A Systematic Approach for Designing Analytical Dynamics and Servo Control of Constrained Mechanical Systems

A systematic approach for designing analytical dynamics and servo control of constrained mechanical systems is proposed. Fundamental equation of constrained mechanical systems is first obtained according to Udwadia-Kalaba approach which is applicable to holonomic and nonholonomic constrained systems no matter whether they satisfy the D'Alember's principle. The performance specifications are modeled as servo constraints. Constraint-following servo control is used to realize the servo constraints. For this inverse dynamics control problem, the determination of control inputs is based on the Moore-Penrose generalized inverse to complete the specified motion. Secondorder constraints are used in the dynamics and servo control. Constraint violation suppression methods can be adopted to eliminate constraint drift in the numerical simulation. Furthermore, this proposed approach is applicable to not only fully actuated but also underactuated and redundantly actuated mechanical systems. Two-mass spring system and coordinated robot system are presented as examples for illustration.      

An extended divide-and-conquer algorithm for a generalized class of multibody constraints

An extension to the divide-and-conquer algorithm (DCA) is presented in this paper to model constrained multibody systems. The constraints of interest are those applied to the system due to the inverse dynamics or control laws rather than the kinematically closed loops which have been studied in the literature. These imposed constraints are often expressed in terms of the generalized coordinates and speeds. A set of unknown generalized constraint forces must be considered in the equations of motion to enforce these algebraic constraints. In this paper dynamics of this class of multibody constrained systems is formulated using a Generalized-DCA. In this scheme, introducing dynamically equivalent forcing systems, each generalized constraint force is replaced by its dynamically equivalent spatial constraint force applied from the appropriate parent body to the associated child body at the connecting joint without violating the dynamics of the original system. The handle equations of motion are then formulated considering these dynamically equivalent spatial constraint forces. These equations in the GDCA scheme are used in the assembly and disassembly processes to solve for the states of the system, as well as the generalized constraint forces and/or Lagrange multipliers.     

受限机器人神经形态的变结构位置/力控制

本文基于Ｊｅａｎ和Ｆｕ（１９９３）建立的受限机器人模型的降型阶形式，利用变结构系统理论，设计了具有未知动态的受限机器人轨道／力追踪控制，提出的学习方法仅仅利用了机器人动态模型的一般结构，不需要其精确信息，计算迅速，易于实现，仿真结果验证了提出的方法的有效性。     

Extension of the divide-and-conquer algorithm for the efficient inverse dynamics analysis of multibody systems

This paper presents a new mathematical framework to extend the Generalized Divide-and-Conquer Algorithm (GDCA) for the inverse dynamics analysis of fully actuated constrained multibody systems. Inverse-GDCA (iGDCA) is a highly parallelizable method which does not create the mass and Jacobian matrices of the entire system. In this technique, generalized driving forces and constraint loads due to kinematic pairs are clearly and separately differentiated from each other in the equations of motion. As such, it can be easily used for control scheme purposes. iGDCA works based on a series of recursive assembly and disassembly passes to form and solve the equations governing the inverse dynamics of the system. Herein, the mathematical formulations to efficiently combine the dynamics of consecutive bodies in the assembly pass for the purpose of inverse dynamics analysis are presented. This is followed by generating the disassembly pass algorithm to efficiently compute generalized actuating forces. Furthermore, this paper presents necessary mathematical formulations to efficiently treat the inverse dynamics of multibody systems involving kinematic loops with various active and passive boundary conditions. This is followed by the design of a new strategy to efficiently perform the assembly–disassembly pass in these complex systems while avoiding unnecessary computations. Finally, the presented method is applied to selected open-chain and closed-chain multibody systems.     

