機械 自動化 外文翻譯 外文文獻 英文文獻 機械臂動力學與控制的研究

1、2009 ieee international conference on robotics and automationkobe international conference centerkobe, japan, may 12-17, 2009control of mobile manipulator using the dynamical systems approachlars-peter ellekildeabstractthe combination of a mobile platform and a manipulator, known as a mobile manipul

2、ator, provides a highly flexible system, which can be used in a wide range of applications, especially within the field of service robotics. one of the challenges with mobile manipulators is the construction of control systems, enabling the robot to operate safely in potentially dynamic environments

3、. 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 approach in which competitive dynamics are used both for the overall coordination of the mobile platform and the manipulator as well as the lower

4、 level fusion of obstacle avoidance and target acquisition behaviors.i. introductionthe 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 combin

5、e 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 western countries causes the number of old people in need of care to increase, w

6、hile there will be less working to actually support them. this requires an increased automation of the service sector, for which robots able to operate safely in indoor and dynamic environments are essential.fig. 1. platform consisting of a segway rmp200 and a kuka light weight robot.the platform us

7、ed 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 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 lon

8、g reach and high payload compared to its own weight, making 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 and the manipulator and combin

9、e 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 reachability and stability, between the two.the control system we propose is based on the dynamical systems approach 5, 6.

10、it is divided into two levels, where we at the lower level consider the mobile platform and 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 app

11、lied to a 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 mobile platform and the manipulator in sections iii and iv. in section

12、v we will show some experiments before concluding the paper in section vi. however, first a summary of work related to the dynamical systems approach will be provided in section i-a.a. related workthe dynamical systems approach 5, 6 provides a framework for controlling a robot through a set of behav

13、iors, such as obstacle avoidance and target acquisition. each behavioris generated through a set of attractors and repellors of a nonlinear dynamical system. these are combined through simple addition of the vector fields to provide the overall behavior of the system. the dynamical systems approach

14、relates to the more widely used potential field method 7, but has certain advantages. where the behavior in the potential field method is the result of following gradients of the field, the behavior variables, such as heading direction and velocity, can be controlled directly using the dynamical sys

15、tems approach.the relative low computational cost associated with the approach, makes it suitable for online control in dynamic environments, and allows it to be implemented even on fairly low-level platforms with limited computational capabilities 8. the robustness to noisy sensors is shown in 9 an

16、d 10 where a combination of infrared sensors and microphones is used for obstacle avoidance and target acquisition. despite being able to solve various tasks it is only a local method, for task and mission-level planning other methods (see e.g. 11) should be applied.a drawback of the approach in 5,

17、6 is the potential creation of spurious attractors when multiple behaviors are combined. to overcome this problem 12 introduces a weighting of the behaviors based on competitive dynamics. the influence of each behavior is controlled using an associated competitive advantage, which together with comp

18、etitive interactions defined between the behaviors, controls the weights. this approach generalizes to an arbitrary number, n, behaviors, but with a o(n2) worst-case complexity, if competitive interactions between all behaviors are needed.real-world indoor experiments using this competitive dynamics

19、 approach can be found in 13, 14. in 13 only the heading direction of the vehicle is used, whereas in 14 both heading direction and velocity are controlled. 15 provides a brief discussion of strategies for the velocity behavior.the dynamical systems approach has not only been used for planar mobile

20、robots, but also for controlling the tool motion of a manipulator 16. more complex dynamical systems using the hopf oscillator for generating limit cycles can also be used. 17 shows how limit cycles with different shapes can be constructed and used for both obstacle avoidance and trajectory generati

21、on. 18 uses the hopf oscillator to generate a timed trajectory, enabling a manipulator to catch a ball rolling down a table. the dynamical systems approach can not only be used for controlling the tool, but also to control the redundancy of a 7 degrees of freedom manipulator as demonstrated in 19.ii

22、. overall architecturethe overall architecture of our system is illustrated in figure 2. to control the mobile platform, in this case a segway, two low level behaviors are use: one for target acquisition and one for obstacle avoidance. using competitive dynamics these are fused together to provide t

