Explicit dynamics of space free-flyers with multiple manipulators via SPACEMAPLE

This paper focuses on the dynamics of a multiple manipulator space free-flying robot (SFFR) with rigid links and issues relevant to the development of appropriate control algorithms. To develop an explicit dynamics model of such complex systems, the Lagrangian formulation is applied. First, the system kinetic energy is derived based on a developed kinematics approach. Then, through vigorous mathematical analyses, three formats are obtained which describe the contribution of each term of kinetic energy to the equations of motion. Next, explicit derivations of a system's mass matrix, and of the vectors of non-linear velocity terms and generalized forces are introduced for the first time. The obtained dynamics model is very useful for dynamics analyses, design and development of control algorithms for such complex systems. The explicit SFFR dynamics can be implemented either numerically or symbolically. Following the latter approach, the developed symbolic code for dynamics modeling, i.e. SPACEMAPLE, and its verification procedure are described, and issues relevant to the development and computation of dynamics models in control algorithms are briefly discussed. Specific dynamic characteristics of SFFRs compared to fixed-base manipulators are pointed out.     

Dynamics and control of multiple cooperating manipulators with rolling contacts

In this article, we investigate the control of multiple cooperating mechanisms manipulating a common object, with rolling contact between the end-effectors and the object. We derive new kinematic and dynamic formulations for the system, in which the rolling degrees of freedom between the end-effector and the object are modeled as one or more unactuated joints of the manipulator. Differential geometric concepts are used to interpret the curvature and torsion forms used in contact kinematic equations derived by Montana. The augmentation of the rolling contacts imparts each manipulator with additional degrees of freedom and could also make it kinematically redundant. This can be exploited for the satisfaction of a secondary subtask criterion, such as collision avoidance, which is demonstrated in the examples. In addition, a control law can be specified that enables simultaneous control of the object trajectory, the internal forces in the object, and the trajectories of the contact points on the object or the end-effectors. © 1996 John Wiley & Sons, Inc.     

On the kinematics of multiple manipulator space free-flyers and their computation

In this article, two basic approaches for kinematics modelling of multiple manipulator space free-flying robots (SFFRs) are developed. In the barycentric vector approach, the center of mass of the whole system is taken as a representative point for the translational motion of the system, and a set of body-fixed vectors which reflect both geometric configuration and mass distribution of the system are used. On the other hand, the direct path method relies on taking a point on the base body (preferably its center of mass) as the representative point for the translational motion of the system. The consequences of using each of the two approaches in deriving dynamics equations and in control design of SFFRs are discussed. It is revealed that the direct path method is a more appropriate approach for modelling multiple arm systems, in the presence of external forces/torques (i.e., free-flying mode). A 14 degree-of-freedom space free-flying system is considered as a benchmark system and a quantitative comparison between the two approaches is presented. The results show that the direct path method requires significantly less computations for position and velocity analyses. © 1998 John Wiley & Sons, Inc.     

Modeling and control of two constrained manipulators

The coordinated control of two manipulators in the presence of environment constraints is studied in this paper. Such a control method is needed in applications in which the two manipulators grasp a common object whose motion is constrained by environments. The two manipulators are not only constrained with each other, but also constrained by the environment in their workspace. It is realized that the motion and constraint equations obtained directly from mechanics are not suitable for the control purpose. A set of equivalent equations are derived, which are in the standard form of the nonlinear system representation with clear state equations and output equations. A nonlinear feedback is found which exactly linearizes and decouples the dynamic nonlinear system of the two constrained manipulators. The coordinated controller design is then carried out based on the linearized system by using linear system theory.     

具有完整性的反馈控制器的设计

本文根据一种具有一般性的传感器与执行器失效的表示方法，针对不同回路失效，提出了系统具有完整性的充要条件。在故障条件已知时，利用互质分解技术，给出了一种对该故障具有完整性的控制器的设计方法。如果不要求系统具有完全的完整性，那么在分析与综合过程中，对象可以是不稳定的。本文也给出了一个设计示例。     

Direct adaptive control of manipulators in cartesian space

A new adaptive-control scheme for direct control of manipulator end effector to achieve trajectory tracking in Cartesian space is developed in this article. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of adaptive feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for on-line implementation with high sampling rates. The control scheme is applied to a two-link manipulator for illustration.     

