轨迹

With the objective of the robot′s steady movement, the trajectory is sampled equably and each segment is considered as uniformly variable motion. To guarantee tracking precision, the relation between the tracking control error and the output torque of the controller is analyzed from the point of engineering.

而按照通常的规划算法所规划出的"最优"参考轨迹在实际中却难以应用，因为这一参考轨迹是基于机器人的精确动力学模型得到的，没有考虑实际系统中存在的模型不确定性，也未考虑控制器的动态特性，因而跟踪精度得不到保证。

There is a holding angle at the vertex of hexagon.

当参考电压矢量位于过调制模式Ⅰ时，其轨迹位于六边形内部的部分仍保持为圆形，其幅值略大于参考电压矢量的模值，以补偿空间矢量在六边形边上的电压损失；在六边形之外的圆形轨迹变为六边形的边沿，此区域内，电压空间矢量的幅值扭曲，相位连续。

This paper starts with the locus of barycentre, separates portrait and landscape of biped walking|chair robot by restrict z|coordinates of barycentre, and plan the gait based on the locus of barycentre, finally calculate the torque of joints of the supported leg with a simplified model to evaluate the correctness and rationality of gait planning.

从重心的轨迹入手，通过约束重心z向坐标实现载人两足步行机器人纵向与横向的分离，进而以重心的轨迹为基础，确定了机器人行走姿态，并通过简化模型计算支撑脚关节扭矩来评估步态规划的正确性与合理性。

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

Aimed at 9-degree of freedom hyper-redundant module robot in intra-vehicular robot system, attention is given to the avoiding joint limits as an optimal mark. Two different iterative algorithms considering fault-tolerance for trajectory planning of redundant robot in Cartesian space are then proposed by using the method of differential locomotion. The first algorithm is for linear-path in which the pose of manipulator can be changed, the second is for circular-path in the plane decided by three noncollinear arbitrary points in the space. Experiments on the specimen robot platform are performed to validate the above algorithms.

以太空舱内机器人系统9-自由度超冗余模块机器人为研究对象，以避关节极限作为优化指标，考虑容错性能，利用微分运动的方法，分别提出了适于计算机迭代计算的冗余机器人在笛卡儿空间进行手爪姿态可变时的直线轨迹优化算法和手爪经过空间中任意不共线3点决定的平面内的圆弧轨迹优化算法。

The trancings of condylar movement of Angle class two division one subdivision malocclusion with mandibular retrusion during mandibular movement are smooth and continual curve. There are no differences with condylar movement distances, condylar inclination and the hinge axis rotation between right and left condyle. There are no variance to movement form of the hinge axis comparing with normal occlusion. But the overlapping gender of condylar movement trace decrease than normal occlusion.

在不同的下颌运动中，双侧髁突在矢状面和水平面的运动轨迹均为光滑连续的弧形曲线，髁突位移、矢状面髁突倾斜度、水平面髁突倾斜度及铰链轴旋转度左右两侧无明显差异，铰链轴运动形态与正常牙合无明显差异，但轨迹的重复性低于正常牙合。2。

During open/close movement, the distance of condylar movement is smaller than normal occlusion(P.05). During protrusion/retrusion movement, protrusion extent increase,the distance of condylar movement is bigger than normal occlusion(P.05). During lateral excursion, the trace in sagittal plane of the non-working side condyle is more incline than protrusion movement trace and the distance of the left non-working side condylar movement is larger than the right. During mediotrusion/right movement, the left biggest space distance is larger than normal occlusion and the transversal condylar inclination is smallar than normal occlusion when the distance of condylar movement is 5mm, the difference is statistically significant.

在开闭口运动时，双侧髁突运动幅度减小、位移量小于正常牙合者(P.05)；前伸后退运动时，前伸幅度增加，位移量大于正常牙合者(P.05)；侧方运动时，非工作侧髁突在矢状面上的轨迹较前伸轨迹向前下方倾斜度增加，非工作侧髁突空间位移左侧大于右侧，向右侧方运动中，左侧髁突空间位移大于正常牙合者，髁突位移5mm时水平面髁突倾斜度小于正常牙合者，差异有统计学意义。

It can also be used to monitor the downhole steeling tool and control the trajectory to approach the target and hit it.

可实时监控井下导向工具，控制井眼轨迹按设计的轨迹逼近靶区并中靶。

But using one's indifferent heart to dig an uncrossable river for the one who loves you

世界上最远的距离，不是星星之间的轨迹，而是纵然轨迹交会，却在转瞬间无处寻觅

In addition, because the trajectory error of the end effector is increasing when the joints are motivated by untuned joint signals, a tuning method of joints is proposed to reduce the trajectory error. The effectiveness of this method is proved in the experiment.

另外，为解决实验中发现的机器人末端轨迹误差较大的问题，根据实验特点设计了机器人关节角输入补偿策略，提高了实验中机器人末端轨迹的跟踪精度。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。