Path Planning For Space Manipulators Exhibiting Nonholonomic Behavior

Nonholonomic behavior is observed in free-floating manipulator systems, and is due to the nonintegrability of the angular momentum. Free-floating manipulators exhibit dynamic singularities which cannot be predicted by the kinematic properties of the system and whose location in the workspace is path dependent. Trouble-free Path Independent Workspaces are defined. A joint space planning technique used to control the orientation of the spacecraft by using joint manipulator motions is reviewed, and its limitations are discussed. Finally, a cartesian space planning method that permits the effective use of a system’s reachable workspace by planning paths that avoid dynamically singular configurations is proposed and demonstrated by an example. I . Introduction Space robotic devices are envisioned to assist in the construction, repair and maintenance of future space stations and satellites. To increase the mobility of such devices, freeflying systems in which one or more manipulators are mounted on a thruster-equipped spacecraft, have been proposed [1-4]. To increase a system’s life, operation in a free-floating mode has been considered [1-6]. In this mode of operation, spacecraft thrusters are turned off, and the spacecraft is permitted to translate and rotate in response to manipulator motions. In practice, this mode of operation can be feasible if the total system momentum is zero; if non zero momentum develops, a system’s thrusters must be used to eliminate it. Free-floating systems exhibit nonholonomic behavior, which is due to the nonintegrability of the angular momentum [5,8]. In addition, in such systems dynamic singularities exist, which are functions of the system mass properties and cannot be predicted from its kinematic structure [6,7]. These characteristics complicate the planning and control of such systems. Joint space planning techniques that take advantage of the nonholonomy in such systems were proposed [1,5]. A Self Correcting Planning technique allows the control of a spacecraft’s orientation using the manipulator’s joint motions [1]. Lyapunov techniques were explored to achieve simultaneous control of a spacecraft’s orientation and its manipulator’s joint angles, using the manipulator’s actuators only. Convergence problems were reported in some cases [5]. In this paper, the fundamental kinematic and dynamic nature of free-floating manipulators is discussed first. The effects of the nonintegrability of the angular momentum and of the dynamic singularities on the behavior of a free-floating system are presented. It is shown that dynamic singularities are path dependent, and that a particular workspace point can induce a dynamic singularity or not, depending upon the path taken to reach it. Path Independent Workspaces are defined as regions in which no dynamic singularities occur. The nonholonomic characteristics of free-floating manipulators can be exploited to control the orientation of the spacecraft by closed joint space paths. A joint space planning technique, called Self Correcting Planning, is reviewed, and potential problems in using it are identified. In particular, it is shown that there exist configurations at which a closed path in the joint space will have no effect on the spacecraft orientation. Finally, a Cartesian space path-planning technique which yields paths connecting any two points in the workspace, is presented. This technique avoids dynamically singular configurations, and hence permits the effective use of the full reachable workspace of a free-floating system. II . Kinematic and Dynamic Modeling of Free-floating Manipulators The kinematic and dynamic equations needed to model a rigid free-floating manipulator system, see Figure 1, were obtained in [6-8]. A key feature of this modeling is expressing the kinematic and dynamic variables of the system as functions of a set of constant length, body-fixed barycentric vectors [8,9]. The dynamics were written using a Lagrangian approach. Here the basic kinematic and dynamic equations are reviewed. The manipulator joint angles and velocities are represented by the N×1 column vectors q and q . . The spacecraft can translate and rotate in response to manipulator movements. The manipulator is assumed to have revolute joints and an open chain kinematic configuration so that, in a system with an N degree-of-freedom (DOF) manipulator, there will be 6+N DOF. Assuming that no external forces act on the system, the system center of mass (CM) does not accelerate, and the system linear momentum is constant. With the further assumption of zero initial momentum, the system C M remains fixed in inertial space, and can be taken as the origin of a fixed frame of reference.