23、he mobile behavior, which specifies the desired motion of the mobile platform. similarly we have target acquisition and obstacle avoidance behaviors for the manipulator fused together based on competitive dynamics, to give the manipulator acquisition behavior. when the target is not within reach, th

24、e manipulator should retract to a safe configuration, which is the purpose of the manipulator retract behavior. the last fusion combines the controls in a safe manner, such that the target acquisition and retract behaviors do not disturb one another and the mobile platform does not start moving towa

25、rds a new target before the manipulator has been retracted. fig. 2. overall architecture of the control systemusing weights ， and to represent the influence of the mobile, manipulator acquisition and manipulator retract behaviors, the control signals and for the mobile platform and the manipulator a

26、re given by （1） (2)where （ ） are control inputs to the left and right wheels of the platform as described in section iii, and are the manipulator joint velocities as described in section iv.a. competitive dynamicsthe competitive dynamics approach used is based on 12, but with the additional paramete

27、r used to control the transition rate as in 14. the dynamical system used is thus given by （3）in which is the competitive advantage of behavior b and r,b is the competitive interaction of behavior upon b.1) mobile: the competitive advantages of the mobile platform should strengthen the behavior when

28、 far away from the target and reduce it when the target is reached. this is achieved through （4）in which determines how rapidly the advantage should change, is the distance to the target and specifies a minimum distance to the target required before the mobile platform should move.the mobile behavio

29、r has no ability to interact and suppress other behaviors, thus its competitive interactions are set to 0.2) manipulator acquisition: this behavior should be strengthened when the mobile platform gets close to its target. the competitive advantage will thus be defined as （5）the activation distance m

30、ust be greater than 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 retract: the retract behavior should be activated opposite the goal behavior, hence （6）except for a very small transition time this p

31、revents the manipulators acquisition and retract behaviors from being active at the same time, thus we can set . for the interaction between the retract and the mobile behaviors we wish retract to deactivate mobile when the manipulator is far away from its home configuration. the interaction is ther

32、efore defined as （7）in which and are the manipulators current and home configurations, q specifies a proximity distance around and specifies how quickly the interaction changes.iii. control of the mobile platformthe control of the mobile platform is constructed very similar to what is presented in 1

33、4, but with a few differences. first of all only the target acquisition and obstacle avoidance behaviors are used. the corridor following and wall avoidance are not included, but would be straight forward extensions. the second area in which this work differs is in how the density of obstacles is ca

34、lculated. details of this will be explained in section iii-d.for the control to actually be able to navigate through the environment, it is necessary with a method for localization. the approach we have used is based on the method described in 20, which combines odometry and laser range measurements

35、 matched against a map of dominating lines in the environment.the control of the platform is encoded using the orientation, and the velocity, , which results in a system with control inputs ; the values of are made up of two parts, and , which are combined as （8）where the weights and are controlled

36、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 and , respectively. to obtain these is integrated to get v, which together with the desired rotational velocity,

37、 the wheel diameter and the distance between the wheels can be used to calculate the control inputs as （9） （10）where is the needed difference in wheel speed given by （12）a. target dynamicsthe basic dynamics of this target behavior is (13) (14)in which and are the strengths of the attractors and is t

38、he direction to the target. the constant gives the relation between the distance to the target and the desired velocity. finally is the maximal velocity allowed for the mobile platform。b. obstacle dynamicsgiven a distance and a direction to the ith obstacle, the dynamics of the obstacle avoidance ar

39、e (15) (16)where the dynamics of consists of 3 elements: (i) the relative direction to the obstacle ，(ii) a scale in which determines the decay depending of the distance, ，and (iii) a scale, , based on the direction to the obstacle and with ensuring the generation of an attractor between two obstacl

40、es if the robot can pass through while ensuring the safety distance ds. see 14 for more details.forthe expression adjusts the velocity towards , but ensures that a minimum velocity ofis kept.to obtain the value of we sum over all obstacles （17）c. competitive dynamicsthe weights for the competitive d