Modelling and simulation of an underwater manipulator

Recently, applications of articulated manipulators have increased to include extreme environments such as underwater and space. Simulation systems to support the design and control of industrial robots have been developed in many laboratories, and some high-speed calculation methods for inverse dynamics analysis of manipulators with series connections have been proposed. This paper deals with the dynamic simulation and modelling of underwater articulated manipulators. The dynamics of the above manipulators are formulated to evaluate the influence of the added mass tensor, the added inertia tensor, and fluid drag, and the lift on each arm according to classical Newton-Euler mechanics. Moreover, by generalizing this model, we can discuss the dynamics of a manipulator with dual arms and simulate some constrained motion of an end-effector. As an example of inverse dynamics analysis, the force and moment of a nine degrees of freedom (d.o.f.) manipulator with dual arms are analysed. As an example of direct dynamics analysis, hybrid control of both the force and the position of a 6 d.o.f. manipulator is simulated.     

Vsc motion and force control of robot manipulators in the presence of environmental constraint uncertainties

Due to task kinematic modelling inaccuracy, constraint functions imposed on robot manipulators may not be known exactly. In this article, a variable structure control (VSC) method is developed for robust motion and constrained force control of robot manipulators in the presence of parametric uncertainties, external disturbances, and constraint function uncertainties. The method is based on a particular structure of the constrained robot, in which motion control and force control are treated together. The proposed VSC controller provides the sliding mode and reaching transient response with prescribed qualities. A sufficient condition to guarantee the robot does not lose contact with the constraint surface is given. Detailed simulation results illustrate the proposed method. © 1994 John Wiley & Sons, Inc.     

Simulation of constraints by compliant joints

Application of models of compliant (flexible) joints instead of constraint equations for systems with closed-loop kinematic chains is considered; this makes it possible to replace differential-algebraic motion equations by stiff ordinary differential equations. For substantiation of this replacement, methods of analysis of singularly perturbed equations are used. Examples of mathematical models of compliant joints and expressions for approximate Jacobian matrices corresponding to these force interactions are given. Numerical solutions of direct and inverse dynamics equations for a number of controlled mechanisms are used for testing the method and its program realization.     

Obstacle avoidance extremum seeking control based on constrained derivative-free optimization

A new control scheme based on extremum seeking control (ESC) which employs a constrained derivative-free optimization algorithm has been proposed in this paper. A theorem has been formulated to prove the convergence result of ESC based on constrained derivative-free optimization. Generalized pattern search method with filter algorithm for constraint is used to generate a sequence of ESC control state. Since generalized pattern search (GPS) method does not require continuously differentiable and Lipschitz conditions, noise cancellation algorithm is added to the proposed ESC algorithm which is then used for multi-agent robot system. The obstacles are expressed as constraint functions instead of the traditional way of calculating the performance function of obstacles. Simulation results illustrate a multi-agent obstacle avoidance system which utilized the control algorithm to avoid obstacles that appear on the path of multi-agent robots. Based on the simulation results, it can be observed that multi-agents maintain their formation as per initial condition and follow the target without colliding into obstacles while navigating in a noisy environment. Performance comparison of the proposed algorithm with a reference algorithm shows the efficiency of the proposed algorithm.     

Impact stabilizing controller for hydraulic actuators with friction: Theory and experiments

Stabilizing manipulators during the transition from free to constraint motion is an important issue in contact task control design. This paper documents the development, theoretical analysis and experimental evaluation of a Lyapunov-based control scheme to regulate the impacts of a hydraulic actuator that comes in contact with a nonmoving environment. Upon sensing a nonzero force, the controller positions the actuator at the location where the force was first sensed, exerting minimal force on the environment. The scheme does not require continuous measurement of force or velocity during the short period of impacts, making it very useful for practical cases. Furthermore, no knowledge of the impact dynamics, friction effects, servovalve dynamics, or hydraulic parameters is required for control action. Stability of the control scheme is verified via analytical analyses. Due to the discontinuous friction model and the discontinuous nature of the proposed control law, the control system is nonsmooth. The existence, continuation and uniqueness of Filippov's solution to the system are, therefore, investigated. The extension of LaSalle's invariance principle to nonsmooth systems is next employed to prove that all the solution trajectories converge to the equilibria. The controller is finally tested experimentally to verify its practicality and effectiveness in collisions with hard and soft environments and with various approach velocities.     

