考虑综合步行约束的仿人机器人参数化3D 步态规划方法

给出了一种三维环境下双足行走的参数化步态规划方法,建立了仿人机器人13 质量块约束动力学模 型．考虑单腿支撑和双腿支撑无冲击连续切换的六点边界约束条件、可行步态物理约束条件以及ZMP 稳定性约束 条件,以关节输出力矩函数的二次型积分值最小作为优化指标,采用参数化步态优化方法,将复杂关节轨迹的规划 问题转化为分段多项式系数组成的有限参数向量的优化问题,得到了快速和慢速两组光滑无振动的优化步态．仿真 和样机实验验证了该方法的有效性．     

五杆四驱动平面双足机器人动态步态规划与非线性控制

以五杆四驱动的平面双足步行机器人为对象，研究了其动态步行的时不变步态规划和限定时间的非线性控制策略．揭示了其模型的欠驱动和完全驱动的混杂和非光滑动力学特性，推导了其碰撞模型．基于虚拟约束的概念，提出时不变步态的输出函数解析设计方法，设计了反馈线性化控制器，将系统转化为双积分环节．然后采用限定时间控制器在一步内零化输出函数．仿真实验表明，动态步行趋于一个稳定的极限环，实现了规划的行走模式，验证了该方法的有效性．     

下肢外骨骼机器人变步长步态规划方法

为了解决下肢外骨骼机器人连续步态规划问题,基于倒立摆模型提出了一种步态规划算法,并针对传统倒立摆模型无法变步长连续行走的问题提出了新的改进方法。将外骨骼机器人分成支撑腿和摆动腿两部分,分别采用D-H法进行运动学分析;利用倒立摆模型和固定函数法,进行等效质心与摆动腿末端轨迹规划;在相邻单脚支撑期之间插入双脚支撑期,使下肢外骨骼机器人在不断改变步行时,利用双脚支撑期进行位置和速度的切换,实现实时步态规划;将规划算法在SIMULINK中实现,并与ADAMS模型进行联合仿真,下肢外骨骼机器人在仿真环境下行走稳定,证明了算法的有效性。     

基于约束满足的多目标双足机器人动态步态参数优化*

目前的步态优化算法仅仅实现了对单一目标的优化,把双足机器人步态优化看做是多目标优化问题,构建了衡量稳定性、能量消耗、步行速度三个目标评价函数。考虑到直接对多个目标加权求和的方法不能很好地处理多目标问题,提出一种新的基于约束满足的多目标步态参数优化算法,其思想是把基于惩罚函数的SPEA2(strength Pareto evolutionary algorithm2 )应用到多目标双足机器人动态步态参数优化问题上,规划出了同时满足这三个目标的动态优化步态。通过仿真实验表明了算法的有效性。     

基于六维力/力矩传感器的拟人机器人实际

ZMP（Zero Moment Point）作为双足步行机器人动态稳定行走的判据,已应用于世界上很多 著名的步行机器人系统．目前国外步行机器人大多采用力/力矩传感器进行ZMP的实际检测计 算,但采用六维力/力矩传感器的却不多,而且其安装位置也各不相同．国内机器人还都处 于离线步态规划阶段,只进行了理论ZMP的计算,并没有进行实时检测． 本文根据清华大学985重点项目“拟人机器人技术及其系统研究”的研究要求,确定了基于 六维力/力矩传感系统的实际ZMP检测方案,确定了传感器安装的最佳位置,推导了单脚支撑 期,双脚支撑期的实际ZMP计算公式,提出了基于ZMP理论的姿态调整方法,以期在实际应用 中进行在线步态规划．     

欠驱动双足机器人动态步态规划方法研究

以欠驱动双足机器人为对象研究其周期稳定的动态步态规划方法。首先建立欠驱动双足机器人的混杂动力学模型,然后采用时不变步态规划策略对机器人步态进行规划,并研究周期步态的收敛条件。步态参数直接决定周期步态的稳定性,采用遗传算法,以能耗最优为目标,以限制条件为约束对步态参数进行选择和优化。最后通过虚拟样机对机器人的行走过程进行动力学仿真。实验表明规划步态收敛于稳定的极限环,实现了高速动态步行,该规划方法是可行的。     

本期摘要

舵机控制步行机器人系统设计 首先设计了两足步行机器人的本体结构,并选择舵机作为驱动源。然后．基于广义坐标对该机器人进行了运动学建模,该方法运算简便直观易懂。重点讨论了动态步行的算法设计,详细分析了基于零力矩点的仿人机器人动态步行运动规划方法。结合机器人的几何约束和运动约束．推导机器人参数化步态设计的推导公式,机器人步态的参数化设计大大方便了机器人的运动学和动力学分析。     

