Control of a Space Robot for Capturing a Tumbling Object

This paper presents an optimal control strategy for a space robot to capture a free-tumbling object under the condition of having minimal impact to the base satellite during the capturing operation. The idea is to first predict a target time, location and speed of the tumbling object for the robot to intercept with such that, when the robot hand physically touches the object, it will transfer a minimal angular impulse to the base satellite. Then, an optimal motion trajectory and the corresponding joint torques will be generated to control the robot to reach the object at the targeted time and location. Joint rate and torque limits will be taken into account in the optimal control solution. Since the control acts before a physical contact happens, it will not affect any existing compliance control capability of the space robot regarding both implementation and operation. Therefore, the proposed method can co-exist with an existing compliance control method in the robot control system. A numerical simulation example is presented to demonstrate the effectiveness of the proposed method. A numerical simulation example is presented to demonstrate the effectiveness of the proposed method. 1. GENERAL SPECIFICATIONS Space manipulators have been successfully used for many applications such as maneuvering astronauts, berthing and deploying large space structures, constructing and maintaining the International Space Station (ISS), exploring and sample-collecting, satellite on-orbit servicing (technology demos only), etc. All of these manipulation activities dealt with cooperative payloads or target objects and thus, the existing robotics technologies can handle them quite well, though many improvements such as the operational efficiency and dexterity may still be done. However, if a manipulator is expected to perform more challenging and riskier tasks, such as to capture an unknown object, like a piece of space debris, or a non-cooperative object, such as a tumbling satellite, the currently available space robotics technologies are still far from being ready. To make these challenging tasks practical, many enabling technologies have to be further advanced. This research develops enabling technology for a space manipulator to capture a tumbling satellite. The operation of capturing a tumbling satellite after completion of the rendezvous process may be divided into four phases. The first phase is the observing and planning phase, which is to acquire motion (mainly rotational motion) information of the target satellite and then determine when and where to grasp the target satellite. The second phase is the final approaching phase, in which the robot is controlled to move its endeffector to the planned grasping location for grasping the target satellite at the planned time. The third phase is the capturing (or interception) phase, in which the robot captures the target satellite. This is the phase where physical contact happens and thus it is also the most risky phase. The last is the post-capture stabilization phase in which the tumbling target satellite is detumbled and stabilized by the robot and servicing satellite. The work reported in this paper is concerned only with the planning part of the first phase and the whole second phase. Our focus on the first phase is to determine an optimal time and location based on the tumbling motion of the target satellite for the robot’s end-effector to intercept with the target satellite. The focus on the second phase is to control the robot to reach the optimal location with a minimal disturbance to the attitude of the servicing satellite for safe capture of the tumbling target satellite. Research on the observation part of the first phase has been done by many researchers in the fields of computer vision and sensing technologies. The third and fourth phases are more risky and challenging because of the involvement of physical contact. Some research work has been done but much more future work is absolutely required in order to have guaranteed safe and successful future missions. We will not discuss these here because they are out of the scope of the paper. The impact minimization problem for capturing a target object has been studied by a few researchers from different perspectives. Yoshida et al [1] modeled the collision dynamics during the capturing process using the extended generalized tensor. They focused on the moments just before and after the impact using velocity relations. Yoshida and Nenchev [2] introduced the concept of reaction null-space to analyze the impact and post-impact moments of the capturing process. They found that choosing configurations within the reaction null-space of the servicing manipulator system can result in an operation with minimum impact to the attitude of the servicing satellite. Papadopoulos and Paraskevas [3] proposed a methodology based on the percussion point of bodies to minimize the forces instead of the momentum transmitted to the base of the manipulator when grasping an object. In all the past studies the contact force was just an assumed impulsive force exerted on the tip of the manipulator without taking into account of the geometry of the contacting bodies and the tumbling motion of the target