Tracking in nonlinear differential-algebraic control systems with applications to constrained robot systems

We consider the design of a feedback control law for control systems described by a class of nonlinear differential-algebraic equations so that certain desired outputs track given reference inputs. The nonlinear differential-algebraic control system being considered is not in state variable form. Assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential-algebraic equations is expressed in a familiar normal form. A nonlinear feedback control law is then proposed which ensures, under appropriate assumptions, that the tracking error in the closed loop differential-algebraic system approaches zero exponentially. Applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints, constrained robot systems with joint flexibility, and constrained robot systems with significant actuator dynamics are discussed.     

Motion/force control scheme for electrically driven cooperative multiple mobile manipulators

This paper presents the motion and force control problem of rigid-link electrically driven cooperative mobile manipulators handling a rigid object. Although, the motion/force control problem of cooperative mobile manipulators has been enthusiastically studied. But there is little research on the motion/force control of electrically driven cooperative mobile manipulators. Due to the inclusion of the actuator dynamics with the manipulator’s dynamics, the controller exhibits some important characteristics. For the electromechanical system, we have designed a novel controller at the dynamic level as well as at the actuator level. In the proposed control scheme, at the dynamic level, uncertain non-linear mechanical dynamics is approximated with a hybrid controller containing model-based control scheme combined with model-free neural network based control scheme together with an adaptive bound. The adaptive bound is used to suppress the effects of external disturbances, friction terms, and reconstruction error of the neural network. At the actuator level, for the approximation of the unknown electrical dynamics, the model-free neural network is utilized. The developed control scheme provides that the position tracking errors, as well as the internal force, converge to the desired levels. Additionally, direct current motors are also controlled in such a way that the desired currents and torques can be attained. In order to make the overall system to be asymptotically stable, online learning of the weights and the parameter adaptation of the parameters is utilized in the Lyapunov function. The superiority of the developed control method is carried out with the numerical simulation results and its superior robustness is shown in a comparative manner.     

具有未建模动态及输入输出约束的单相全桥逆变器动态面事件触发控制

全桥逆变器是一类典型的开关型非线性系统,系统中存在很多非线性和不确定因素,易导致系统性能下降,甚至造成不稳定.对于具有未建模动态和时变输出约束的单相全桥逆变器系统,利用动态信号处理未建模动态,设计辅助动态系统补偿控制信号,提出一种事件触发的自适应动态面跟踪控制策略;引入跟踪误差变换,解决输出约束问题;对控制输入进行约束,使用模糊系统调节参数向量的欧氏范数作为自适应参数,设计事件触发控制,这些技术的采用可有效降低控制器计算量,保证实际系统的可实现性,完善了具有输入约束条件下动态面控制方法的稳定性分析和证明.逆变器精确模型无需已知,实际控制系统具有较好的稳定性和鲁棒性.理论分析表明,闭环系统的所有信号半全局一致终结有界,所提出方案的有效性通过仿真实验得到进一步验证.     

Hybrid force and motion control of flexible joint parallel manipulators using inverse dynamics approach

An inverse dynamics control algorithm is developed for hybrid motion and contact force trajectory tracking control of flexible joint parallel manipulators. First, an open-tree structure is considered by the disconnection of adequate number of unactuated joints. The loop closure constraint equations are then included. Elimination of the joint reaction forces and the other intermediate variables yield a fourth-order relation between the actuator torques and the end-effector position and contact force variables, showing that the control torques do not have an instantaneous effect on the end-effector contact forces and accelerations because of the flexibility. The proposed control law provides simultaneous and asymptotically stable control of the end-effector contact forces and the motion along the constraint surfaces by utilizing the feedback of positions and velocities of the actuated joints and rotors. A two degree of freedom planar parallel manipulator is considered as an example to illustrate the effectiveness of the method.     

