Simultaneous stabilization and trajectory tracking of underactuated mechanical systems with included actuators dynamics

The paper deals with a novel control algorithm for simultaneous stabilization and trajectory tracking of underactuated nonlinear mechanical systems (UNMS) with included actuators dynamics. Simultaneous stabilization and trajectory tracking refer to arbitrary chosen actuated and unactuated degrees of freedom (DOF) of the system. The proposed control approach can be applied both to the second-order nonholonomic systems and the systems with input coupling, while a general model of actuators dynamics includes electrical, pneumatic, and hydraulic drives. Control law is based on linear combination of two control signals, where the first signal is designed to separately control only actuated DOF, and second to separately control only unactuated DOF. Simulation example of rotational inverted pendulum driven by electrical DC motor is presented, showing the effectiveness of the proposed approach.     

Feedback-based event-driven parts moving

A collection of unactuated disk-shaped "parts" must be brought by an actuated manipulator robot into a specified configuration from arbitrary initial conditions. The task is cast as a noncooperative game played among the parts-which in turn yields a feedback-based event-driven approach to plan generation and execution. The correctness of this approach, an open question, has been demonstrated in simpler settings and is further suggested by the extensive experiments reported here using an actual working implementation with EDAR-a mobile robot operating in a purely feedback-based event-driven manner. These results verify the reliability of this approach against uncertainties in sensory information and unanticipated changes in workspace configuration.     

含有非驱动关节机器人的学习控制

含有非驱动关节的机器人的运动控制比一般的机器人要困难得多．因为非驱动关节 不能直接控制，系统属于非完全可控系统，一般的光滑反馈控制方法对这样的系统是无效的 ．本文提出了一种学习控制的方法，通过学习获得高精度的前馈控制，实现欠驱动机器人的 高精度运动控制，并在一台实际的欠驱动机器人上进行了实验，给出了实验结果．     

Generation and application of prestress in redundantly full-actuated parallel manipulators

This paper addresses the inverse dynamics of redundantly actuated parallel manipulators. Such manipulators feature advantageous properties, such as a large singularity-free workspace, a high possible acceleration of the moving platform, and higher dexterity and manipulability. Redundant actuation further allows for prestress, i.e., internal forces without generating end-effector wrenches. This prestress can be employed for various goals. It can potentially be used to avoid backlash in the driving units or to generate a desired tangential end-effector stiffness. In this paper, the application of prestress is addressed upon the inverse dynamics solution. A general formulation for the dynamics of redundantly actuated parallel manipulators is given. For the special case of simple redundancy, a closed-form solution is derived in terms of a single prestress parameter. This yields an explicit parametrization of prestress. With this formulation an open-loop prestress control is proposed and applied to the elimination of backlash. Further, the generation of tangential end-effector stiffness is briefly explained. The approach is demonstrated for a planar 4RRR manipulator and a spatial heptapod.     

Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment

The paper deals with the workspace and dynamic performance evaluation of the PRR–PRR parallel manipulator in spray-painting equipment. Functional workspace of planar fully parallel robots is often limited because of interference among their mechanical components. The proposed 3-DOF planar parallel manipulator with two kinematic chains connecting the moving platform to the base can reduce interference while still maintaining 3 DOFs. Based on the kinematics, four working modes are analyzed and singularity is studied. The workspace is investigated and the inverse dynamics is formulated using the virtual work principle. The dynamic performance evaluation indices are designed on the basis of maximum and minimum magnitude of acceleration vector of the moving platform produced by a unit actuated force. The index not only can evaluate the accelerating performance of a manipulator, but also can reflect the isotropy of accelerating performance. Workspace and dynamic performances of the four working modes are compared and the optimal working mode for the painting of a large object with conical surface is determined.     

Kinematic analysis of a flexible six-DOF parallel mechanism.

