CN115552486A - 用于表征物体姿态检测和测量系统的系统和方法 - Google Patents

用于表征物体姿态检测和测量系统的系统和方法 Download PDF

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CN115552486A
CN115552486A CN202080098846.7A CN202080098846A CN115552486A CN 115552486 A CN115552486 A CN 115552486A CN 202080098846 A CN202080098846 A CN 202080098846A CN 115552486 A CN115552486 A CN 115552486A
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A.卡尔拉
A.卡当比
K.文卡塔拉曼
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Abstract

一种用于表征姿态估计系统的方法，包括：从姿态估计系统接收第一场景中的物体的排列的第一姿态；从该姿态估计系统接收第二场景中的物体的排列的第二姿态，该第二场景是该第一场景的物体的排列相对于该姿态估计系统的刚性变换；计算该第一场景和第二场景之间的粗略场景变换；匹配该第一姿态和第二姿态之间的对应的姿态；基于粗略场景变换、该第一姿态和第二姿态，计算该第一场景和第二场景之间的精细化的场景变换；基于精细化的场景变换来变换该第一姿态，以计算变换的第一姿态；以及基于该变换的第一姿态和第二姿态之间的差异来计算该姿态估计系统的平均旋转误差和平均平移误差。

Description

用于表征物体姿态检测和测量系统的系统和方法
相关申请的交叉引用
本申请要求2020年1月29日在美国专利商标局提交的美国临时专利申请第62/967,487号的优先权和权益，其全部公开内容通过引用结合于此。
技术领域
本公开的实施例的各方面涉及传感器领域，尤其是用于表征物体姿态测量系统的准确度和精度的系统和方法。
背景技术
在许多自动化领域，如机器人，传感器用于确定现实世界中物体的物理关系。例如，机器人系统经常使用感测系统来测量各种物理物体的位置，以例如抓取可能从各种定向到达的物体，将物体重新定向到期望的位置，并将物体连接到另一个物体。物体相对于参考坐标系的位置和定向可以被称为“姿态”，并且在三维坐标系中，通常包括六个自由度——围绕三个轴的旋转和沿着三个轴的平移。
发明内容
本公开的实施例的各方面涉及用于表征物体姿态测量系统的准确度和精度的系统和方法。
根据本公开的一个实施例，一种用于表征姿态估计系统的方法，包括：由包括处理器和存储器的表征系统从姿态估计系统接收第一场景中的物体的排列的第一多个姿态；由表征系统从姿态估计系统接收第二场景中的物体的排列的第二多个姿态，第二场景是第一场景的物体的排列相对于姿态估计系统的刚性变换；由表征系统计算第一场景和第二场景之间的粗略场景变换；由表征系统匹配第一多个姿态和第二多个姿态之间的对应的姿态；由表征系统基于粗略场景变换、第一姿态和第二姿态来计算第一场景和第二场景之间的精细化的场景变换；由表征系统基于精细化的场景变换来变换第一多个姿态，以计算多个变换的第一姿态；以及基于变换的第一姿态和第二多个姿态之间的差异来计算姿态估计系统的平均旋转误差和平均平移误差。
物体的排列相对于姿态估计系统的刚性变换可以包括：物体的排列的旋转。
物体的排列可以在支撑平台上，并且表征系统可以被配置为控制支撑平台相对于姿态估计系统刚性地变换物体的排列。
与物体的排列相邻的基准可以在第一场景中成像，随物体的排列刚性变换，并在第二场景中成像，并且可以基于计算在第一场景中成像的基准的第一姿态和在第二场景中成像的基准的第二姿态来计算第一场景和第二场景之间的粗略场景变换。
第一多个姿态和第二多个姿态之间的对应的姿态的匹配可以通过以下步骤来执行：根据粗略场景变换来变换第一多个姿态，以计算多个粗略变换的第一姿态；并且对于第一粗略变换的第一姿态中的每个粗略变换的第一姿态：识别第二姿态中最接近粗略变换的第一姿态的第二姿态；以及当粗略变换的第一姿态和最接近粗略变换的第一姿态的第二姿态之间的距离小于假阳性阈值距离时，确定变换的第一姿态和最接近粗略变换的第一姿态的第二姿态匹配。
第一多个姿态和第二多个姿态之间的对应的姿态的匹配可以通过以下步骤来执行：根据粗略场景变换来变换第一多个姿态，以计算多个粗略变换的第一姿态；并且对于第一粗略变换的第一姿态的每个粗略变换的第一姿态：识别第二姿态中最接近粗略变换的第一姿态的第二姿态；识别对应于粗略变换的第一姿态和第二姿态的物体的类型；将物体类型的第一3-D模型定位在粗略变换的第一姿态；将物体类型的第二3-D模型定位在粗略变换的第二姿态；以及当定位的第一3-D模型和定位的第二3-D模型之间的交集满足假阳性阈值交集时，确定粗略变换的第一姿态和最接近粗略变换的第一姿态的第二姿态匹配。
计算精细化的场景变换可以包括：基于粗略场景变换来初始化当前场景变换；计算由当前场景变换变换的多个第一姿态；以及根据降低基于第二姿态和由当前场景变换变换的第一姿态之间的差异计算得到的成本函数来更新当前场景变换。
可以基于变换的第一姿态和第二多个姿态的旋转分量之间的差异之间的旋转误差之和来计算平均旋转误差，并且可以基于变换的第一姿态和第二多个姿态的平移分量之间的差异之间的平移误差之和来计算平均平移误差。
可以根据以下公式来计算平均旋转误差Rerr：
Figure BDA0003854186150000031
以及
其中，可以根据以下公式来计算平均平移误差Terr：
Figure BDA0003854186150000032
其中，
Figure BDA0003854186150000033
是第一姿态的第i个姿态，
Figure BDA0003854186150000034
是第二姿态的第i个姿态，
Figure BDA0003854186150000035
是从第一场景S1到第二场景S2的精细化的场景变换，并且n是第一姿态的数量和第二姿态的数量。