41、ynamics are controlled by equation (3) as explained above. below are the competitive advantages and interactions for the two behaviors.1) target: the competitive advantage is set towhenever a target is present, otherwise.the target behavior has the ability to interact with and suppress the obstacle

42、avoidance behavior, when the ratio between the distance to the target and the closest object is sufficient to ensure the movement towards the target will be collision free. this is modeled as （18）in whichis the distance to the closest obstacle, is a gain constant giving how quickly the behavior shou

43、ld interact andexpresses the ratio between the distances to obstacle and target for which we will start to suppress obstacle avoidance.2) obstacle: the competitive advantage of the obstacle behavior is given by （19）in whichis the obstacle density as defined in section iii-d.the interaction is define

44、d as （20）the first part, suppresses the target behavior when the obstacle density exceeds the threshold. the last part,makes sure this only happens when the obstacle avoidance is not being suppressed due to.d. calculation of obstacle densitygiven a set of distances, , between the mobile platform and

45、 obstacles the density, , is calculated as （21）this density function differs from 14 in whichis used. the main problem with this formulation is that we cannot distinguish between many objects relative far away and a single object closed by. for example having 5 objects 2 meters away will give the sa

46、me density as a single object 40 centimeters away. with the exponential function a single object in the scene can never causeto exceed 1. the threshold for switching to the obstacle avoidance behavior will thus have to be less than 1, but given a scene with multiple obstacles the threshold of 1 will

47、 often be too low.furthermore it is found that usinginstead of made tuning the parameters easier as we could now think of the density as the inverse of the distance. it also caused the density to grow very rapidly when getting close to an obstacle, thereby quickly forcing the behaviors to change.iv.

48、 control of manipulatorwe will start by dividing the problem into two parts:1) determining the motion of the tool from the current position to the target while avoiding obstacles.2) inverse kinematics calculating joint velocities needed for the tool motion.the second part is a well understood proble

49、m, which in this work is solved using the inverse kinematics strategy presented in 23. this method incorporates both kinematics and dynamics limitations of the robot, such as joint position, velocity and acceleration limits. furthermore this approach, based on quadratic optimization, has shown to be

50、 very robust with respect to singularities.the motion of the tool is controlled using the manipulators target and obstacle behaviors, to which the weightsandare associated. as input the inverse kinematics needs a 6d velocity screwthus the behaviors must find a changewhich can be integrated to give a

51、 desired tool velocity, ,as （22）where ，andare the contributions from the target and obstacle avoidance behaviors.a. target behaviorthe inputs to the target behavior are the current and desired tool transformationsandfrom these we can compute a desired 6d velocity-screw .to avoid requiring unrealisti

52、c fast motionsis scaled such that andwhereandhere represent the maximal allowed linear and rotational velocities of the tool.calculating （23）we obtain a desired change to the current velocity.b. obstacle-behavioras input the obstacle avoidance behavior takes the current cartesian velocity, and a set

53、 of closest obstacles as vectors, giving direction and distance between tool and obstacle i . we now wish to compute a change to the cartesian velocity based on the direction and distance to obstacles, denotedandrespectively.1) dynamics for direction: from the current velocity of the tool, v, and th

54、e vectorwe compute the angle, between the two as （24）the size of the change in direction of the tool is then calculated as （25）in which is the strength of the repellor, control the decay based the distance andcontrols the relation with the angle to the obstacle. is then used to calculate a desired c

55、hange in the direction of the tool as （26）summing up the contributions from all obstacles we can calculate the change in motion of the tool based on direction to obstacles as （27）2) dynamics for velocity: the dynamics of the velocity are controlled similar to eq. (16). the contribution of obstacle i

56、 . is （28）withsumming up over all obstacles the total contribution becomes （29）c. competitive dynamics1) target behavior: as for the mobile platform the competitive advantage of the target behavior is set to 0.5 when a target is present and 0.5 otherwise. the competitive interaction of the target upon the obstacle behavior is again designed such that when the ratio between the distance to the target and to the nearest obstacle is greater then the thresholdthe obstacle avoidance is suppres