Robust Hybrid Control of Constrained Robot Manipulators via Decomposed Equations

Basing on a constraint Jacobian induced orthogonal decomposition of the task space and by requiring the force controller to be orthogonal to the constraint manifold, the dynamics of the constrained robots under hybrid control is decomposed into a set of two equations. One describes the motion of robots moving on the constraint manifold, while the other relates the constraint force with the hybrid controller. This decomposition does not require the solution of the constraint equation in partition form. In this setting, the hybrid control of constrained robots can be essentially reduced to robust stabilization of uncertain nonlinear systems whose uncertainties do not satisfy the matching condition. A continuous version of the sliding-mode controller (from Khalil [12]) is employed to design a position controller. The force controller is designed as a proportional force error feedback of high gain type. The coordination of the position controller and the force controller is shown to achieve ultimately bounded position and force tracking with tunable accuracy. Moreover, an estimate of the domain of attraction is provided for the motion on the constraint manifold. Simulation for a planar two-link robot constraining on an ellipse is given to show the effectiveness of a hybrid controller. In addition, the friction effect, viewed as external disturbance to the system, is also examined through simulations.     

Exponential trajectory tracking control in the workspace of a class of flexible robots

In this paper, we present a control strategy that ensures the exponential stability of the tracking error in the virtual joint space of a class of mechanical systems made up of rigid links that form a chain that ends with a flexible beam. Virtual joints are defined so as to be related kinematically to the workspace. Thus, when the inverse kinematics is nonsingular, trajectory tracking in the virtual joint space is equivalent to trajectory tracking in the workspace. The method proposed in this paper calls for the transformation of the trajectory from the virtual joint space to the joint and deformation space. The robot is a non-minimum-phase system in the virtual joint space. However, this transformation, which involves the dynamics of the flexible part, can be solved using a causal–anticausal iterative approach. The controller is then designed using an input–output feedback linearization scheme, with regard to the joints, and two linear control laws with regard to the joint and to the deformation variable tracking errors. Analysis based on the passivity theorem, hierarchical systems stability, and linear matrix inequalities then allows us to determine the controller gains that ensure that the tracking errors in the virtual joint space are well damped and exponentially stable. Finally, the strategy is validated by simulating a controller that incorporates the proposed laws and that drives a two-link manipulator that has one rigid and one flexible link. The simulation results demonstrate the good performance of the proposed control system. © 1998 John Wiley & Sons, Inc.     

推进器饱和约束的水面无人艇固定时间精准跟踪控制

针对复杂扰动、完全未知系统动态以及推进器饱和约束的水面无人艇高精度跟踪控制问题,提出一种基于固定时间非奇异终端滑模的无模型固定时间精准跟踪控制(MFPTC)方案.首先,设计有限时间集总观测器,精确重构和补偿集总未知项;其次,引入自适应辅助系统消除推进器饱和特性,使得MFPTC方案在饱和约束下实现期望时间内对预定轨迹的精准跟踪;进而,基于反正切函数构造固定时间幂次趋近律,加快滑模变量收敛速度且有效削弱控制抖振;最后,采用CyberShip Ⅱ实验模型进行仿真研究,结果验证所提出MFPTC方案的有效性与优越性.     

A rotationless formulation of multibody dynamics: Modeling of screw joints and incorporation of control constraints

In the present work, a new energy-momentum conserving time-stepping scheme for multibody systems comprising screw joints is developed. In particular, it is shown that the underlying rotationless formulation of multibody dynamics along with a specific coordinate augmentation technique makes possible the energy-momentum discretization of the screw pair. In addition to that, control (or servo) constraints are treated within the rotationless framework of multibody dynamics. The control constraints are used to partially prescribe the motion of a multibody system. In particular, control constraints, in conjunction with the coordinate augmentation technique, make possible to solve inverse dynamics problems by applying the present simulation approach.     

轮式移动机器人的数据驱动轨迹跟踪滑模约束控制

针对有输入饱和约束的轮式移动机器人(WMR)的轨迹跟踪问题,提出一种抗饱和无模型自适应积分终端滑模控制方案.该方案基于紧格式动态线性化技术,构建WMR系统的在线数据驱动模型.在积分终端滑模控制器设计过程中,引入动态抗饱和补偿器,以解决WMR系统轨迹跟踪过程中执行器饱和问题.控制器设计仅利用控制系统的输入输出数据,与WMR系统模型信息无关.因此,针对不同类型的WMR系统,该方案均可实现.最后,通过仿真实验将所提出的方法与PID方法的控制效果进行对比,仿真结果表明,所提出的控制算法的跟踪误差更小且响应速度更快.