University of Pennsylvania ScholarlyCommons Technical Reports (CIS) Department of Computer & Information Science March 1992 Coordinating Locomotion and Manipulation of a Mobile Manipulator Yoshio Yamamoto University of Pennsylvania Xiaoping Yun University of Pennsylvania Follow this and additional works at: https://repository.upenn.edu/cis_reports Recommended Citation Yoshio Yamamoto and Xiaoping Yun, "Coordinating Locomotion and Manipulation of a Mobile Manipulator", . March 1992. University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-92-18. This paper is posted at ScholarlyCommons. https://repository.upenn.edu/cis_reports/407 For more information, please contact [email protected]. Coordinating Locomotion and Manipulation of a Mobile Manipulator Abstract A mobile manipulator in this study is a manipulator mounted on a mobile platform. Assuming the end point of the manipulator is guided, e.g., by a human operator to follow an arbitrary trajectory, it is desirable that the mobile platform is able to move as to position the manipulator in certain preferred configurations. Since the motion of the manipulator is unknown a priori, the platform has to use the measured joint position information of the manipulator for motion planning. This paper presents a planning and control algorithm for the platform so that the manipulator is always positioned at the preferred configurations measured by its manipulability. Simulation results are presented to illustrate the efficacy of the algorithm. The use of the resulting algorithm in a number of applications is also discussed. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MS- CIS-92-18. This technical report is available at ScholarlyCommons: https://repository.upenn.edu/cis_reports/407 Coordinating Locomotion and Manipulation Of A Mobile Manipulator MS-CIS-92-18 GRASP LAB 304 Yoshio Yamamoto Xiaoping Yun University of Pennsylvania School of Engineering and Applied Science Computer and Information Science Department Philadelphia, PA 19104-6309 March 1992 Coordinating Locomotion and Manipulation of a Mobile Manipulator Yoshio Yamalnoto and Xiaoping Yun General Robotics and Active Sensory Perception (GRASP) Laboratory University of Pennsylvania 3401 Walnut Street, Room 301C Philadelphia, PA 19104-6228 ABSTRACT nipulator end point is unknown a priori, e.g., driven by a visual sensor or guided by a human operator, then the A mobile manipulator in this study is a manipulator path planning has to be made locally and in real time mounted on a mobile platform. Assuining the end rather than globally and off-line. This paper presents a point of the manipulator is guided , e.g., by a human planning and control algorithm for the platform in the operator to follow an arbitrary trajectory, it is desir- latter case, which takes the measured joint displace- able that the mobile platform is able to move as to ment of the maiiipulator as the input for inotion plan- position the manipulator in certain preferred configu- ning, and controls the platform in order to bring the rations. Since the motion of the manipulator is un- manipulator into a preferred operating region. While known a priori, the platform has to use the measured this region can be selected based on any meaningful joint position information of the manipulator for mo- criterion, the inanipulability measure [I] is utilized in tion planning. This paper presents a planning and con- this study. By using this algorithm, the mobile plat.- trol algorithm for the platfornl so that the manipula- form will be able to "understand the intention of its tor is always positioned at the preferred configurations inanipulator and respond accordingly." measured by its manipulability. Simulation results are This control algorithin has a number of iminidiate presented to illustrate the efficacy of t,he algorithm. applications. First, a human operator can easily move The use of the resulting algorithm in a number of ap- around the mobile manipulator by "dragging" the end plications is also discussed. point of the manipulator while the manipulator is in the free mode (compensating the gravity only). Sec- 1 Introduction ond, if the manipulator is force-controlled, the mobile manipulator will be able to push against and follow When a human writes across a board, he posit,ions his an external moving surface. Third, when two mobile arm in a comfortable writing configuration by mov- manipulators transport a large object with one being ing his body rather than reaching out his arm. Also the illaster and the other being slave, this algorithm when humans transport a large and/or heavy object can be used to control the slave mobile manip~lat~orto coorperatively, they tend to prefer certain configura- support the object and follow the motion of the mas- tions depending on various factors, e.g., the shape and ter, resulting in a cooperative control algorithm for two the weight