一类多体系统非完整运动最优规划的拟牛顿算法

研究带有非完整约束的一类多体系统运动规划问题。多体系统中的非完整约束通常是由不可积的速度约束或不可积的守恒律引起。在系统动量和动量矩守恒情况下,动力学方程降阶为非完整形式约束方程,系统的控制问题可转化为无漂移系统的非完整运动规划问题。文中首先导出具有多体开链系统的非完整运动模型。利用最优控制理论和最优化技术,采用输入参数化的方法将连续的最优控制问题转化为离散的最优控制问题,提出一种非完整多体系统运动规划的拟牛顿算法。最后将该方法用于自由漂浮的空间三连杆机构,仿真结果验证了该方法的有效性。     

An analytical control law of length rate for tethered satellite system

Based on the nonlinear dynamic equations of a tethered satellite system with three-dimensional attitude motion, an analytical tether length rate control law for deployment is derived from the equilibrium positions of the system and the scheme of the value range of the expected in-plane pitch angle. The proposed control law can guarantee that the tensional force acting on the end of the tether remains positive. The oscillation of the out-of-plane roll motion in conjunction with the in-plane pitch motion is effectively suppressed during deployment control. The analytical control law is still applicable, even if the system runs on a Keplerian elliptical orbit with a large eccentricity. The local stability of the non-autonomous system during deployment control is analyzed using the Floquet theory, and the global behavior is numerically verified using simple cell mapping. The numerical simulations in the paper demonstrate the proposed analytical control law.     

亚音速气流作用下薄板结构混沌运动的时滞反馈控制

研究了亚音速气流下非线性二维薄板结构在横向周期载荷作用下的混沌运动及控制问题。基于von Karman大变形板理论和分离变量法,建立了亚音速下薄板结构的运动控制方程。对于未控系统,采用Melnikov方法判断其混沌运动阈值,并用Runge-Kutta法进行数值验证。对处于混沌运动状态的系统,采用时滞反馈控制方法对混沌运动进行控制。结果表明,Melnikov方法可以有效地预测系统的混沌运动行为,时滞反馈控制方法可以有效地将系统的混沌运动转化为周期运动。     

Optimized adaptive tracking control for an underactuated vibro-driven capsule system

This paper studies the issue of adaptive trajectory tracking control for an underactuated vibro-driven capsule system and presents a novel motion generation framework. In this framework, feasible motion trajectory is derived through investigating dynamic constraints and kernel control indexes that underlie the underactuated dynamics. Due to the underactuated nature of the capsule system, the global motion dynamics cannot be directly controlled. The main objective of optimization is to indirectly control the friction-induced stick–slip motions to reshape the passive dynamics and, by doing so, to obtain optimal system performance in terms of average speed and energy efficacy. Two tracking control schemes are designed using a closed-loop feedback linearization approach and an adaptive variable structure control method with an auxiliary control variable, respectively. The reference model is accurately matched in a finite-time horizon. The key point is to define an exogenous state variable whose dynamics is employed as a control input. The tracking performance and system stability are investigated through rigorous theoretic analysis. Extensive simulation studies are conducted to demonstrate the effectiveness and feasibility of the developed trajectory model and optimized adaptive control system.     

Control of underactuated mechanical systems with servo-constraints

This paper deals with a class of controlled mechanical systems in which the number of control inputs, equal to the number of desired system outputs, is smaller than the number of degrees of freedom. The related inverse dynamics control problem, i.e., the determination of control input strategy that force the underactuated system to complete the partly specified motion, is a challenging task. In the present formulation, the desired system outputs, expressed in terms of the system states, are treated as servo-constraints on the system, and the problem is viewed from the constrained motion perspective. Mixed orthogonal-tangent realization of the constraints by the available control reactions is stated, and a specialized methodology for solving the “singular” control problem is developed. The governing equations are manipulated to index three differential-algebraic equations, and a simple numerical code for solving the equations is proposed. The feedforward control law obtained as a solution to these equations can then be enhanced by a closed-loop control strategy with feedback of the actual servo-constraint violations to provide stable tracking of the reference motion in the presence of perturbations and modeling uncertainties. An overhead trolley crane executing a load-prescribed motion serves as an illustration. Some results of numerical simulations are reported.     

Biquaternion solution of the kinematic control problem for the motion of a rigid body and its application to the solution of inverse problems of robot-manipulator kinematics

The problem of reducing the body-attached coordinate system to the reference (programmed) coordinate system moving relative to the fixed coordinate system with a given instantaneous velocity screw along a given trajectory is considered in the kinematic statement. The biquaternion kinematic equations of motion of a rigid body in normalized and unnormalized finite displacement biquaternions are used as the mathematical model of motion, and the dual orthogonal projections of the instantaneous velocity screw of the body motion onto the body coordinate axes are used as the control. Various types of correction (stabilization), which are biquaternion analogs of position and integral corrections, are proposed. It is shown that the linear (obtained without linearization) and stationary biquaternion error equations that are invariant under any chosen programmed motion of the reference coordinate system can be obtained for the proposed types of correction and the use of unnormalized finite displacement biquaternions and four-dimensional dual controls allows one to construct globally regular control laws. The general solution of the error equation is constructed, and conditions for asymptotic stability of the programmed motion are obtained. The constructed theory of kinematic control of motion is used to solve inverse problems of robot-manipulator kinematics. The control problem under study is a generalization of the kinematic problem [1, 2] of reducing the body-attached coordinate system to the reference coordinate system rotating at a given (programmed) absolute angular velocity, and the presentedmethod for solving inverse problems of robotmanipulator kinematics is a development of the method proposed in [3–5].     