根据本公开的一个实施例，一种用于表征姿态估计系统的系统包括：处理器；以及存储指令的存储器，当由处理器执行时，该指令使得处理器：从姿态估计系统接收第一场景中的物体的排列的第一多个姿态；从姿态估计系统接收第二场景中的物体的排列的第二多个姿态，第二场景是第一场景的物体的排列相对于姿态估计系统的刚性变换；计算第一场景和第二场景之间的粗略场景变换；匹配第一多个姿态和第二多个姿态之间的对应的姿态；基于粗略场景变换、第一姿态和第二姿态，计算第一场景和第二场景之间的精细化的场景变换；基于精细化的场景变换变换第一多个姿态，以计算多个变换的第一姿态；以及基于变换的第一姿态和第二多个姿态之间的差异来计算姿态估计系统的平均旋转误差和平均平移误差。
物体的排列相对于姿态估计系统的刚性变换可以包括物体的排列的旋转。
该系统还可以包括支撑平台，并且存储器还可以存储指令，当由处理器执行时，该指令使得处理器控制支撑平台将物体的排列相对于姿态估计系统从第一场景刚性变换到第二场景。
与物体的排列相邻的基准可以在第一场景中成像，随物体的排列刚性变换，并在第二场景中成像，并且可以基于计算在第一场景中成像的基准的第一姿态和在第二场景中成像的基准的第二姿态来计算第一场景和第二场景之间的粗略场景变换。
该存储器还可以存储指令，当由处理器执行时，该指令使得处理器通过以下步骤来匹配第一多个姿态和第二多个姿态之间的对应的姿态：根据粗略场景变换来变换第一多个姿态，以计算多个变换的第一姿态；并且对于第一变换的第一姿态中的每个变换的第一姿态：识别第二姿态中最接近变换的第一姿态的第二姿态；以及当变换的第一姿态和最接近变换的第一姿态的第二姿态之间的距离小于假阳性阈值距离时，确定变换的第一姿态和最接近变换的第一姿态的第二姿态匹配。
该存储器还可以存储指令，当由处理器执行时，该指令使得处理器通过以下步骤来匹配第一多个姿态和第二多个姿态之间的对应的姿态：根据粗略场景变换来变换第一多个姿态，以计算多个变换的第一姿态；并且对于第一变换的第一姿态中的每个变换的第一姿态：识别第二姿态中最接近变换的第一姿态的第二姿态；识别对应于变换的第一姿态和第二姿态的物体的类型；将物体类型的第一3-D模型定位在变换的第一姿态；将物体类型的第二3-D模型定位在第二姿态；以及当定位的第一3-D模型和定位的第二3-D模型之间的交集满足假阳性阈值交集时，确定变换的第一姿态和最接近变换的第一姿态的第二姿态匹配。
该存储器还可以存储指令，当由处理器执行时，该指令使得处理器通过以下步骤来计算精细化的场景变换：基于粗略场景变换来初始化当前场景变换；计算由当前场景变换变换的多个第一姿态；以及根据降低基于第二姿态和由当前场景变换变换的第一姿态之间的差异计算得到的成本函数来更新当前场景变换。
该存储器还可以存储指令，当由处理器执行时，该指令使得处理器：基于变换的第一姿态和第二多个姿态的旋转分量之间的差异之间的旋转误差之和来计算平均旋转误差，以及基于变换的第一姿态和第二多个姿态的平移分量之间的差异之间的平移误差之和来计算平均平移误差。
可以根据以下公式计算平均旋转误差Rerr：
Figure BDA0003854186150000041
以及
可以根据以下公式计算平均平移误差Terr：
Figure BDA0003854186150000042
其中
Figure BDA0003854186150000043
是第一姿态的第i个姿态，
Figure BDA0003854186150000044
是第二姿态的第i个姿态，
Figure BDA0003854186150000045
是从第一场景S1到第二场景S2的精细化的场景变换，并且n是第一姿态的数量和第二姿态的数量。
附图说明
附图与说明书一起示出了本发明的示例性实施例，并且与说明书一起用于解释本发明的原理。
图1是描绘根据本公开的一个实施例的用于表征姿态估计系统的表征系统的示意图；
图2是根据本公开的一个实施例的用于表征姿态估计系统的方法的流程图；
图3是第一场景中的物体的排列相对于姿态估计系统的刚性变换(rigidtransform)以形成相对于姿态估计系统的第二场景的示意图，包括第一场景S1中的排列中的物体的估计的姿态
Figure BDA0003854186150000051
和第二场景S2中的排列中的物体的估计的姿态
Figure BDA0003854186150000052
的描绘；
图4是根据本公开的一个实施例、根据粗略场景变换Tcoarse来计算第二场景S2中的变换的第二姿态
Figure BDA0003854186150000053
Figure BDA0003854186150000054
Figure BDA0003854186150000055
的第一姿态
Figure BDA0003854186150000056
的变换的示意图；
图5是根据本公开的一个实施例的将粗略变换的第一姿态
Figure BDA0003854186150000057
叠加到第二姿态
Figure BDA0003854186150000058
上的示意图；以及
图6是根据本公开的一个实施例的示意性描绘，其中第一姿态
Figure BDA0003854186150000059
由精细化的场景变换
Figure BDA00038541861500000510
来变换，以产生比粗略变换的第一姿态
Figure BDA00038541861500000511
更接近它们的对应的姿态
Figure BDA00038541861500000512
的变换的第一姿态
Figure BDA00038541861500000513
具体实施方式
在下面的详细描述中，通过说明的方式，仅示出和描述了本发明的某些示例性实施例。如本领域技术人员将认识到的，本发明可以以许多不同的形式实施，并且不应被解释为限于这里阐述的实施例。
姿态估计通常是指用于估计或预测物体的位置和定向的计算机视觉技术。一些形式的姿态估计是指检测人体的物理姿态，例如人的头、臂、腿和关节的位置和定向。姿态估计也可以更一般地指场景中各种有生命或无生命的物理物体的位置和定向。例如，自主导航机器人可以保持关于其周围物体的物理姿态的信息，以避免碰撞并预测其他移动物体的轨迹。作为另一个示例，对于用于生产制造的机器人，机器人可以使用姿态估计来检测组件的位置和定向，使得机器人臂可以从正确的角度接近组件，以适当地夹持组件，从而与制造的产品的其他组件组装在一起(例如，夹持螺钉的头部并将螺钉拧入孔中，而通过尖端夹持螺钉会使其难以插入孔中)。