In this paper, a new type of six-degrees of freedom (DOF) flexible parallel mechanism (FPM) is presented. This type of parallel mechanism possesses several favorable properties: (1) its number of DOFs is independent of the number of serial chains which make up the mechanism; (2) it has no kinematical singularities; (3) it is designed to move on rails, and therefore its workspace is much larger than that of a conventional parallel manipulator; and (4) without changing the number of DOFs and the kinematics of the mechanisms, the number of the serial chains can be reconfigured according to the needs of the tasks. These properties make the mechanism very preferable in practice, especially for such tasks as joining huge ship blocks, in which the manipulated objects vary dramatically both in weights and dimensions. Furthermore, the mechanism can be used as either a fully actuated system or an underactuated system. In the fully actuated case, the mechanism has six DOF motion capabilities and manipulation capabilities. However, in the underactuated case, the mechanism still has six DOF motion capabilities, but it has only five DOF manipulation capabilities. In this paper, both the inverse and forward kinematics are studied and expressed in a closed form. The workspace and singularity analysis of the mechanism are also presented. An example is presented to illustrate how to calculate the kinematics of the mechanism in both fully-actuated and underactuated cases. Finally, an application of such a mechanism to manufacturing industry is introduced.     

欠驱动冗余度空间机器人优化控制

欠驱动控制是空间技术中容错技术的重要方面.本文研究了被动关节中有制动器的欠驱动冗余度空间机器人系统的运动优化控制问题.从系统动力学方程出发,分析了欠驱动冗余度空间机器人的优化能力和控制方法;给出了主、被动关节间的耦合度指标;提出了欠驱动冗余度空间机器人系统的“虚拟模型引导控制”方法,在这种方法中采用与欠驱动机器人机构等价的全驱动机器人作为模型来规划机器人的运动,使欠驱动系统在关节空间中逼近给出的规划轨迹,实现了机器人末端运动的连续轨迹运动优化控制;通过末关节为被动关节的平面三连杆机器人进行了仿真,仿真的结果证明了提出算法的有效性.     

Maximum DLCC of Spatial Cable Robot for a Predefined Trajectory Within the Workspace Using Closed Loop Optimal Control Approach

One of the most important applications of cable robots is load carrying along a specific path. Control procedure of cable robots is more challenging compared to linkage robots since cables can’t afford pressure. Meanwhile carrying the heaviest possible payload for this kind of robots is desired. In this paper a nonlinear optimal control is proposed in order to control the end-effector within a predefined trajectory while the highest Dynamic Load Carrying Capacity (DLCC) can be carried. This purpose is met by applying optimum torque distribution among the motors with acceptable tracking accuracy. Besides, other algorithms are applied to make sure that the allowable workspace constraint is also satisfied. Since the dynamics of the robot is nonlinear, feedback linearization approach is employed in order to control the end-effector on its desirable path in a closed loop way while Linear Quadratic Regulator (LOR) method is used in order to optimize its controlling gains since the state space is linearized by the feedback linearization. The proposed algorithm is supported by doing some simulation studies on a two Degrees of Freedom (DOF) constrained planar cable robot as well as a six DOFs under constrained cable suspended robot and their DLCCs are calculated by satisfying the motor torque, tracking error and allowable workspace constraints. The results including the angular velocity, motors’ torque, actual tracking of the end-effector and the DLCC of the robot are calculated and verified using experimental tests done on the cable robot. Comparison of the results of open loop simulation results, closed loop simulation results and experimental tests, shows that the results are improved by applying the proposed algorithm. This is the result of tuning the motors’ torque and accuracy in a way that the highest DLCC can be achieved.     

A Virtual Work Based Algorithm for Solving Direct Dynamics Problem of a 3-RRP Spherical Parallel Manipulator

In this paper, we use principle of virtual work to obtain the direct dynamics analysis of a 3-RRP spherical parallel manipulator, also called spherical star-triangle (SST) manipulator (Enferadi et al., Robotica 27, 2009). This manipulator has good accuracy and relatively a large workspace which is free of singularities (Enferadi et al., Robotica, 2009). The direct kinematics problem of this manipulator has eight solution (Enferadi et al., Robotica 27, 2009). Given a desired actuated joint trajectories, we first present an algorithm for selecting the admissible solution. Next, direct velocity and direct acceleration analysis are obtained in invariant form. The concept of direct link Jacobian matrices is introduced. The direct link Jacobian matrix relates motion of any link to vector velocity of actuated joints. Finally, dynamical equations of the manipulator are obtained using the principle of virtual work and the concept of direct link Jacobian matrices. This method allows elimination of constraint forces and moments at the passive joints from motion equations. Two examples are presented and trajectory of moving platform are obtained. Results are verified using a commercial dynamics modeling package as well as inverse dynamics analysis (Enferadi et al., Nonlinear Dyn 63, 2010).     