采用DDPG的双足机器人自学习步态规划方法

为解决多自由度双足机器人步行控制中高维非线性规划难题,挖掘不确定环境下双足机器人自主运动潜力,提出了一种改进的基于深度确定性策略梯度算法（DDPG）的双足机器人步态规划方案。把双足机器人多关节自由度控制问题转化为非线性函数的多目标优化求解问题,采用DDPG算法来求解。为解决全局逼近网络求解过程收敛慢的问题,采用径向基（RBF）神经网络进行非线性函数值的计算,并采用梯度下降算法更新神经网络权值,采用SumTree来筛选优质样本。通过ROS、Gazebo、Tensorflow的联合仿真平台对双足机器人进行了模拟学习训练。经数据仿真验证,改进后的DDPG算法平均达到最大累积奖励的时间提前了45.7%,成功率也提升了8.9%,且经训练后的关节姿态角度具有更好的平滑度。     

一种类人机器人步行鲁棒控制器

提出了一种应用于类人步行机器人研究平台的鲁棒控制算法,当机器人在步行过程中受到一定程度的 外界冲力等干扰时,它可以使机器人自主达到动态平衡,而且该算法具有一定的实时性．通过一个九连杆的仿人平 面机械系统,分析了机器人步行的动态过程;应用科氏力向量等建立起机器人步行的动力学模型,通过非线性补偿, 得出其渐近稳定控制的约束性条件;进而构造出理想的李亚普诺夫函数,并应用遗传算法进行参数优化,设计出具 备一定实时性能的鲁棒控制算法;仿真计算出机器人各个关节的角位移误差,其零力矩点（ZMP）始终在支撑脚的 范围内,重心轨迹在地面的投影基本位于正弦曲线上．将该算法应用于实际的类人步行机器人行走控制中,实验证 明,在受到一定程度的外扰影响时,该机器人可在短执行周期内自主达到动态平衡．     

智能决策改进的四足机器人ZMP爬行步态算法

提出了一种基于反馈控制和贪婪决策的四足机器人爬行步态规划算法。该算法利用机载惯性传感器IMU（Inertial Measurement Unit）来实时计算零力矩点和姿态角,以稳态裕度为指标在支撑平面内实时规划期望零力矩点（Zero Moment Point,ZMP）轨迹,结合非线性反馈控制器实现对机体ZMP点的连续平滑调节,保证机器人在按给定速度矢量进行连续爬行的同时具有抵抗一定外力扰动的能力。步态规划采用动态步态周期,基于机器人结构约束和贪婪决策实现跨腿的自动触发,提高了步态自适应性。最终通过样机行走实验验证了所提算法应用于微型四足机器人中的可行性,机器人实现了在平坦地面上稳定地全向行走和旋转,所提算法同时兼顾了自适应性和稳定裕度。     

Explicit output-feedback nonlinear predictive control based on black-box models

Nonlinear model predictive control (NMPC) algorithms are based on various nonlinear models. A number of on-line optimization approaches for output-feedback NMPC based on various black-box models can be found in the literature. However, NMPC involving on-line optimization is computationally very demanding. On the other hand, an explicit solution to the NMPC problem would allow efficient on-line computations as well as verifiability of the implementation. This paper applies an approximate multi-parametric nonlinear programming approach to explicitly solve output-feedback NMPC problems for constrained nonlinear systems described by black-box models. In particular, neural network models are used and the optimal regulation problem is considered. A dual-mode control strategy is employed in order to achieve an offset-free closed-loop response in the presence of bounded disturbances and/or model errors. The approach is applied to design an explicit NMPC for regulation of a pH maintaining system. The verification of the NMPC controller performance is based on simulation experiments.     

The advanced-step NMPC controller: Optimality, stability and robustness

Widespread application of dynamic optimization with fast optimization solvers leads to increased consideration of first-principles models for nonlinear model predictive control (NMPC). However, significant barriers to this optimization-based control strategy are feedback delays and consequent loss of performance and stability due to on-line computation. To overcome these barriers, recently proposed NMPC controllers based on nonlinear programming (NLP) sensitivity have reduced on-line computational costs and can lead to significantly improved performance. In this study, we extend this concept through a simple reformulation of the NMPC problem and propose the advanced-step NMPC controller. The main result of this extension is that the proposed controller enjoys the same nominal stability properties of the conventional NMPC controller without computational delay. In addition, we establish further robustness properties in a straightforward manner through input-to-state stability concepts. A case study example is presented to demonstrate the concepts.     

A formulation of nonlinear model predictive control using automatic differentiation

An efficient algorithm is developed to alleviate the computational burden associated with nonlinear model predictive control (NMPC). The new algorithm extends an existing algorithm for solutions of dynamic sensitivity from autonomous to non-autonomous differential equations using the Taylor series and automatic differentiation (AD). A formulation is then presented to recast the NMPC problem as a standard nonlinear programming problem by using the Taylor series and AD. The efficiency of the new algorithm is compared with other approaches via an evaporation case study. The comparison shows that the new algorithm can reduce computational time by two orders of magnitude.     

