【文章內(nèi)容簡介】 he centroid of space base to the joint one. li : vector pointing from joint i to joint i+1 Jb: Jacobian matrix for the space base variables Jm: Jacobian matrix for the manipulatorxb: The position/orientation of the space base xe: The position/orientation of the endeffector ф: ф: Joint variable of the manipulator Dynamics of Space Robot It is a general problem to derive the dynamics equation of space robotstem. Wutilize RobersonWittenburg’s method [Robert E. Roberson (1997)] to derive the rigid dynamics of multibody system. This method utilizes the mathematical graph theory [Jens Wittenburg (1997)]escribe the interconnecting of the multibody. The advantage of this method is that the various multibody systems can be described by the uniform mathematical model. So far, there are many studies on the dynamics of space robot system. Therefore we will directly express the dynamic equation according to the assumed model. The motion equation of the space robot system is expressed in the following form [Y. Xu and T. Kanade (1992)].The symbols in the above equations are defined asfollowings:mi: The mass of link i of the space manipulatorω: The total mass of the whole space robot systemri : The position vector of centroid of the link ipi : The position vector of joint iki: Unit vector indicating joint axis direction of the link i rg: The position vector of the total centroid of the space robot systemIi:Inetia tenor of the link i with respect to its masscentercb: Velocity dependent nonlinear term for these cm: Velocitydependentnonlinearterm for he manipulator armFb: The External force and torque on the space base Fh: The external force and torque on the endeffector τ: The joint torque of the manipulator armHb: The inertial matrix of the space baseHm: The inertial matrix for the manipulatorHbm: The coupling inertial matrix between the space base and manipulatorAll vectors are described with respect to the inertial coordinate systemΣI, cb and cm can be obtained by inverse dynamic. The inverse dynamic putation is useful for a puted torque control. Here, the authors use norder recursive NewtonEuler approach [J. S. , M. W. Walker and R. P. (1980)] [K. Yoshida (1997)] to pute inverse dynamics. In addition, calculating inverse dynamics can obtain the reaction force/moment on the space base.where: Fi, Ni are inertial force and moment exterting onthe centroid of link i. Otherwise we define force andmoment fi, ni exterting on the joint, fci and nci exterting onthe endeffector. Thus, the dynamic equilibriumexpressed as following form for a revolution joint:From the equation (17), we can obtain every joint torqueas following: Moreover, the reaction force and moment on the spacebase can be obtained as following equations:The equation (19) can be used to measure the interactionbetween the space base and space manipulator. These parameters are very important reference for designing the attitude control system and orbit control system. Moreover, the coordinate control of space base and space manipulator needs these parameters.The symbols in equation (17), (18) and (19) are defined as followings: sij: the elementofIncidencematrixs,thedetaileddefinitioseesmathematicalgraphtheory. sei: the element of Incidence matrix sej (j = 1,…,n), that represents a j is link. lij: vector from joint i to joint j, from , we know lij =cijcii. cij : vector from the centroid of link i to joint j.For whole space robot system, the external force or torque on the space base Fb, which can be generated by jet thrusters or reaction wheels, and Fe can be assumed zero before the endeffector contacts the objective. Therefore the linear and angular momenta of whole system are conservative when Fh= 0. The motion of system isgoverned by only inertial force/torque on the manipulator joint τ. Thus, we can obtain the following momenta equation from equation (3)At the beginning, assume0 for simplification, thus,from equation (20), we obtain, the matrix Jg is calledGeneralized Jacobian Matrix (GJM) or Space JacobianMatrix (SJG). GJM is used to calculate the joint angularvelocity and endeffector velocity. Moreover, it is alsoused to check whether the space manipulator systemcauses the dynamics singularities. When the determinantof GJM is equal to zero or the GJM loses full rank, themanipulator appears the dynamics singularities. Inaddition, the GJM can be used to design controller mentioned above is the fundamental knowledgeabout space robot system. The following trackingtrajectory planning and control is base on this dynamicMotion Estimation of USSIn this section, we describe to estimate the motion state and equation of USS. The USS to be rescued has unique characteristics as follows: the orbital information such as altitude and inclination of the USS will be known by the ground control station. The size, shape and mass property of the USS are also well known in advance from design phase information. The handle location will be identified by human decision. Therefore we also assume that the USS is equipped with visual marker, signal reflectors, GPS, and so on for simplification.Here, we assume that the USS is nearly axissymmetric shape with a grapple handle on the maximum momentum axis in order to simplify the plicated problem. Moreover, there are some mark points on the USS so that the CCD cameras equipped in manipulator endeffector can measure the position, orientation and estimate its spinning velocity. Hence, the grapple handle is the key point of tracking trajectory of space manipulator. Therefore, the mission of CCD cameras is to measure the position and orientation from manipulator endeffector coordinate ΣE to the coordinate frame ΣO attached to the USS. Define XUSS = [PUSS,