Adaptive control of robot manipulators in task space

Adaptive control of robotic manipulators in task space or Cartesian space is considered. A general Lyapunov-like concept is used to design an adaptive control law. It is shown that the global stability and convergence can be achieved for the adaptive control algorithm. The algorithm has the advantage that the inverse of Jacobian matrix is not required. The algorithm is further modified so that the requirement for the bounded inverse of estimated inertia matrix is also eliminated. In addition, two approaches are presented to achieve robustness to bounded disturbances     

On the dynamics and control of flexible joint space manipulators

Space manipulator systems are designed to have lightweight structure and long arms in order to achieve reduction of fuel consumption and large reachable workspaces, respectively. Such systems are subject to link flexibilities. Moreover, space manipulator actuators are usually driven by harmonic gear mechanisms which lead to joint flexibility. These types of flexibility may cause vibrations both in the manipulator and the spacecraft making the positioning of the end-effector very difficult. Here, both types of flexibilities are lumped at the joints and the dynamic equations of a general flexible joint space manipulator are derived. Their internal structure is highlighted and similarities and differences with fixed-base robots are discussed. It is shown that one can exploit the derived dynamic structure in order to design a static feedback linearization control law and obtain an exact linearization and decoupling result. The application of such controllers is desired in space applications due to their small computational effort. In case of fixed-base manipulators, the effective use of a static feedback controller is feasible only if a simplified model is considered. Then, the proposed static feedback linearization control law is applied to achieve end-effector precise trajectory tracking in Cartesian space maintaining a desirable non-oscillatory motion of the spacecraft. The application of the proposed controller is illustrated by a planar seven degrees of freedom (dof) system.     

模糊CMAC的柔性空间机器人轨迹跟踪自学习控制

针对不确定自由漂浮柔性空间机器人系统,采用模糊CMAC神经网络自学习控制策略来解决轨迹跟踪控制问题.首先建立漂浮基空间机器人的动力学方程,然后利用具有快速学习能力的模糊CMAC神经网络来逼近非线性柔性臂的逆动力学模型.网络参数采用改进的有监督的Hebb学习规则进行自适应在线调整,并通过关联搜索进行自学习和自组织,其误差代价函数由PID控制器提供.仿真结果表明,这种模糊CMAC逆模PID控制器能够达到较高的控制精度,具有一定的工程应用价值.     

Time-optimal control of multiple cooperating manipulators with trajectory and motion program constraints

Two types of problems associated with time-optimal control of multiple manipulators moving a commonly held object along specified trajectories are studied. The first problem involves finding the minimum traveling time and the optimal control torques for any desired motion programs of the given trajectory. The second problem involves finding the optimal velocity distribution along the trajectory such that the motion can be completed in the minimum time. To solve these problems, a parametric form of the generalized dynamic equation is derived. An iterative search procedure is developed for solving the first problem. During the search, the lower bound of the traveling time at any point of the given trajectory is determined by using the linear programming technique. The second problem is solved by integrating the parametric dynamic equation along the given trajectory based on the phase-plane switching curve approach. The maximum acceleration and the upper bound of the operation speed at each integration instance are determined from two linear programs. The proposed methods are applicable to various complex multi-robot systems and can handle nonlinear torque-speed characteristics of the joint actuators. © 1996 John Wiley & Sons, Inc.     

A combined modal-joint space control approach for continuum manipulators

Continuum manipulators continue to gain popularity due to their ability to operate within difficult to reach environments, and their inherent safety characteristics. However, their flexible nature makes them prone to both steady-state positioning errors and undesirable vibrations. We propose a combined control system incorporating both a tracking position controller to reduce steady-state error, and a modal-space controller to improve the dynamic properties of the manipulator. To this end, we develop a lumped parameter model for use as a modal-space observer. Simulation results based on a planar two-segment manipulator and experimental results from a single-segment manipulator both show marked improvement using our combined approach. The improvements observed in both simulation and experimental results include reduced settling time, higher bandwidth trajectory control capability, and an improved response to external disturbances.     

Reliable decentralised control of delayed MIMO plants

Reliable decentralised proportional–integral–derivative controller synthesis methods are presented for closed-loop stabilisation of linear time-invariant plants with two multi-input, multi-output (MIMO) channels subject to time delays. The finite-dimensional part of plants in the classes considered here are either stable or they have at most two poles in the unstable region. Closed-loop stability is maintained with only one of the two controllers when the other controller is turned off and taken out of service.     

Adaptive robust coordinated control of multiple mobile manipulators interacting with rigid environments

In this paper, we consider multiple mobile manipulators grasping a common object in contact with a rigid surface, and propose a new version of adaptive robust control extended to the actuator level for multiple mobile manipulators carrying a common object in a cooperative manner. The proposed controls are robust not only to parametric uncertainties including mass variation and electrical parameters but also to external disturbances. Simulation results are presented to validate that the motion/force tracking errors converge to zero whereas the internal force tracking error remains bounded and can be made arbitrarily small.     