satellite. In this research, we move a step forward to consider the tumbling motion of the target satellite in the robot control strategy for achieving minimal attitude impact to the servicing satellite. The problem of optimal trajectory planning for a space manipulator was addressed earlier by Duvowsky and Torres [4]. They introduced an enhanced disturbance map, which can aid in selecting a path that reduces the disturbances of the base spacecraft by identifying the direction of each joint movement which results in minimum or maximum disturbances. Agrawal and Xu [5] proposed a global optimum path planning for redundant space manipulators using a variational approach to minimize the objective functional with constraints in the linear and angular momentum. Lampariello et al [6] proposed an optimal motion planning method using criteria in the joint space. Huang et al [7] proposed an optimal approach trajectory planning method for minimizing the impact on the base satellite, the optimal trajectory is found based on a genetic algorithm and in the dynamic coupling factor. Aghili in [8] designed an optimal controller to capture a tumbling satellite using an objective function minimizing the operation time and relative velocity between the robot tip and the target. T. Oki et al [9] also proposed an optimal control method to capture a tumbling satellite but they focused mainly on minimizing the operational time for fast capture. The main difference between our approach and those optimal control approaches is that we focus on the minimization of the reaction torque on the servicing satellite for safe capture operation. In this paper, the terms “servicing satellite” and “base satellite” are exchangeable, so are the terms “target object” and “target satellite” and the terms “manipulator” and “robot”. 2. DYNAMICS MODELLING 2.1. Basic assumptions The development of the methodology described in this paper is based on following basic assumptions: (a) Both the servicing satellite and the target object are assumed to be rigid bodies. The manipulator also consists of rigid links. (b) The mass properties and motion state of both the base satellite and the target object are assumed known. (c) The maneuvers are in close proximity range and thus the effect of orbital mechanics is neglected. (d) The attitude of the base satellite is fully controlled unless otherwise stated. Assumption (a) is a very usual assumption in the robotics field, especially for development and practical implementation of control methodologies because a rigid-body dynamical system is much easier to model and analyze. In many applications such assumption is also practically sufficient. This assumption may be too off reality for a long space manipulator to capture a fast tumbling object. Assumption (b) is to focus the research on the robot control problem and avoid dealing with the inertia identification and motion state estimation problems, which are two research areas having been well studied and are continuously being studied by many other researchers. Assumption (c) is to focus the research to the scope of proximity rendezvous and capture, where the forces/moments related to orbital mechanics are negligible compared to the inertia forces caused by the robot motion and the contact forces caused by the physical interception. Assumption (d) has been a common approach for all the practical capturing operations in space because uncontrolled attitude can significantly increase the possibility of mission failure. We are well aware that these assumptions may not be realistic in many application cases. They are imposed to facilitate our early development of the technology. We will be relaxing these assumptions in the future research. 2.2. Dynamics Modelling of the Servicing System The multibody system of the servicing satellite and the manipulator consists of 1 n rigid bodies connected by n joints, as shown in Fig. 1. Body 0 is the satellite which is also the base of the robot and body ( 1,2, , ) i i n  is the -th i link of the manipulator. Joint 0 has 6 degrees of freedom which connects the inertia frame to the servicing satellite and Joint ( 1,2, , ) i j n  has only one degree of freedom which articulates links i-1 and i. The symbols appearing in Fig. 1 are defined as follows: : n R  θ generalized joint coodinates : generalized joint torques n R  τ 3 : position vector of the CM of Body i R i  r 3 : position vector of the mass center of the entire servicing system c R  r 3 : position vector of the manipulator end-effector e R  r 3 : intrabodyvector of link expressedin frame i i R i F  a 3 : position vector of the CM of Link measured from Joint i R i i  c 3 : rotational axis of the th joint i R i  z 3 : linear velocity of the mass center of Link i R i  v 3 : angular velocity of the th link i R i  ω 3 0 : linear velocity of the servicing satellite R  v 3 0 : angular velocity of the servicing satellite R  ω 3 : linear velocity of the end-effector e R  v 3 : angular velocity of the end-effector e R  ω 6 : external force and moment exerted on the end-effector e R  f 6 0 : external force and moment exerted on the servicing satellite R  f 3 : reaction forces at the the root of the manipulator r R  f 3 : reaction torque at the the root of the manipulator r R  τ Body 0 (B0 ) Service Satellite