This paper presents an omnidirectional aerial manipulation platform for robust and responsive interaction with unstructured environments, toward the goal of contact-based inspection. The fully actuated tilt-rotor aerial system is equipped with a rigidly mounted end-effector, and is able to exert a 6 degree of freedom force and torque, decoupling the system’s translational and rotational dynamics, and enabling precise interaction with the environment while maintaining stability.
本文提出了一种全向空中操纵平台，用于与非结构化环境进行稳健和响应式交互，以实现基于接触的检查的目标。 全驱动倾转旋翼系统配备刚性安装的末端执行器，能够施加 6 个自由度的力和扭矩，将系统的平移和旋转动力学解耦，在保持稳定性的同时实现与环境的精确交互 .
An impedance controller with selective apparent inertia is formulated to permit compliance in certain degrees of freedom while achieving precise trajectory tracking and disturbance rejection in others
具有选择性表观惯性的阻抗控制器被制定为允许在某些自由度上服从，同时在其他自由度中实现精确的轨迹跟踪和干扰抑制
Experiments demonstrate disturbance rejection, pushand-slide interaction, and on-board state estimation with depth servoing to interact with local surfaces. The system is also validated as a tool for contact-based non-destructive testing of concrete infrastructure
实验展示了干扰抑制、推-滑交互以及通过深度伺服与局部表面交互的机载状态估计。 该系统还被验证为基于接触的混凝土基础设施无损检测工具
The demand for aerial robotic workers for a wide range of applications has been steadily gaining the attention of research communities, industry, and the general public [14]. As a compelling example, the status of aging concrete infrastructure is a growing concern due to the rising amount of required inspection, and a lack in capacity to meet the need by traditional means [3]. New technologies using non-destructive testing (NDT) contact sensors, such as potential mapping [2], permit detection of corrosion far earlier than visual assessment. While aerial vehicles have already been embraced as a solution for efficient visual inspection of infrastructure [7], contactbased NDT still requires extensive human labor, road closure, and the use of large supporting inspection equipment.
对空中机器人工人的需求已经稳步获得研究界、行业和公众[14]的关注。作为一个令人信服的例子，由于所需的检查数量不断增加，以及缺乏通过传统手段[3]来满足需求的能力，老化的混凝土基础设施的状况日益受到关注。使用无损检测(NDT)接触传感器的新技术，如潜在的映射[2]，允许比视觉评估更早地检测腐蚀。虽然飞行器已经被视为基础设施[7]的高效视觉检查的解决方案，但基于接触的NDT仍然需要大量的人工劳动、道路封闭和使用大型辅助检查设备。
Recent developments in omnidirectional aerial vehicles begin to bridge the gap, from using unmanned aerial vehicles (UAVs) as efficient visual industrial inspection agents, to interacting with the structures they inspect. The ability of omnidirectional aerial systems to exert a 6 degrees of freedom (DoF) force and torque allows for decoupling of the system’s translational and rotational dynamics, enabling precise interaction with the environment while maintaining stability. However, making this solution a viable alternative to traditional inspection requires the design of an aerial system with on-board power and sensing, high force and torque capabilities in all directions, and precise and reliable interaction control in 6 DoF.
全向飞行器的最新发展开始弥合这一差距，从使用无人机(uav)作为高效的视觉工业检查代理，到与它们所检查的结构相互作用。全方位空中系统施加6自由度(DoF)力和扭矩的能力，允许系统的平移和旋转动力学解耦，从而在保持稳定性的同时与环境进行精确的相互作用的能力。然而，要使这种解决方案成为传统检查的可行替代方案，需要设计一个具有车载功率和传感、在各个方向的高力和扭矩能力，以及在6自由度中精确可靠的交互控制的空中系统。
We propose a novel omnidirectional aerial system: a hexarotor with actively tilting double propeller groups, resulting in high force and torque capabilities in all directions while maintaining efficient flight in horizontal hover. The configuration also permits omnidirectional orientation of the vehicle. The current work extends upon the system concept presented in [6, 9], with the addition of a rigidly attached end-effector for interaction. The simplicity of the system dynamic model as a single rigid body and the high degree of overactuation in propeller orientations allow for robust and responsive interaction and disturbance rejection. In this paper we present the system design of a fully actuated aerial manipulation platform capable of on-board computation, state estimation, power, and sensing, allowing for direct deployment in the field.