有多种用于执行姿态估计的技术，包括捕获关于场景的深度信息的三维(3-D)扫描仪。例如，可以通过使用立体视觉系统(例如，基于来自立体的深度)捕获图像来执行姿态估计，立体视觉系统可以是主动的(具有主动光发射器，其可以发射光图案或结构光)。作为另一个示例，飞行时间的感测可以用于基于光的发射和其反射的检测之间的时间来测量场景中的表面的深度。例如使用卷积神经的实例分割的其他计算机视觉技术也可以用于将各个物体彼此分开，并且可以执行进一步的计算机视觉分析来确定物体相对于彼此的姿态。这些不同的姿态估计技术可以表现出关于例如准确度、精度、延迟、功耗等的不同折衷。
姿态估计的一些应用可能需要比其他应用更高的精度，因此基于那些任务的设计约束，不同的姿态估计的方法可能更适合于不同的任务。
通常，表征系统的误差率包括计算系统的输出与已知真值或实际值(“基本事实”)之间的差，并合计这些差，例如通过计算平均绝对误差(MAE)、均方误差(MSE)或均方根误差(RMSE)。
然而，通常难以获得用于表征姿态估计系统的姿态的基本事实集合，至少因为很少有用于测量物体姿态的技术。主要有三个主要原因。首先，用于准确估计姿态的方法限于非常高的分辨率的点云，随后是应用迭代最近点算法来对准点云的一些版本。这些方法成本高，并且不能保证获得高质量基本事实所需的准确度。第二，姿态必须总是相对于特定的坐标空间，为了比较两个姿态，它们必须在同一个坐标空间。以无错误的方式获得变换是很重要的。例如，如果坐标空间之间的变换精确到100微米，而应用规范要求准确度达到40微米，则无法使用估计的变换以40微米的更高精度进行测量。第三，例如小物体和透明物体(例如，由玻璃或透明塑料制成)的某些物体在光学上给成像造成了困难，并且比较性的3-D扫描或感测系统不能获得这些物体类型的高分辨率密集点云。
因此，本公开的实施例的各方面涉及用于表征姿态估计系统的系统和方法，例如表征由姿态估计系统以高精度计算得到的姿态中的旋转误差和平移误差。例如，本公开的一些实施例能够以30微米和0.3度的分辨率表征姿态估计系统中的姿态误差。在类似条件下运行的比较性系统通常限于300微米或更多的准确度。
图1是描绘根据本公开的一个实施例的用于表征姿态估计系统的表征系统的示意图。如图1所示，姿态估计系统10(或姿态估计器)被排列成使得其视场12捕获物体22的排列20。在图1所示的实施例中，姿态估计器10位于支撑平台40上方(例如，沿着重力定向与物体22间隔开)，但是本公开的实施例不限于此——例如，姿态估计器可以被排列成具有物体22的向下角度的视图。
在一些实施例中，基准30(或标记)，例如ChArUco板(例如，交替的黑色和白色正方形的棋盘图案，在每个白色正方形中具有ArUco基准标记，其中ArUco标记例如在Garrido-Jurado,Sergio,et al."Automatic generation and detection of highly reliablefiducial markers under occlusion."Pattern Recognition 47.6(2014):2280-2292中有所描述。物体22和基准30的排列20可以放置在可移动的支撑平台40(例如可旋转的转盘)上。
支撑平台40被配置为相对于姿态估计器10执行物体22连同基准30的排列20的物理刚性变换，同时保持物体22相对于彼此和基准30的相对位置和定向基本固定。例如，在使用转盘作为可移动支撑平台40的情况下，刚性变换可以是围绕垂直轴(例如，与重力对准的轴)的旋转(如箭头所示)。
根据本公开的各种实施例的表征系统100被配置为表征姿态估计器10的性能，例如预测或计算由姿态估计器10计算的物体22的估计的姿态中的平均姿态误差(例如，旋转误差和平移误差)。
更详细地，姿态估计器10被配置为估计在其视场12内检测到的物体的姿态。在图1所示的实施例中，物体22被抽象地描绘为简单的三维实体，例如球体、直角棱镜和圆柱体。然而，本公开的实施例不限于此，并且姿态估计器的表征可以使用任何任意物体来执行，对于该任意物体，可以清楚地定义相对于相机的姿态。
具体而言，“姿态”是指物体相对于参考坐标系的位置和定向。例如，参考坐标系可以被定义为以姿态估计系统10为原点，其中沿着姿态估计系统10的光轴的定向(例如，通过其视场12的中心的定向)被定义为坐标系的z轴，并且x轴和y轴被定义为彼此垂直并且垂直于z轴。(本公开的实施例不限于该特定坐标系，并且本领域普通技术人员将理解，姿态可以在不同坐标系之间变换。)
每个物体22还可以与其自己的对应的坐标系相关联，该坐标系是相对于其特定形状来定义的。例如，具有不同长度的边的矩形棱柱可以具有定义的规范坐标系，其中x轴平行于其最短定向，z轴平行于其最长定向，y轴正交于x轴和z轴，并且原点位于物体22的质心。
通常，在三维坐标系中，物体22具有六个自由度——围绕三个轴的旋转(例如，围绕x轴、y轴和z轴的旋转)和沿着三个轴的平移(例如，沿着x轴、y轴和z轴的平移)。为了清楚起见，这里不再详细讨论物体22的对称性，但是可以例如通过识别相对于不同对称性的多个可能的姿态(例如，在选择直角棱柱的z轴的正对负定向的情况下)，或者通过忽略姿态的一些旋转分量(例如，正圆柱体围绕其轴旋转对称)来解决。
在一些实施例中，假设表示物体的排列20中的每种物体22的类型的规范或理想版本的三维(3-D)模型或计算机辅助设计(CAD)模型是可用的。例如，在本公开的一些实施例中，物体22是从一个组件到下一个组件具有基本一致外观的制造出来的组件的单独实例。这种制造出来的组件的示例包括螺钉、螺栓、螺母、连接器和弹簧，以及特殊组件，例如电子电路组件(例如，封装的集成电路、发光二极管、开关、电阻器等)、实验室用品(例如，试管、PCR管、瓶子、帽、盖子、移液管吸头、样品板等)，以及制造出来的部件(例如，手柄、开关帽、灯泡等)。因此，在这些情况下，定义排列20中任何特定物体22的理想或规范形状的CAD模型可以用于定义物体的坐标系(例如，在CAD模型的表示中使用的坐标系)。
基于参考坐标系(或相机空间，例如，相对于姿态估计系统定义的)和物体坐标系(或物体空间，例如，相对于物体之一定义的)，物体的姿态可以被认为是从物体空间到相机空间的刚性变换(旋转和平移)。物体1在相机空间1中的姿态可以表示为
Figure BDA0003854186150000081
并且从物体1空间到相机空间的变换可以由以下矩阵表示：
Figure BDA0003854186150000082
其中旋转子矩阵R：
Figure BDA0003854186150000091
表示沿三个轴从物体空间到相机空间的旋转，以及平移子矩阵T：
Figure BDA0003854186150000092
