Nonlinear Dynamics 9: 1-19, 1996.
© 1996 Kluwer Academic Publishers. Printed in the ,Netherlands.
Free-Floating Closed-Chain Planar Robots: Kinematics
and Path Planning
S. K. AGRAWAL, R. GARIMELLA, and G. DESMIER
Department of Mechanical Engineering, Ohio University, Athens, OH 45701, U.S.A.
(Received: 7 September 1994; accepted: 5 October 1994)
Abstract. The study of free-floatingmanipulators is important for the successof roboticsprogram in space and in
the design of innovativerobot systemswhich can operate over a large workspace.In order to studythe fundamental
theoretical and experimental issues encountered in space robotics, a closed-chain planar manipulator was built at
Ohio University (OU) which floats on a flat table using air bearings. Due to the absence of external forces in the
plane of the table and couples normal to this plane, the linear momentum in the plane and the angular momentum
normal to this plane are conserved. It is well known that the linear momentum equations are holonomic while the
angular momentum equation is nonholonomic. Due to this nonholonomic behavior, the path-planning schemes
commonly used for fixed-base manipulators do not directly apply to free-floating manipulators. In this paper,
we present an algorithm for motion planning of planar free-floating manipulators based on the inverse position
kinematics of the mechanism. It is demonstrated that the inverse position kinematics algorithms, commonlyused
for fixed-base manipulators, can be successfully applied to free-floating manipulators using an iterative search
procedure to satisfy the nonholonomic angular momentum constraints. This procedure results in paths identical
to those predicted by inverse rate kinematics. The inverse position kinematics algorithm is then used to avoid
singularities during motion to result in successful paths. The results of the simulation of this algorithm using
parameter estimates of the OU free-floatingrobot are presented.
Key words: Free-floatingrobots, motion planning, space robotics.
1. Introduction
Satellite-mounted manipulators will play an important role in the construction of the space
station and in the future missions for space inspection and repair. Over the last decade, several
research have been reported on manipulation systems which have free-floating base. Long-
man et al. [1] presented a way to control the end-effector trajectories accounting for base
motions. Umetani and Yoshida [2] presented the notion of generalized Jacobians. Alexander
and Cannon [3] reported experiments on a free-floating manipulator. Vafa [4] presented the
notion of 'virtual manipulators' applied to open-chain free-floating manipulators. Papadopou-
los and Dubowsky [5] studied control algorithms for free-floating manipulators. Schneider
and Cannon [6] presented a strategy for cooperative manipulation of floating robots. AgrawaI
and coworkers [7, 8] reported studies on workspace and dynamic simulations of free-floating
closed chain-manipulators. Nakamura and Mukherjee [9] proposed path planning algorithms
for space manipulators using integration of rate kinematic equations. From these studies, it is
now well established that free-floating manipulators are characterized by nonholonomic con-
straints. Due to nonholonomic constraints, the conventional path-planning schemes applied
to fixed-base manipulators are not directly applicable to free-floating manipulators,
The algorithms proposed in the literature for motion-planning of free-floating manipulators
are either aimed at computing the joint torques using the dynamic equations of motion of
the system [2, 3, 5] or the joint rates using the rate kinematics of the system [9]. The