of the object, the transportation velocity, mobile manipulators. the number of people iilvolved in a task, and so on. Altl~oughthere has been a vast amount of research Therefore when a mobile illanipulator perforins a ma- effort on mobile platforms (commonly referred to as nipulation task, it is desirable to bring the manipulator mobile robots) in the literature, the study on mobile into certain preferred configurations by appropriately inanip~lat~orsis very limited. Joshi and Desrochers planning the motion of the mobile platform. If the considered a two link manipulator on a moving plat- trajectory of the manipulator end point in a fixed co- form subject to random disturbances in its orientation ordinate system (world coordinate system) is known a [2]. Wien studied dynamic coupling between a planar priori, then the motion of the mobile platform can be vehicle and a one-link manipulator on the vehicle [3]. planned accordingly. However, if the inotioii of the ma- Dubowsky, Gu, and Deck derived the dynamic equa- tions of a fully spatial mobile manipulator with link 2 Nonholonomic Systems flexibility [4]. Recently, Hootsmans proposed a mobile manipulator control algorithm (the Mobile Manipula- 2.1 Dynamic Equations of Motion tor Jacobian Transpose Algorithm) for a dyilamically Consider a mechanical system with n generalized co- coupled mobile manipulator [5]. He showed that with ordinates q subject to m bilateral constraints whose the algorithm the manipulator could successfully com- equations of motion are described by pensate a trajectory error caused by vehicle's passive suspension with the help of limited sensory information from mobile vehicle. where M(q) is the n x n inertia matrix, V(q, q) is the What makes the coordination problem of locomo- vector of position and velocity dependent forces, E(y) tion and manipulation a difficult one is twofold. First, is the n x r input transformatioll matrix1, T is the 1.- a manipulator and a mobile platform, in general, have dimensional input vector, A(q) is the m x n Jacobian different dynamic characteristics, namely, a mobile matrix, and X is the vector of constraint forces. The platform has slower dynamic response than a manipu- m constraint equations of the mechanical system can lator. Second, a wheeled mobile platform is subject to be written in the form nonholonomic constraints while a manipulator is usu- ally unconstrained. These two issues must be taken into consideration in developing a planning and con- If a constraiilt equation is in the form Ci(y) = 0, or trol algorithm. call be integrated into this form, it is a l~olonomiccon- straint. Otherwise it is a kinematic (not geometric) Dynamic modeling of mechanical systenw with non- constraint and is termed nonholonomic. holonomic constraints is richly documented by work We assume that we have L holonomic and 712- L now ranging from Neimark and Fufaev's comprehensive holonomic independent constraints, all of which can be book [GI to more recent developments (see for example, written in the form of [7]). However, the literature on control properties of such systems is sparse [8]. The interest in control of nonholonomic systems has been stimulated by t.he re- Let s~(~),. ., s,-,(q) be a set of smooth and linearly cent research in robotics. The dynamics of a wheeled independent vector fields in the null space of A(y), z.e., mobile robot is nonholonoinic [9], and so is a multi-arm system manipulating an object through the .ivhole arm -4(q)si(q) = 0 i= 1,..., n-m.. manipulation [lo]. Let S(q) be the full rank matrix made up of these vectors Bloch and McClamroch [8] first deilloilstrated that S(q) = is1 (9) ~n-m(q)l (4) a nonholonomic system cannot be feedback stabilized . to a single equilibrium point by a smooth feedback. and let A be the distribution spanned by these vector In a follow-up paper [ll],they showed that the sys- fields tem is small-time locally controllable. Campion et a1 A = span{sl(q), . 3 sn-na(q) > [12] showed that the system is coiltrollable regardless It. follows that q E 4. A may or may not be involutive. of the structure of nonholonomic constraiiits. h'lotion For that reason, we let A* be the smallest involut.ive planning of mobile robots has been an active topic in distributioil containing A. It is clear that dim(4) 5 robotics in the past several years [13, 14, 9, 15, 161. dim(A*). There are three possible cases (as observed Nevertheless, much less is known about the dynamic by Campion, et al. in [12]). First, if L = m, that is. control of mobile robots with nonholonomic constraints all the const,raints are holonomic, then A is involutive and the developments in this area are very recent itself. Second, if k = 0, that is, all the coilstraints are [17, 18, 191. nonholonomic, then A" spans the entire space. Finally, if 0 < k < nz, the k constraints are integrable and In this paper, we first present the theoretic formula;.