表示沿三个轴从物体空间到相机空间的平移。
如果两个物体——物体A和物体B——在相同的相机C坐标框架中，则符号PCA用于指示物体A相对于相机C的姿态，并且PCB用于指示物体B相对于相机C的姿态。为了方便起见，这里假设基于参考坐标系来表示物体的姿态，因此物体A和B相对于相机空间C的姿态可以分别表示为PA和PB。
如果物体A和物体B实际上是相同的物体，但是在不同的姿态估计测量期间被执行，并且残差姿态(residual pose)Perr或PAB(PAB＝Perr)被用于指示从姿态PA到姿态PB的变换，则下面的关系应该成立：
PAPerr＝PB (1)
因此
Figure BDA0003854186150000093
理想地，假设物体在姿态估计PA和PB的测量之间没有相对于姿态估计器10移动(例如，平移或旋转)，则PA和PB应该是相同的，并且Perr应该是单位矩阵(例如，指示姿态之间没有误差)：
Figure BDA0003854186150000094
类似地，如果物体经历了已知的刚性变换T，并且在将估计的姿态变换回原始场景之后，姿态PB表示估计的姿态P′B(PB＝P′BT)，或者可替换地，如果在将变换T应用于估计的姿态以将其变换到新场景之后，姿态PA表示估计的姿态(PA＝P′AT)，则上式将成立。
基于姿态估计器10计算的估计值而计算得到的实际测量值Perr和单位矩阵之间的差值可以被认为是误差：
Rerr＝||R(Perr)|| (3)
Terr＝||T(Perr)|| (4)
其中Rerr是旋转误差，Terr是平移误差。函数R()将Perr变换成轴角，其中幅度是旋转差，并且函数T()提取姿态矩阵的平移分量。
旋转矩阵R的轴角表示由以下公式给出：
Tr(R)＝1+2cosθ (5)
Figure BDA0003854186150000101
其中Tr()表示矩阵迹(矩阵的对角元素之和)，θ表示旋转角度。
因此，本公开的实施例的一些方面涉及应用上述姿态比较框架来表征姿态估计系统10。
图2是根据本公开的一个实施例的用于表征姿态估计系统的方法的流程图。在本公开的一些实施例中，使用表征系统100来执行根据本公开的实施例的方法，该表征系统100可以包括计算设备(例如，膝上型计算机、台式计算机、嵌入式系统等)，该计算设备包括处理器和存储器(例如，动态随机存取存储器和大容量存储设备)，其中存储器存储指令，该指令将计算设备配置为通过在处理器上执行指令来执行专用操作，用于执行姿态估计器10的表征。在一些实施例中，由表征系统100计算的输出用于生成关于姿态估计器10的性能的报告，可以用于向姿态估计器10提供反馈(例如，以校准姿态估计器10)，和/或可以作为输入提供给其他过程，例如用于记录姿态估计器10关于特定测试的性能。
参考图2，在操作210中，表征系统100接收第一场景S1的排列20中的物体22的第一多个姿态。这些姿态可以表示为第一场景S1中的
Figure BDA0003854186150000102
姿态估计器10可以基于其特定的内部技术来计算物体22的第一姿态，这超出了本公开的范围。计算姿态估计的方法的一个示例是使用来自立体的深度(depth-from-stereo)从多个角度捕获场景的图像，并使用块匹配和视差测量来计算场景中各种表面的深度，应用实例分割来将场景分割成各种物体的单独实例(例如，将一个形状与另一个形状分开)，并通过将场景中检测到的每个实例与对应的物体类型的规范三维模型配准(register)来执行物体的每个实例的姿态估计(例如，确定质心的位置和物体相对于参考坐标系的旋转)(例如，将已知形状和大小的圆柱体实例配准到圆柱体的规范三维模型，例如通过应用迭代最近点，参见例如Arun,Somani；Thomas S.Huang；Steven D.Blostein(1987)."Least-square fitting oftwo 3-D point sets".IEEE Pattern Analysis and Machine Intelligence)。
因此，姿态估计器10估计第一场景S1的排列20中的各个物体22之一的第一多个姿态。例如，多个姿态可以被表示为矩阵的集合(例如，阵列)，该矩阵的集合表示各个物体从它们的规范物体空间到相机空间的旋转和平移。姿态还可以包括关于物体的分类的信息(例如，在图1所示的示例中，每个姿态是否对应于球体、矩形棱柱或圆柱体的姿态)。在一些情况下，姿态估计器10能够仅计算排列20中的物体22的子集的姿态，例如仅计算基本上没有被其他物体遮挡的顶层物体的姿态(例如，其中物体的表面没有被其他物体遮挡)。
在操作220中，物体22的排列20被刚性变换以形成基于第一场景S1的第二场景S2。更详细地，相对于姿态估计器10，将刚性变换应用于作为整体的排列20保持了物体22相对于彼此的物理关系(例如，不改变物体22之间的物理距离或物体相对于彼此的定向)，但是改变了排列和姿态估计器10的物理关系。
如图1所示，物体22的排列20位于支撑平台40上，该支撑平台40被配置为执行物体22的排列20的刚性变换，而不干扰排列20(例如，基本上不改变物体相对于彼此的物理关系)。在一些实施例中，表征系统100被配置为通过指定刚性变换的形式(例如，排列20的平移和/或旋转)来控制支撑平台40。例如，支撑平台40可以包括一个或多个马达(例如，步进马达)或其他电控致动器，用于旋转和/或平移位于支撑平台40上的物体。
在某些情况下，通过以保持物体22在姿态估计系统10的视野12中的排列20的方式旋转和/或平移姿态估计系统10来形成第二场景在功能上可能是等效的。
图3是相对于姿态估计系统对第一场景S1中的物体的排列进行刚性变换以形成相对于姿态估计系统的第二场景S2的示意图。特别地，在图3所示的实施例中，物体22的排列20位于转盘上，排列20的质心位于旋转轴上。图3的左侧描绘了第一场景S1，而图3的右侧描绘了通过控制转盘顺时针旋转60度，从而刚性地将排列20旋转60度而形成的第二场景S2。
虽然图1和图3描绘了支撑平台40是围绕排列20的质心旋转物体22的排列20的转盘的实施例，但是本公开的实施例不限于此，并且还可以包括支撑平台40执行排列20的旋转和平移的情况，例如通过放置物体22的排列20使得其质心不与转盘的旋转轴对准，或者通过使用能够执行平移的支撑平台40。
在操作230中，表征系统100接收第二场景S2的排列20中的物体22的第二多个姿态，其中物体22的第二多个姿态由与第二场景S2中的第一多个姿态相同的姿态估计系统10来计算。第二多个姿态可以表示为
