【正文】 ge 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 change 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 . is （28）WithSumming up over all obstacles the total contribution bees （29）C. Competitive Dynamics1) Target Behavior: As for the mobile platform the petitive advantage of the target behavior is set to when a target is present and － otherwise. The petitive 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 suppressed. This is acplished by （30）In whichis the distance between the tool and the target and is a gain factor specifying how quickly to change the value of.2) Obstacle Behavior: The petitive advantage of the obstacle behavior is the same as in Section IIIC, （31）With the density calculated using Eq. (21), but w。 hman, . Wernersson, The Hough transform inside the feedback loop of a mobile robot, Proceedings of ICRA, Vol 1, 1993, pp. 791798.[22] . Arras, . Siegwart, Feature Extraction and scene interpredation for mapbased nagivation and map building, Proceedings of SPIE, Mobile Robotics XII, Vol. 3210, 1997, pp. 4253.[23] . Ellekilde, P. Favrholt, M. Paulin, . Petersen, Robust control for highspeed visual servoing applications, International Journal of Advanced Robotic Systems , Vol. 4, No. 3, 2007, pp. 272292.Control of Mobile Manipulator using the Dynamical Systems ApproachLarsPeter EllekildeAbstract—The bination of a mobile platform and a manipulator, known as a mobile manipulator, 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. 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 petitive 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. 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 bine 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, while 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 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 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 pared 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 bine 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]. 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 bined 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 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 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 IA.A. Related WorkThe dynamical systems approach [5], [6] provides a framework for controlling a robot through a set of behaviors, such as obstacle avoidance and target acquisition. Each behavioris generated through a set of attractors and repellors of a nonlinear dynamical system. These are bined through simple addition of the vector fields to provide the overall behavior of the system. The dynamical systems approach 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