Identifying and mitigating residual vibrations in wave-based control of lumped,flexible systems

Meccanica - Wave-based control (WBC) is a technique for motion control of under-actuated flexible systems. It envisages actuator motion as launching a motion wave into the system, while...     

动态规划求解空间双臂机器人非完整运动最优控制问题

通过自适应动态规划研究自由漂浮空间双臂机器人运动的最优控制问题．针对空间双臂机器人的非完整性运动,采用自适应动态规划(Adaptive Dynamic Programming, ADP)方法求解其最优控制问题．根据多体动力学理论,推导了载体位置、姿态均无控制条件下,双臂空间机器人满足的系统动量守恒关系的非完整约束方程,并将其转化为控制系统的状态方程,从而将双臂空间机器人的非完整运动规划问题转化为对非线性系统的控制问题．文中根据自适应动态规划网络结构,利用神经网络来近似性能指标函数,进而用龙格库塔法求解状态变量．并给出了适合该类问题的一种效用函数具体表达式,保证了空间双臂机器人到达期望位置后不再继续运动．实现了对空间双臂机器人非完整运动规划的最优控制．数值仿真实验验证了ADP对求解空间双臂机器人非完整运动规划最优控制问题的有效性．     

Output Feedback Modular Adaptive Control of a Nonlinear Prototypical Wing Section

The paper presents nonlinear adaptive control systems for the control of limit cycle oscillations of a prototypical wing section with structural nonlinearities using only output feedback. The chosen model describes the plunge and pitch motion of a wing. The model includes plunge and pitch nonlinearities, and has a single control surface for the purpose of control. Using a canonical representation of the aeroelastic system, a modular output feedback adaptive control system consisting of an input-to-state stabilizing controller and a passive identifier (an observer and adaptation law) is derived. In the closed-loop system, asymptotic stabilization of the pitch and plunge motion is accomplished. Simulation results show that the control system is effective in regulating the state vector to the origin in spite of large parameter uncertainties.     

引导混沌运动到周期运动的自适应控制策略

提出一种自适应控制策略，对控制参数作线性反馈将非线性动力系统由混沌运动引导到指定的周期运动．所解决的关键问题是将反馈控制强度的确定转化为扩维相空间中的极点配置问题．给出了将该策略用于控制Ｌｏｇｉｓｔｉｃ映射和受迫Ｄｕｆｉｎｇ振子的仿真．     

Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system

The problem of the brachistochronic motion of a holonomic scleronomic mechanical system is analyzed. The system moves in an arbitrary field of known potential forces. The problem is formulated as an optimal control task, where generalized speeds are taken as control variables. The problem considered is reduced to solving the corresponding two-point boundary-value problem (TPBVP). In order to determine the global minimal solution of the TPBVP, an appropriate numerical procedure based on the shooting method is presented. The global minimal solution represents the solution with the minimum time of motion. The procedure is illustrated by an example of determining the brachistochronic motion of a disk that performs plane motion in a vertical plane in a homogeneous field of gravity.     

空间机械臂捕获卫星过程的碰撞动力学模拟及镇定运动的鲁棒控制

讨论了漂浮基空间机械臂捕获未知运动目标卫星的接触碰撞动力学建模和接触碰撞后系统镇定运动的控制问题。利用第二类拉格朗日方法和牛顿-欧拉法分别建立了接触碰撞前漂浮基空间机械臂和目标卫星两分体系统的动力学模型;以此为基础借助于空间机械臂与目标卫星接触点间的运动几何关系、力传递关系,计算了接触碰撞所产生的影响效应;捕获卫星后,联立空间机械臂与卫星接触碰撞前的动力学模型,建立了接触碰撞后两系统组合体动力学模型;并设计了增广鲁棒控制算法,以对受碰撞冲击后处于不稳定的组合体系统进行镇定运动控制。上述控制方法能应用于空间机械臂载体位置不受控情况,并能使组合体系统控制方程关于卫星不确定参数呈线性化关系。最后,利用数值仿真模拟捕获过程系统运动状态,验证了上述鲁棒控制镇定运动的效果。     

碰摩裂纹转子轴承系统的周期运动稳定性及实验研究

根据碰摩裂纹耦合故障转子轴承系统的非线性动力学方程，利用求解非线性非自治系统周期解的延拓打靶法，研究了系统周期运动的稳定性。研究发现，小偏心量下系统周期运动发生Hopf分岔，大偏心量下系统周期运动发生倍周期分岔，偏心量的加大使周期解的稳定性明显降低；系统碰摩间隙变小，碰摩影响了油膜涡动的形成，使失稳转速有所提高；裂纹深度的加大降低了系统周期运动的稳定性。本文的研究为转子轴承系统的安全稳定运行提供了理论参考。     