Figure BDA0003854186150000121
为了讨论的目的，假设第一姿态
Figure BDA0003854186150000122
和第二姿态
Figure BDA0003854186150000123
都包括相同的n个物体的姿态n。然而，本公开的实施例不限于此，下面将描述用于解决失配的技术。
给定第一场景S1中物体的第一多个估计的姿态
Figure BDA0003854186150000124
和第二场景S2中相同物体的第二组多个估计的姿态
Figure BDA0003854186150000125
然后可以比较这些姿态以测量姿态估计器10的误差特性。然而，与刚性变换
Figure BDA0003854186150000126
(例如，由支撑平台40应用的)相关联的精确值是未知的，从而使得难以比较第一多个姿态与第二多个姿态的相对值。因此，本公开的实施例的各方面涉及计算刚性变换
Figure BDA0003854186150000127
的估计。
在操作240中，表征系统100计算第一场景S1和第二场景S2之间的粗略场景变换Tcoarse。在本公开的一些实施例中，独特的标记或基准30被包括在物体22的排列20中，并且均出现在第一场景S1和第二场景S2中，其中基准30与物体22的排列20一起被刚性变换，使得基准30和物体22之间的物理关系通过变换得以保持，从而使得基准30能够为计算粗略场景变换Tcoarse提供参考。在图1和图3所示的实施例中，ChArUco板被用作基准30，并被放置在物体22的排列20旁边。通常，ChArUco板是棋盘图案，四个角上有黑色或深色方块，白色方块上有ArUco标记(或其他标记)。ChArUco板中的每个ArUco标记都有不同的图案，其编码不同的标识符。因此，计算机视觉系统可以基于ChArUco板内各个ArUco标记的位置和排列来检测ChArUco板在图像中的姿态。通过分别应用刚性变换之前和之后的ChArUco板的图像计算ChArUco板的姿态
Figure BDA0003854186150000128
和
Figure BDA0003854186150000129
根据本公开的一些实施例的表征系统100计算从第一场景S1到第二场景2的粗略场景变换Tcoarse。
Figure BDA00038541861500001210
在本公开的一些实施例中，其他类型的基准30被放置在场景中并用于计算粗略场景变换，例如ArUco标记的网格(例如，没有棋盘)、增强现实标签(ARTag)、AprilTag、一个或多个尺子、一个或多个量角器等。
在本公开的各种其他实施例中，可以使用其他技术来计算粗略的场景变换。例如，在本公开的实施例中，其中可以高精度控制支撑平台40，可以基于由支撑平台40应用的已知变换来计算粗略场景变换。作为另一示例，可以基于将点姿态视为点云(例如，仅考虑位置)并配准或对准点云(例如，通过应用迭代最近点算法)来计算粗略场景变换。作为另一个示例，可以使用图形匹配方法来匹配这两个姿态。姿态估计器10根据从姿态集合S1中的每个组件到姿态集合S2中的每个其他组件来计算3-D连通图。然后，姿态估计器使用它自己和它最近的邻居(例如，它的五个最近的邻居)之间的相对变换(R和T)来计算S1中的每个元素和S2中的每个元素的特征向量。然后，这些相对变换被用于计算S1和S2之间的对应关系(例如，在S1和S2中找到与其最近邻居具有相似相对变换的姿态)。在找到姿态和姿态之间的对应关系之后，姿态估计器10使用例如随机样本一致性(RANSAC)来计算一个或多个3-D刚体变换估计值，其中内点(inlier)被定义为小于阈值距离(例如，3mm)的对应关系。具有最多内点的估计的刚体变换可以被用作Tcoarse。
在操作250中，表征系统100将第一场景S1中的物体的第一姿态
Figure BDA0003854186150000131
中的对应的姿态与第二场景S2中的相同物体的第二多个估计的姿态
Figure BDA0003854186150000132
进行匹配。图3是第一场景中的物体的排列相对于姿态估计系统的刚性变换以形成相对于姿态估计系统的第二场景的示意图，包括对第一场景S1中的该排列中的物体的估计的姿态
Figure BDA0003854186150000133
和第二场景S2中的该排列中的物体的估计的姿态
Figure BDA0003854186150000134
的描绘。图3描绘了从第一场景S1中的物体22中的一些到第二场景S2中的对应的物体22的虚线箭头(例如，匹配不同场景中相同物体的不同视图)。在图3所示的排列中，由姿态估计系统10为第一场景S1计算的第一估计的姿态
Figure BDA0003854186150000135
被描绘为具有斜条纹阴影的三角形，并且第二估计的姿态
Figure BDA0003854186150000136
被描绘为具有点阴影的三角形，其中三角形的中心与它们相应物体的估计质心对准，并且三角形的旋转角度指示(在页面的二维约束中)对应的物体的估计旋转姿态。
在本公开的一些实施例中，表征系统100基于贪心搜索执行第一场景S1中的物体的
Figure BDA0003854186150000137
中的第一姿态与第二场景S2中的相同物体的第二多个估计的姿态
Figure BDA0003854186150000141
之间的匹配。在这样的实施例中，基于粗略场景变换Tcoarse，变换由第一场景S1中可见物体的姿态
Figure BDA0003854186150000142
所表示的可见物体的质心，并且与第二场景S2中的第二姿态
Figure BDA0003854186150000143
相匹配。图4是根据本公开的一个实施例、根据粗略场景变换Tcoarse来变换第一姿态
Figure BDA0003854186150000144
从而计算第二场景S2中粗略变换的第一姿态
Figure BDA0003854186150000145
的示意图：
Figure BDA0003854186150000146
图5是根据本公开的一个实施例的将粗略变换的第一姿态
Figure BDA0003854186150000147
叠加到第二姿态
Figure BDA0003854186150000148
上的示意图。在图5所示的示例中，粗略变换的第一姿态
Figure BDA0003854186150000149