Adaptive horizon economic nonlinear model predictive control

In this paper, we present a computationally efficient economic NMPC formulation, where we propose to adaptively update the length of the prediction horizon in order to reduce the problem size. This is based on approximating an infinite horizon economic NMPC problem with a finite horizon optimal control problem with terminal region of attraction to the optimal equilibrium point. Using the nonlinear programming (NLP) sensitivity calculations, the minimum length of the prediction horizon required to reach this terminal region is determined. We show that the proposed adaptive horizon economic NMPC (AH-ENMPC) has comparable performance to standard economic NMPC (ENMPC). We also show that the proposed adaptive horizon economic NMPC framework is nominally stable. Two benchmark examples demonstrate that the proposed adaptive horizon economic NMPC provides similar performance as the standard economic NMPC with significantly less computation time.     

Development of a Complete Dynamic Model of a Planar Five-Link Biped and Sliding Mode Control of Its Locomotion During the Double Support Phase

This paper presents a complete dynamic model of a planar five-link biped walking on level ground. The single support phase (SSP), double support phase (DSP) and double impact occurring at the heel strike are included in the model. By modifying the conventional definition of certain physical parameters of the biped system, it is shown that the procedure of the derivation of the dynamic equations and their final forms are significantly simplified. For motion regulation during the DSP, our dynamic model is formulated as the motion of biped system under holonomic constraints, and the hip position and the trunk orientation are selected as the independent generalized coordinates to describe the constraint system and to eliminate the constraint forces from the equations of motion. Based on the presented dynamic formulation, we develop a sliding mode controller for motion regulation during the DSP where the biped is treated as a redundant manipulator. The stability and the robustness of the controller are investigated, and its effectiveness is demonstrated by computer simulations. To the best of our knowledge, it is the first time that a sliding mode controller is developed for biped walking during the DSP. This work makes it possible to provide robust sliding mode control to a full range of biped walking and to yield dexterity and versatility for performing specific gait patterns.     

基于SQP/GA混合优化算法的双容水箱非线性预测控制

为了计算控制序列，非线性模型预测控制可以转换为一个带约束的非线性优化过程．本文分析了三种约束处理方案，根据遗传算法的特点，将等式约束用于状态量计算，在搜索空间降维的同时消除遗传算法难以求解的等式约束．对双容水箱进行遗传算法和序列二次规划仿真试验和实际控制，结果表明遗传算法对控制量的优化效果优于序列二次规划．为克服遗传算法耗时较长、优化结果存在随机抖动的缺点，结合序列二次规划提出一种混合优化算法，仿真和实控结果表明其可行性和有效性．     

基于信赖域二次规划的非线性模型预测控制优化算法

针对非线性预测控制如何在有限时域内有效的求解非凸非线性规划这一关键问题, 本文采用序列二次规划方法, 将非线性规划转化为一系列二次子规划求解. 首先根据非线性规划联立方法将系统状态和控制量同时作为优化变量, 得到以控制量步长为优化变量, 只包含不等式约束的子二次规划问题, 并用它取代原SQP子规划, 减小了子问题的规模; 随后采用基于信赖域二次规划的方法求解子规划问题, 保证每次迭代的可行性; 同时采用一种能够保持SQP问题Hessian矩阵稀疏结构的更新方法, 也在一定程度上降低了算法的复杂程度.最后的仿真结果表明了该方法的有效性.     

Theoretical analysis of unconstrained nonlinear model predictive control

Model predictive control (MPC) is a well-established controller design strategy for linear process models. Because many chemical and biological processes exhibit significant nonlinear behaviour, several MPC techniques based on nonlinear process models have recently been proposed. The most significant difference between these techniques is the computational approach used to solve the nonlinear model predictive control (NMPC) optimization problem. Consequently, analysis of NMPC techniques is often connected to the computational approach employed. In this paper, a theoretical analysis of unconstrained NMPC is presented that is independent of the computational approach. A nonlinear discrete-time, state-space model is used to predict the effects of future inputs on future process outputs. It is shown that model inverse, pole-placement, and steady-state controllers can be obtained by suitable selection of the control and prediction horizons. Moreover, the NMPC optimization problem can be modified to yield nonlinear internal model control (NIMC). The computational requirements of NIMC are considerably less than NMPC, but the NIMC approach is currently restricted to nonlinear models with well-defined and stable inverses. The NIMC controller is shown to provide superior servo and regulatory performance to a linear IMC controller for a continuous stirred tank reactor.     

Advanced-multi-step nonlinear model predictive control

Nonlinear model predictive control (NMPC) has gained widespread attention due to its ability to handle variable bounds and deal with multi-input, multi-output systems. However, it is susceptible to computational delay, especially when the solution time of the nonlinear programming (NLP) problem exceeds the sampling time. In this paper we propose a fast NMPC method based on NLP sensitivity, called advanced-multi-step NMPC (amsNMPC). Two variants of this method are developed, the parallel approach and the serial approach. For the amsNMPC method, NLP problems are solved in background multiple sampling times in advance, and manipulated variables are updated on-line when the actual states are available. We present case studies about a continuous stirred tank reactor (CSTR) and a distillation column to show the performance of amsNMPC. Nominal stability properties are also analyzed.