自由下落猫姿态最优控制的混合优化策略

研究猫自由下落时的转体运动对探索宇航员在太空失重状态下的空间运动规律具有重要的参考价值.针对猫自由下落时四肢先着地现象的姿态最优控制问题,提出一种由Gauss伪谱法求解可行解与直接打靶法求解最优精确解相结合的混合优化策略.首先,根据猫在自由下落过程中的角动量守恒原理,推导出简化后的两对称刚体系统的非完整姿态运动方程;然后基于Gauss伪谱法将此无漂移系统的姿态非完整运动规划问题离散为非线性规划问题,并在不考虑实际性能指标函数的条件下利用序列二次规划算法求解此非线性规划问题在较少节点时对应的控制变量可行解,再通过三次样条插值获取较多节点时的控制变量值;最后基于直接打靶法将插值得到的控制值作为序列二次规划算法的初始猜测值,从而求解得到最优的控制输入,再代入系统姿态运动方程,通过数值积分得到落体猫的转体姿态运动曲线.通过数值仿真,求解得到的姿态运动曲线是光滑的,能以较高的精度到达预定的目标姿态;最优控制输入也能满足预先设计的零边界控制要求以及最大控制要求;结果表明了此混合优化策略具有较强的鲁棒性和有效性.     

漂浮基柔性关节空间机器人自适应滑模运动控制及振动主动抑制

讨论了关节柔性且系统参数不确定的漂浮基空间机器人系统的动力学建模过程、运动轨迹跟踪控制算法设计及系统柔性振动的主动抑制问题。利用系统动量、动量矩守恒关系和拉格朗日法对系统动力学进行分析,并建立系统动力学方程。基于奇异摄动法将系统分解为表示系统刚性运动部分的慢变子系统和表示系统柔性运动部分的快变子系统。针对慢变子系统提出了一种自适应滑模控制算法。该控制算法是由基于滑模面的等效控制项、自适应控制项和PID反馈控制项组成。因此,它集合了滑模控制、自适应算法和PID技术的优点,且弥补了三种算法各自的缺点。该控制算法能够有效地补偿系统的转动误差和不确定参数,提高控制系统的精度。针对快变子系统,提出基于速度差值的反馈控制算法来抑制柔性关节引起的系统柔性振动,保证系统的稳定性。最后,通过仿真实验证明了提出的混合控制算法的有效性。     

轮式移动机器人非完整运动规划的最优控制方法

本文讨论轮式动机器人非完整运动的最优规划问题,利用约束与最优控制理论建立数学模型,考虑系统的非完整约束特性,提出轮式移动机器人运动规划的最优控制算法。通过数值仿真,表明该方法的有效性。     

非自治时滞反馈控制系统的周期解分岔和混沌

研究时滞反馈控制对具有周期外激励非线性系统复杂性的影响机理,研究对应的线性平衡态失稳的临界边界,将时滞非线性控制方程化为泛函微分方程,给出由Hopf分岔产生的周期解的解析形式．通过分析周期解的稳定性得到周期解的失稳区域,使用数值分析观察到时滞在该区域可以导致系统出现倍周期运动、锁相运动、概周期运动和混沌运动以及两条通向混沌的道路：倍周期分岔和环面破裂．其结果表明,时滞在控制系统中可以作为控制和产生系统的复杂运动的控制“开关”．     

非自旋航天器混沌姿态运动及其参数开闭环控制

研究万有引力场中受大气阻力且存在结构内阻尼的非自旋航天器在椭圆轨道上平面天平动的混沌及其参数开闭环控制问题．在建立数学模型的基础上确定出现混沌的必要条件并数值验证混沌的存在性，提出非线性振动系统混沌运动的参数开闭环控制并应用于控制航天器的混沌姿态运动．     

Taking into account the influence of elastic elements of a free structure on the accuracy of its stabilization under a bang-bang control

We consider the problem of stabilization with respect to a prescribed position for the translational motion of a rigid body with interior material points connected with each other and with the exterior body by linear viscoelastic constraints. The motion occurs under the action of a constant exterior perturbation and a bang-bang control force that are directed along the line of motion. We assume that the bang-bang force control channel has a fixed delay, so that arbitrarily frequent switchings are impossible. We suggest a positional control ensuring the solution of this problem. We estimate the amplitude of the rigid body vibrations about the center of mass of the entire structure and the accuracy of stabilization of the prescribed position of the rigid body depending on the mechanical characteristics of the system and the control force magnitude. We also consider the problem of maximizing the stabilization accuracy depending on the control parameters. By way of example, we consider the controlled motion of a two-mass oscillatory system. This work is closely related to [1–3] and continues the studies of the guaranteed optimal bang-bang controllers with delay in the control channel [4–9]. The dynamics of a rigid body with elastic and dissipative elements was studied in [10] under the assumption that the period of natural vibrations and their decay time are small compared with the characteristic time of motion.