Adaptive synchronised tracking control for multiple robotic manipulators with uncertain kinematics and dynamics

In this study, a new adaptive synchronised tracking control approach is developed for the operation of multiple robotic manipulators in the presence of uncertain kinematics and dynamics. In terms of the system synchronisation and adaptive control, the proposed approach can stabilise position tracking of each robotic manipulator while coordinating its motion with the other robotic manipulators. On the other hand, the developed approach can cope with kinematic and dynamic uncertainties. The corresponding stability analysis is presented to lay a foundation for theoretical understanding of the underlying issues as well as an assurance for safely operating real systems. Illustrative examples are bench tested to validate the effectiveness of the proposed approach. In addition, to face the challenging issues, this study provides an exemplary showcase with effectively to integrate several cross boundary theoretical results to formulate an interdisciplinary solution.     

On the adaptive control of robot manipulators with velocity observers

To achieve accurate tracking control of robot manipulators many schemes have been proposed. A common approach is based on adaptive control techniques, which guarantee trajectory tracking under the assumption that the robot model structure is perfectly known and linear in the unknown parameters, while joint velocities are available. Despite tracking errors tend to zero, parameter errors do not unless some persistent excitation condition is fulfilled. There are few works dealing with velocity observation in conjunction with adaptive laws. In this note, an adaptive control/observer scheme is proposed for tracking position of robot manipulators. It is shown that tracking and observation errors are ultimately bounded, with the characteristic that when a persistent excitation condition is matched then they, as well as the parameter errors, tend to zero. Simulation results are in good agreement with the developed theory.     

地面和空间机械臂的动力学等效条件与控制相似律

针对如何在地面机械臂上有效验证空间机械臂控制律的问题,本文研究空间机械臂和地面机械臂系统间的动力学等效条件和控制相似律.首先,基于量纲分析研究地面机械臂和空间机械臂之间的动力学等效条件,并基于等效条件设计地面机械臂系统.其次,基于量纲分析建立空间和地面机械臂系统间的控制相似律,设计的空间机械臂控制律通过控制相似律将可以转化为地面机械臂相应的控制律.最后,考虑地面机械臂基座往往无法和空间机械臂的基座航天器一样进行全6自由度运动,以及地面机械臂运动时受到重力影响,使得地面机械臂不再满足动力学等效条件,基于反馈线性化技术设计一种地面机械臂的动力学误差补偿策略,使得地面机械臂和空间机械臂具有相似的闭环动力学行为.这样,空间机械臂的控制律可以在设计的地面机械臂上进行验证,仿真中以在地面机械臂上验证空间机械臂的PID控制器为例说明所提方法的有效性.     

Adaptive control of free-floating space manipulators using dynamically equivalent manipulator model

In this paper, adaptive control of free-floating space manipulators is considered. The dynamics based on the momentum conservation law for the free-floating space manipulator has non-linear parameterization properties. Therefore, the adaptive control based on a linear parameterization model cannot be used in this dynamics. In this paper, the dynamics of the free-floating space manipulator system are derived using the Dynamically Equivalent Model (DEM) approach. The DEM is a fixed-base manipulator system and allows us to linearly parameterize the dynamic equations. Using this linearly parameterized dynamic equation, an adaptive control method is developed to control the system in joint space. Parameter identification and torque calculations are done using the DEM dynamics. Simulations show that the tracking errors of the manipulator joints to a given desired trajectory become zero when the calculated torques act on the joints of the space manipulator system.     

Adaptive control of multiple mobile manipulators transporting a rigid object

International Journal of Control, Automation and Systems - This paper presents a nonlinear control scheme for multiple mobile manipulator robots (MMR) moving a rigid object in coordination. The...     

具有时滞的柔性关节多机械臂协同自适应位置/力控制

由于关节机械臂长期运行后,齿轮间隙扩大产生的时间滞后将使得系统跟踪性能降低.针对此问题,本文提出了一种自适应位置/力控制策略来保证闭环系统稳定性以及位置/力跟踪性能.首先,对多机械臂和物体系统进行任务空间动力学建模.随后,利用Pade理论将时间滞后近似为二阶有理分式.同时,利用神经网络自适应算法克服模型建模误差对系统稳定性的影响,利用同时包含位置误差和力误差的线性滑模项,设计位置/力控制器.通过李雅普诺夫稳定性理论,证明控制策略能实现位置误差和内力误差的渐近收敛.最后,仿真验证证明所设计控制策略的有效性.     

Combined direct and indirect adaptive control of robot manipulators using multiple models

A novel methodology is proposed for the adaptive control of rigid robotic manipulators. The proposed method utilizes multiple adaptive models for the identification and control of the manipulator. The present study is an extension of our previous work which utilized an indirect adaptive control approach with multiple models for better transient performance. The proposed scheme uses a composite approach where both prediction and tracking errors are used in a combined direct and indirect adaptive control framework. Simulation results are given to demonstrate the efficient use of the methodology.