在位置上接近对应的第二姿态之一
Figure BDA00038541861500001410
例如，对于每个粗略变换的第一姿态
Figure BDA00038541861500001411
基于位置找到最接近的第二姿态
Figure BDA00038541861500001412
其中贪心搜索搜索第一姿态与第二姿态的不同配对，以最小化总误差(例如，粗略变换的第一姿态和第二姿态之间的位置差之和)。更详细地，在一些实施例中，姿态估计器10构建大小为NxM的成本矩阵，其中场景1(S1)中的姿态数是i..N并且场景2(S2)中的姿态数是j..M，并且其中成本矩阵的每个元素是每个姿态之间的质心差。然后姿态估计器10执行线性和分配以确定最佳匹配。
在本公开的一些实施例中，表征系统100基于二分图问题中的最大匹配来执行第一场景S1中的物体的
Figure BDA00038541861500001413
中的第一姿态与第二场景S2中的相同物体的第二多个估计的姿态
Figure BDA00038541861500001414
之间的匹配，其中边缘将使用粗略场景变换Tcoarse变换到第二场景S2的第一场景S1中的估计的姿态
Figure BDA00038541861500001415
与从第二场景S2中的第二姿态
Figure BDA00038541861500001416
中选择的可匹配的估计的姿态相连接。如果得到的匹配包括连接第一场景S1中的物体的姿态和第二场景S2中的对应的姿态的边缘，则认为估计的姿态是正确匹配的。
在本公开的一些实施例中，可能存在姿态的不匹配。例如，姿态估计系统10可以估计第一场景S1中不同数量的物体相对于第二场景S2的姿态，或者估计不同物体的姿态(例如，第一场景S1中的五个物体A、B、C、D和E以及第二场景S2中的五个物体A、B、D、E和F)。这些差异可能是由于例如姿态估计系统10中的噪声或不稳定性或者姿态估计系统10的性能不对称。
在本公开的一些实施例中，不是使用贪心搜索来执行姿态的匹配，而是应用假阳性阈值方法来将粗略变换的第一姿态
Figure BDA0003854186150000151
与第二姿态
Figure BDA0003854186150000152
进行匹配。更详细地，对于粗略变换的第一姿态
Figure BDA0003854186150000153
中的每个姿态
Figure BDA0003854186150000154
表征系统100识别第二姿态
Figure BDA0003854186150000155
的最接近的姿态
Figure BDA0003854186150000156
如果第二姿态
Figure BDA0003854186150000157
中最接近的姿态
Figure BDA0003854186150000158
距离粗略变换的第一姿态
Figure BDA0003854186150000159
的当前姿态
Figure BDA00038541861500001510
小于假阳性阈值距离(例如，3毫米)(例如，其中姿态位于对应的物体的质心处)，则该最接近的第二姿态
Figure BDA00038541861500001511
被视为匹配或对应的姿态。如果最接近的第二姿态
Figure BDA00038541861500001512
大于假阳性阈值距离，则这些姿态被视为异常值，并且出于改进变换的目的，在匹配姿态中不作计数。在本公开的另一个实施例中，代替比较质心的距离，根据对应于物体的CAD模型计算的姿态被放置和定向CAD模型，然后两个CAD模型(对于粗略变换的第一姿态
Figure BDA00038541861500001513
和最接近的第二姿态
Figure BDA00038541861500001514
)的交集的体积除以CAD模型中的单个CAD模型的体积(或者根据交集/并集度量除以两个CAD模型的并集的体积)。在姿态得到完美测量的情况下，商是1，而在CAD模型根本不对准的情况下，商是0。因此，在一些实施例中，可以基于交集度量(例如，单个实例上的交集或并集上的交集)来设置假阳性阈值，其中超过假阳性阈值交集的交集度量(例如，其中交集度量是大于0.80的值)被确定为满足用于确定粗略变换的第一姿态
Figure BDA00038541861500001515
和最接近的第二姿态
Figure BDA00038541861500001516
匹配的阈值。
在执行匹配之后，假设第一姿态
Figure BDA00038541861500001517
和第二姿态
Figure BDA00038541861500001518
分别指代第一场景S1和第二场景S2中的同一物体i。
在操作260中，从粗略场景变换Tcoarse(例如，初始设置Tcurrent＝Tcoarse)开始，表征系统100计算从第一场景S1到第二场景S2的精细化的场景变换
Figure BDA00038541861500001519
其中当前刚性变换Tcurrent的精细化是基于改进变换的第一姿态与其对应的匹配第二姿态的对准，如在操作250中所计算的。更详细地，本公开的实施例的一些方面涉及通过最小化所有匹配姿态
Figure BDA00038541861500001520
的以下成本函数来细化变换：
Figure BDA00038541861500001521
其中xj是预定义的一组点(例如[0,0,1]、[0,1,0]和[1,0,0])，尽管本公开的实施例不限于此)。如果点被设置为[0,0,0]，则该函数相当于3-D刚体变换。
例如，返回参考图5，变换的第一姿态
Figure BDA00038541861500001522
的位置和定向接近第二姿态
Figure BDA00038541861500001523
但是不与第二姿态精确对准。这些姿态的位置差异在上述成本函数(8)中由差：
Figure BDA0003854186150000161
来表示。
在本公开的一些实施例中，细化过程是迭代操作(例如通过应用梯度下降)以更新当前刚性变换Tcurrent，直到成本函数达到最小化(例如，直到满足阈值条件，例如达到设定的迭代次数或者从一次迭代到下一次迭代的改进小于阈值)，此时输出更新的值Tcurrent作为细化的场景变换
Figure BDA0003854186150000162
因此，在操作260中，表征系统100通过最小化成本函数(例如，在第一场景S1和第二场景S2中捕获的物体的姿态之间的误差或差异)来计算精细化的场景变换
