi to the i’th obstacle, the dynamics of the obstacle avoidance aref mobile,φ obs,i = λmobile,φ obs (φ ? ψi)e?cmobile obs dobs,ie?(φ?ψi)22σ2 i (15)f mobile,v obs,i =? ???

38、λmobile,v obs (v ? vmin) for v vmax,i(16)where vmax,i = max(kobsdobs,i, vmin). The dynamics of φ consists of 3 elements: (i) The relative direction to the obstacle (φ ? ψi), (ii) a scale e?cmobile obs dobs,iin which cmo

39、bile obs determines the decay depending of thedistance, dobs,i, and (iii) a scale, e?(φ?ψi)22σ2 i , based on the direction to the obstacle and with σi = arcsin( 1+Ds1+dobs,i ) ensuring the generation of an attractor betw

40、een two obstacles if the robot can pass through while ensuring the safety distance Ds. See [14] for more details. For f mobile,v obs,i the expression adjusts the velocity towards kobsdobs,i, but ensures that a minimum ve