Design and evaluation of an actuated exoskeleton for examining motor control in stroke thumb

Chronic hand impairment is common following stroke. This paper presents an actuated thumb exoskeleton (ATX) to facilitate research in examining motor control and hand rehabilitation. The ATX presented in this work aims to provide independent bi-directional actuation in each of the 5 degrees of freedom (DOF) of the thumb using a novel flexible shaft-based mechanism that has 5 active DOF and 3 passive DOF. A prototype has been built and experiments have been conducted to measure the allowable workspace at the thumb and evaluate the kinematic and kinetic performance of the ATX. The experimental results show that the ATX is able to provide individual actuation at all five thumb joints with high joint velocity and torque capacities. Further improvement and future work are discussed.     

Nonlinear Feedback Control of a Gravity-Assisted Underactuated Manipulator With Application to Aircraft Assembly

A nonlinear feedback scheme for a gravity-assisted underactuated manipulator with second-order nonholonomic constraints is presented in this paper. The joints of the hyper articulated arm have no dedicated actuators but are activated by gravity. By tilting the base link appropriately, the gravitational torque drives the unactuated links to a desired angular position. With simple locking mechanisms, the hyperarticulated arm can change its configuration using only one actuator at the base. This underactuated arm design was motivated by the need for a compact snake-like robot that can go into aircraft wings and perform assembly operations using heavy end-effectors. The dynamics of the unactuated links are essentially second-order nonholonomic constraints for which there are no general methods to design closed-loop control. We propose a nonlinear closed-loop control law that is guaranteed to be stable in positioning one unactuated joint at a time. We synthesize a Lyapunov function to prove the convergence of this control scheme. The Lyapunov function also generates estimates of the domain of convergence of the control law for various control gains. The control algorithm is implemented on a prototype three-link system. Finally, we provide some experimental results to demonstrate the efficacy of the control scheme.     

A limit set stabilization by means of the Port Hamiltonian system approach

A solution to the stabilization problem of a compact set by means of the Interconnection and Damping Assignment Passivity‐Based Control methodology, for an affine nonlinear system, was introduced. To this end, we expressed the closed‐loop system as a Port Hamiltonian system, having the property of almost all their trajectories asymptotically converge to a convenient limit set, except for a set of measure zero. It was carried out by solving a partial differential equation (PDE) or single matching condition, which allows the desired energy level or limit set E to be shaped explicitly. The control strategy was tested using the magnetic beam balance system and the pendulum actuated by a direct current motor (DC‐motor), having obtained satisfactory results. Copyright © 2014 John Wiley & Sons, Ltd.     

含有未驱动关节的空间机器人控制

含有未驱动关节的自由潭浮空间机器人具有不可积分的速度和加速度约束，因而是一个二阶非完整系统，通过分析系统的动力学结构，本文设计了一种全 基于速度控制的方法控制未驱动关节，然后采用多步混合控制策略实现空间机器人的定位跟踪。     

On simultaneous control of the energy and actuated variables of underactuated mechanical systems – example of the acrobot with counterweight

The energy-based control approach aiming to control both the total mechanical energy and actuated variables of underactuated mechanical systems has generated renewed interest in recent years. Different from the reports of successful applications of this approach, we investigate whether there exists an underactuated mechanical system for which we fail to control both the total mechanical energy and actuated variable(s) to some given desired values by studying a CWA (Counter-Weighted Acrobot), which is a modified Acrobot with its first link having a counterweight and only its second link being actuated. By analyzing globally the solution of the closed-loop system consisting of the CWA and the controller designed via the energy-based control approach, we show that unless the CWA is linearly controllable at the up–up equilibrium, where links 1 and 2 are in the upright position, the controller fails to achieve the goal of controlling the energy to the potential energy at the equilibrium and controlling the actuated joint variable to zero. We also provide corresponding results for the up–down, down–up, and down–down equilibriums of the CWA, where up and down denote that the link is in the upright and downward positions, respectively. We present numerical simulation results to validate the theoretical results.     