Figure BDA0003854186150000163
图6是根据本公开的一个实施例的示意图，其中通过精细化的场景变换
Figure BDA0003854186150000164
来变换第一姿态
Figure BDA0003854186150000165
以产生比粗略变换的第一姿态
Figure BDA0003854186150000166
更接近其对应的姿态
Figure BDA0003854186150000167
的变换的第一姿态(或精细化变换的第一姿态)
Figure BDA0003854186150000168
然而，注意，尽管精细化的场景变换
Figure BDA0003854186150000169
使第一姿态更接近第二姿态
Figure BDA00038541861500001610
但姿态的位置和定向仍存在一些差异。这些剩余差异表示姿态估计系统10的姿态误差，包括平移和旋转误差。
在操作270中，表征系统100基于精细化的场景变换
Figure BDA00038541861500001611
和计算得到的第一和第二姿态来表征姿态估计系统100。具体而言，在最小化上述成本函数以计算最小化如第一场景S1和第二场景S2中所描绘的物体22的排列20的姿态估计之间的差异的精细化的场景变换之后，估计的姿态中的任何剩余差异被假设为由姿态估计系统100引起的误差或不准确性的结果(例如，基于应用于物体的排列的物理刚性变换没有引起物体的相对位置的任何偏移的假设)。更正式地，可以根据等式(1)和(2)来计算误差，其中精细化的场景变换
Figure BDA00038541861500001612
表示应用于从第一场景S1的第一姿态
Figure BDA00038541861500001613
到从第二场景S2的第二姿态
Figure BDA00038541861500001614
的刚性变换：
Figure BDA00038541861500001615
Figure BDA00038541861500001616
这样，遵循等式(3)和(4)的方法，表征姿态估计系统10的误差的旋转误差Rerr和平移误差Terr可以被计算为：
Figure BDA00038541861500001617
Figure BDA00038541861500001618
其中，如上所述，函数R()将其自变量变换成轴角，其中幅度是旋转差，并且函数T()从其自变量中提取姿态矩阵的平移分量。具体而言：
Figure BDA0003854186150000171
Figure BDA0003854186150000172
在图6所示的示例中，姿态配对
Figure BDA0003854186150000173
和
Figure BDA0003854186150000174
展示出更大的旋转误差Rerr，而姿态配对
Figure BDA0003854186150000175
和
Figure BDA0003854186150000176
展示出更大的平移误差Terr。
该过程可以在多对场景(例如，不同物体的多种不同排列，其中排列被刚性变换以产生场景对)上重复，以计算特定姿态估计系统的各种姿态误差测量值的方差、最大值和期望值。然后，这些值使得不同姿态估计系统的性能能够相互比较。
在根据本公开的实施例的方法的一些实验中，姿态表征系统被用于准确地预测由姿态估计器产生的姿态误差，其精度为平移误差Terr小于等于30微米，旋转误差Rerr小于或等于0.3度。这使得能够评估这样的姿态估计系统是否能够执行特定的高精度设计约束，例如在大约1米的距离处小于200微米的平移误差和小于1度的旋转误差的期望精度，否则姿态估计系统的误差表征的这种高精度测量值可能不可能实现或者实现起来很昂贵。
这样，本公开的实施例的各方面提供了用于以高精度水平表征姿态估计系统的性能(例如，准确度和精度)的系统和方法，而不依赖于基本事实的外部源。
虽然已经结合某些示例性实施例描述了本发明，但是应当理解，本发明不限于所公开的实施例，而是相反，旨在涵盖包括在所附权利要求及其等同物的精神和范围内的各种修改和等同排列。

Claims (18)

1.一种用于表征姿态估计系统的方法，包括：
由包括处理器和存储器的表征系统从姿态估计系统接收第一场景中的物体的排列的第一多个姿态；
由所述表征系统从所述姿态估计系统接收第二场景中的物体的排列的第二多个姿态，所述第二场景是所述第一场景的物体的排列相对于所述姿态估计系统的刚性变换；
由所述表征系统计算所述第一场景和所述第二场景之间的粗略场景变换；
由所述表征系统匹配所述第一多个姿态和所述第二多个姿态之间的对应的姿态；
由所述表征系统基于粗略场景变换、所述第一姿态和所述第二姿态来计算所述第一场景和所述第二场景之间的精细化的场景变换；
由所述表征系统基于所述精细化的场景变换来变换所述第一多个姿态，以计算多个变换的第一姿态；以及
基于所述变换的第一姿态和所述第二多个姿态之间的差异来计算所述姿态估计系统的平均旋转误差和平均平移误差。
2.根据权利要求1所述的方法，其中，所述物体的排列相对于所述姿态估计系统的刚性变换包括：所述物体的排列的旋转。
3.根据权利要求1所述的方法，其中，所述物体的排列在支撑平台上；以及
其中所述表征系统被配置为控制所述支撑平台以相对于所述姿态估计系统刚性地变换所述物体的排列。
4.根据权利要求1所述的方法，其中，与所述物体的排列相邻的基准在所述第一场景中成像，随所述物体的排列刚性变换，并在所述第二场景中成像；以及
其中，基于计算在所述第一场景中成像的基准的第一姿态和在所述第二场景中成像的基准的第二姿态来计算所述第一场景和所述第二场景之间的粗略场景变换。
5.根据权利要求1所述的方法，其中，匹配所述第一多个姿态和所述第二多个姿态之间的对应的姿态通过以下步骤来执行：
根据所述粗略场景变换来变换所述第一多个姿态，以计算多个粗略变换的第一姿态；以及
对于所述第一粗略变换的第一姿态中的每个粗略变换的第一姿态：
识别所述第二姿态中最接近所述粗略变换的第一姿态的第二姿态；以及
当所述粗略变换的第一姿态和最接近所述粗略变换的第一姿态的第二姿态之间的距离小于假阳性阈值距离时，确定所述变换的第一姿态和最接近所述粗略变换的第一姿态的第二姿态匹配。
6.根据权利要求1所述的方法，其中，匹配所述第一多个姿态和所述第二多个姿态之间的对应的姿态通过以下步骤来执行：
根据所述粗略场景变换来变换所述第一多个姿态，以计算多个粗略变换的第一姿态；以及
