Reactionless space and ground robots: novel designs and concept studies

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Abstract

For conventional designs of space and earth robots, manipulator motions result in forces and moments on the base. These forces and moments cause translation and rotation of the free-floating base of a space robot. For earth robots, the same forces and moments get transmitted to the base and may cause undesirable base excitations.

The objective of this paper is to systematically analyze the fundamentals of reactionless space and earth robots. Based on this analysis, design of two distinct classes of planar robots is proposed, with appropriate choices of geometric and inertial parameters. Due to underlying principle of conservation of angular momentum for these special robots, the trajectory must satisfy additional constraints. We illustrate the reactionless feature of these robots and trajectory planning of these robots through computer simulations. Currently, we are fabricating such reactionless robots to illustrate the underlying concepts.

Introduction

In the literature, a number of methods have been proposed for static balancing of machines through passive means using counterweights and springs ([2], [11], [12], [16], [17], [18], [19]). These methods have been applied to serial and parallel mechanisms.

Center of mass is an important property of a machine. Force balancing of machines is achieved by ensuring that the system center of mass remains stationary during motion [13]. At the turn of last century, the noted biomechanician Fischer investigated the use of auxiliary linkages to study the motion of center of mass of a human body ([4], [9]). In recent years, Gokce and Agrawal [10] revised this concept. Subsequently, they fabricated a design where the center of mass of the system was physically located through the addition of parallelogram linkages [2].

There are some research works on dynamic balancing of linkages, specially four-bar linkages ([3], [5], [6], [7], [8]). They use counterweights or idler-loops to cancel or minimize the effects of forces and moments which are transmitted to the base. Ricard and Gosselin [15] have recently applied dynamically balanced four-bar linkages as the legs of a 3-DOF planar dynamically balanced planar mechanism. Also, there are some published works on dynamic balancing of open loop systems [1] and the issue of reactionless control of a space robot keeping the base inertially fixed ([14], [20]). In most research, dynamic balancing of the mechanisms is attained by proper choice of geometric and inertial parameters. In this paper, it is achieved by using passive joint connection between the manipulator and the base.

The main contributions of this paper are: (i) systematic study of the necessary and sufficient conditions for reactionless machines; (ii) design of two broad classes of planar mechanisms using counterweights and auxiliary parallelograms that satisfy the reactionless conditions for both ground and space robotics.

The organization of the paper is as follows: Section 2 reviews dynamic behavior of coupled bodies in open-chain and multi-loop configurations. Section 3 uses these dynamic equations to find the necessary and sufficient conditions for design of reactionless machines. Based on the underlying mathematical concepts, two classes of planar robots that use counterweights and auxiliary parallelograms are described in Section 4. Detailed mathematical models are presented for these two classes. Trajectory planning for these robots are presented in Section 5 using the underlying principle of conservation of angular momentum. Section 6 describes designs of space robots that satisfy the conditions of reactionless machines.

Section snippets

Theoretical background

In this section, we first address the conditions for reactionless machines when the bodies are arranged in a serial chain and are numbered from 1 to n as shown in Fig. 1(a). This serial chain consists of n rigid bodies connected by revolute joints and we assume that the center of mass and gravity coincide. We consider the body i in the chain to be connected to body i−1 at Oi and to i+1 at Oi+1 along the respective axes of motion. The center of mass of the body i is labeled as Ci. At the

Reactionless machines

Eqs. , , , , , characterize the overall behavior of a machine connected to a base body. These equations can now be studied for the design of reactionless machines. In this section, we consider single contact systems.

For a single open-chain system, Eqs. , , are the governing equations. For a multi-contact system, the motion is governed by Eqs. , , and for a single contact, m=1. In this section, we assume that the contact between the system and the ground happens either at C or O1. These two

Design of planar robots

In this section, we present two classes of manipulators whose motion are in a plane normal to the direction of gravity and satisfy the conditions for reactionless manipulation. The first class consists of a serial manipulator with n links connected by revolute joints. This manipulator is designed such that the center of mass of the whole system is located at the first joint connection to the base. The second design is a planar manipulator with auxiliary parallelograms [2] to locate the center

Trajectory planning

This section describes algorithms for trajectory planning with both models to move the end-effector from an initial position to a desired final position. Even though the methods presented in this section apply both to n-link open chains with counterweights and n-link chains augmented with parallelograms, we illustrate these methods on 3-link manipulators.

The two designs of reactionless 3-link manipulators satisfy the integrable rate Eqs. , . In the second case, the geometric and inertial

Space robots

We consider the design of free-floating robots in zero gravity space environment. The design consists of a free-floating base with a robot arm mounted on it. The robot arm may have an open chain or a multi-loop structure. We assume that the arm is connected to the base through a single contact.

Let the floating base be denoted by B and the robot arm by R. The robot and the base together are denoted by S, as depicted in Fig. 8a. Since all external forces and moments on S are zero, the center of

Conclusion

The paper provided a systematic study of necessary and sufficient conditions for reactionless spatial and planar robots for ground and space applications. Detailed design and simulations were presented for two broad classes of planar robots that use counterweights and auxiliary parallelograms to locate the center of mass at a desired place. It was shown that these designs do not apply a force or moment on a supporting base if the motion is restricted to a plane normal to the gravity direction.

Acknowledgements

The authors thank National Science Foundation for support of this work through their ‘Presidential Faculty Fellows’ program. The second author would also like to thank Isfahan University of Technology for its financial support during his sabbatical leave.

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