Ratio Control for Continuously Variable Transmissions with Minimal Sensor Configuration

In this paper, a model‐based controller for an electrically actuated hybrid belt continuously variable transmission is developed. The main goal is to track a desired transmission ratio. A nonlinear model of the transmission dynamics is presented and an identification procedure for the unknown model parameters given. A control structure with two degrees of freedom is used to achieve the desired tracking performance. The proposed concept allows a straightforward realization of the control algorithm, the number of required sensors is reduced to a minimum. It is demonstrated by means of test rig experiments, that the proposed approach yields very satisfactory results over the entire operation range.     

Design-by-Optimization and Control of Redundantly Actuated Parallel Kinematics Sliding Star

The paper deals with the design and control of an example of redundantly actuated parallel kinematic structure that can be a machine tool. The principle of redundant actuation brings parallel kinematic structures which do not have singular positions in workspace and which has increased dynamic, stiffness and accuracy properties. There is proposed a parallel kinematic structure called Sliding Star that has promising dynamic and stiffness properties. The conceptual design-by-optimization of this structure is briefly described. The redundantly actuated parallel kinematics have control problem due to mutual fighting of redundant drives. There is described the solution of this problem. Based on the investigated redundantly actuated parallel kinematics there has been built a laboratory prototype. The experimental results from the control of this prototype are briefly presented.     

Multi-Criteria Optimization of a Hexapod Machine

Alternative designs of a hexapod machine are proposed and investigated with the aims to reduce flexibility and to eliminate singular kinematic configurations that appear in the workspace for the current design of the machine. The hexapod is modeled as a rigid multibody system. Articular coordinates associated with desired tool trajectories are computed by inverse kinematics. Hence, dynamic forces and torques are not considered and, as there is no closed-loop control realized in the model, the actual rotational and translational position of the tool deviates from the desired position due to machining loads. These deviations serve as objective functions during a multi-criteria optimization in order to determine the best design regarding stiffness/flexibility of the machine. Further, a general approach for evaluating flexibility behavior of the machine in the complete workspace is introduced and the results from the optimization are verified. Besides flexibility, a crucial point for machining tools is the size of the feasible workspace. Therefore, the influence of the design modification on the workspace is also taken into account.     

Adaptive Neural Region Tracking Control of Multi-fully Actuated Ocean Surface Vessels

In this paper, adaptive neural network region tracking control is designed to force a group of fully actuated ocean vessels with limited sensing range to track a common moving target region, in the presence of uncertainties and unknown disturbances. In this control concept, the desired objective is specified as a moving region instead of a stationary point, region or a path. The controllers guarantee the connectivity preservation of the dynamic interaction network, and no collisions happen between any ocean vessels in the group. The tracking control design is based on the artificial potential functions, approximation-based backstepping design technique, and Lyapunov's method. It is proved that under the adaptive neural network control law, the tracking error of each ocean vessel converges to an adjustable neighborhood of the origin, although some of them do not access the desired target region directly. Simulation results are presented to illustrate the performance of the proposed approach.      

Synchronized multiple spacecraft rotations

The objective of this paper is to present formation control laws for maintaining attitude alignment among a group of spacecraft in either deep space or earth orbit. The paper presents two control strategies based on emergent behavior approaches. Each control strategy considers the desired formation behaviors of convergence to the final formation goal, formation keeping, and the desire to rotate the spacecraft about fixed axes. The first approach uses velocity feedback and the second approach used passivity-based damping. In addition, we prove analytically that our approach guarantees formation keeping throughout the maneuver. Simulation results demonstrate the effectiveness of our approach.     

A New Assessment of Singularities of Parallel Kinematic Chains

This paper presents a novel assessment of singularities of general parallel kinematic chains. Hierarchical levels in which different critical phenomena originate are recognized. At each level, the causes of singular events are identified and interpreted, and on their basis, a comprehensive taxonomy is proposed. First, the unactuated kinematic chain is studied. The concepts of leg and passive-constraint singularities are described, and stationary and increased instantaneous mobility configurations are identified. Then, a set of motorized joints is chosen. The effects of first-level singularities on the actuated chain are investigated, and further phenomena are identified, such as redundancy singularities and active-constraint singularities. The notions of reaction and action spaces are originally discussed. The consequences on the ability of the actuated chain to effectively govern its local and global freedoms are analyzed, and the complex interactions between the various singular events are studied. The instantaneous redundancy of actuators, which occur when these work either against each other or against joint constraints, is also evaluated. Finally, when the input–output mechanism is considered, the events described at the previous stages are interpreted within the perspective of the machine's desired use.