对于所述第一粗略变换的第一姿态中的每个粗略变换的第一姿态：
识别所述第二姿态中最接近所述粗略变换的第一姿态的第二姿态；
识别对应于所述粗略变换的第一姿态和所述第二姿态的物体的类型；
将所述物体的类型的第一3-D模型定位在所述粗略变换的第一姿态；
将所述物体的类型的第二3-D模型定位在所述第二姿态；以及
当定位的第一3-D模型和定位的第二3-D模型之间的交集满足假阳性阈值交集时，确定所述粗略变换的第一姿态和最接近所述粗略变换的第一姿态的第二姿态匹配。
7.根据权利要求1所述的方法，其中计算所述精细化的场景变换包括：
基于所述粗略场景变换来初始化当前场景变换；
计算由所述当前场景变换变换的多个第一姿态；以及
根据降低基于所述第二姿态和由所述当前场景变换变换的第一姿态之间的差异而计算得到的成本函数来更新所述当前场景变换。
8.根据权利要求1所述的方法，其中，所述平均旋转误差基于所述变换的第一姿态和第二多个姿态的旋转分量之间的差异之间的旋转误差之和来计算；以及
其中，所述平均平移误差基于所述变换的第一姿态和所述第二多个姿态的平移分量之间的差异之间的平移误差之和来计算。
9.根据权利要求8所述的方法，其中根据以下公式计算所述平均旋转误差Rerr：
Figure FDA0003854186140000031
以及
其中根据以下公式计算所述平均平移误差Terr：
Figure FDA0003854186140000032
其中，
Figure FDA0003854186140000033
是所述第一姿态的第i个姿态，
Figure FDA0003854186140000034
是所述第二姿态的第i个姿态，
Figure FDA0003854186140000035
是从所述第一场景S1到所述第二场景S2的精细化的场景变换，并且n是所述第一姿态的数量和所述第二姿态的数量。
10.一种用于表征姿态估计系统的系统，包括：
处理器；以及
存储指令的存储器，当由所述处理器执行时，所述指令使所述处理器：
从姿态估计系统接收第一场景中的物体的排列的第一多个姿态；
从所述姿态估计系统接收第二场景中的物体的排列的第二多个姿态，所述第二场景是所述第一场景的物体的排列相对于所述姿态估计系统的刚性变换；
计算所述第一场景和所述第二场景之间的粗略场景变换；
匹配所述第一多个姿态和所述第二多个姿态之间的对应的姿态；
基于粗略场景变换、所述第一姿态和所述第二姿态来计算所述第一场景和所述第二场景之间的精细化的场景变换；
基于所述精细化的场景变换来变换所述第一多个姿态，以计算多个变换的第一姿态；以及
基于所述变换的第一姿态和所述第二多个姿态之间的差异来计算所述姿态估计系统的平均旋转误差和平均平移误差。
11.根据权利要求10所述的系统，其中，所述物体的排列相对于所述姿态估计系统的刚性变换包括所述物体的排列的旋转。
12.根据权利要求10所述的系统，还包括支撑平台；并且
其中，所述存储器还存储指令，当由所述处理器执行时，所述指令使得所述处理器控制所述支撑平台将物体的排列相对于所述姿态估计系统从所述第一场景刚性变换到所述第二场景。
13.根据权利要求10所述的系统，其中，与所述物体的排列相邻的基准在所述第一场景中成像，随所述物体的排列刚性变换，并在所述第二场景中成像；以及
其中，基于计算在所述第一场景中成像的基准的第一姿态和在所述第二场景中成像的基准的第二姿态来计算所述第一场景和所述第二场景之间的粗略场景变换。
14.根据权利要求10所述的系统，其中，所述存储器还存储指令，当由所述处理器执行时，所述指令使所述处理器通过以下方式匹配所述第一多个姿态和第二多个姿态之间的对应的姿态：
根据所述粗略场景变换来变换所述第一多个姿态，以计算多个变换的第一姿态；以及
对于所述第一变换的第一姿态中的每个变换的第一姿态：
识别所述第二姿态中最接近变换的第一姿态的第二姿态；以及
当所述变换的第一姿态和最接近所述变换的第一姿态的第二姿态之间的距离小于假阳性阈值距离时，确定所述变换的第一姿态和最接近所述变换的第一姿态的第二姿态匹配。
15.根据权利要求10所述的系统，其中，所述存储器还存储指令，当由所述处理器执行时，所述指令使所述处理器通过以下方式匹配所述第一多个姿态和第二多个姿态之间的对应的姿态：
根据所述粗略场景变换来变换所述第一多个姿态，以计算多个变换的第一姿态；以及
对于所述第一变换的第一姿态中的每个变换的第一姿态：
识别所述第二姿态中最接近所述变换的第一姿态的第二姿态；
识别对应于所述变换的第一姿态和所述第二姿态的物体的类型；
将所述物体的类型的第一3-D模型定位在所述变换的第一姿态；
将所述物体的类型的第二3-D模型定位在所述第二姿态；以及
当定位的第一3-D模型和定位的第二3-D模型之间的交集满足假阳性阈值交集时，确定所述变换的第一姿态和最接近所述变换的第一姿态的第二姿态匹配。
16.根据权利要求10所述的系统，其中，所述存储器还存储指令，当由所述处理器执行时，所述指令使得所述处理器通过以下步骤来计算所述精细化的场景变换：
基于所述粗略场景变换来初始化当前场景变换；
计算由所述当前场景变换变换的多个第一姿态；以及
根据降低基于所述第二姿态和由所述当前场景变换变换的第一姿态之间的差异而计算得到的成本函数来更新所述当前场景变换。
17.根据权利要求10所述的系统，其中，所述存储器还存储指令，当由所述处理器执行时，所述指令使所述处理器：
基于所述变换的第一姿态和第二多个姿态的旋转分量之间的差异之间的旋转误差之和来计算所述平均旋转误差；以及
基于所述变换的第一姿态和第二多个姿态的平移分量之间的差异之间的平移误差之和来计算所述平均平移误差。
18.根据权利要求17所述的系统，其中根据以下公式计算所述平均旋转误差Rerr：
Figure FDA0003854186140000051
以及
其中，根据以下公式计算所述平均平移误差Terr：
Figure FDA0003854186140000052
其中，
Figure FDA0003854186140000053
是所述第一姿态的第i个姿态，
Figure FDA0003854186140000054
是所述第二姿态的第i个姿态，
Figure FDA0003854186140000055
是从所述第一场景S1到所述第二场景S2的精细化的场景变换，并且n是第一姿态的数量和第二姿态的数量。
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