我们提出了一种新颖的全向空中系统：一个主动倾斜双螺旋桨组，能在水平悬停的同时，保持高效飞行的高力和扭矩能力。该配置还允许飞行器的全向飞行。目前的工作扩展了在[6,9]中提出的系统概念，增加了一个刚性连接的末端执行器来进行相互作用。系统动力学模型作为一个单一的刚体的简单性和在螺旋桨方向上的过驱动允许鲁棒和响应的相互作用和扰动抑制。在本文中，我们提出了一个完全驱动的空中操作平台的系统设计，能够进行机载计算、状态估计、功率和传感，允许直接部署在现场。
However, making this solution a viable alternative to traditional inspection requires the design of an aerial system with on-board power and sensing, high force and torque capabilities in all directions, and precise and reliable interaction control in 6 DoF.
然而，要使该解决方案成为传统检测的可行替代方案，需要设计一个具有机载电源和传感、全方位高力和扭矩能力以及 6 DoF中精确可靠的交互控制的航空系统。
The current work extends upon the system concept presented in [6, 9], with the addition of a rigidly attached end-effector for interaction.
目前的工作扩展了 [6, 9] 中提出的系统概念，增加了一个刚性连接的末端执行器进行交互。
In this paper we present the system design of a fully actuated aerial manipulation platform capable of on-board computation, state estimation, power, and sensing, allowing for direct deployment in the field.
在本文中，我们介绍了一个完全驱动的空中操纵平台的系统设计，该平台能够进行机载计算、状态估计、电源和传感，允许在现场直接部署。
In particular, this paper presents the following contributions:
• The system design of a novel omnidirectional tilt-rotor micro aerial vehicle (MAV) with a rigid manipulator arm.
• A 6 DoF impedance control approach with selective apparent inertia for a fully-actuated flying system.
• Experimental validations showing precise interaction control, and demonstration of the system as a viable platform for contact-based NDT of concrete infrastructure.
特别是，本文提出了以下贡献：
• 具有刚性机械臂的新型全向倾转旋翼微型飞行器（MAV）的系统设计。
• 一种用于全驱动飞行系统的具有选择性表观惯性的 6 自由度阻抗控制方法。
• 实验验证显示了精确的交互控制，并展示了该系统作为基于接触的混凝土基础设施无损检测的可行平台。
Aerial interaction has been approached extensively in literature over the past decade with various systems [14], addressing the problem of underactuation by adding DoFs in a manipulator arm, and handling the resulting dynamic complexity. While interaction control has been demonstrated on many underactuated systems equipped with manipulators [1, 15], lateral force magnitudes and disturbance rejection capabilities are limited due to coupled rotational and translational dynamics.
在过去的十年中，空中相互作用已经在广泛的文献中使用各种系统[14]，通过在机械臂中添加自由度来解决驱动不足的问题，并处理由此产生的动态复杂性。虽然相互作用控制已经在许多配备了操纵器[1,15]的欠驱动系统上得到了证明，但由于耦合的旋转和平移动力学，横向力的大小和扰动抑制能力受到了限制。
In the past few years, fully actuated aerial manipulators have emerged to address these issues. Several platforms achieve full actuation by fixedly tilting the propeller groups of a traditional MAV to generate internal forces that are optimized for interaction [17, 18, 19, 20, 11]. These platforms are limited in roll and pitch, requiring additional DoFs in a manipulator arm. Full pose-omnidirectionality has been achieved in [12] by an optimization of propeller orientations, and using a fixed end-effector for interaction. While the platform demonstrates a high down-force, lateral and upward force exertion are limited due to the internal forces needed for omnidirectionality. Recent publications have demonstrated push-and-slide interaction and disturbance rejection, as well as various industrial applications [12, 19, 20, 11]. Our approach combines omnidirectionality with high force and torque capabilities to eliminate the need for an actuated manipulator arm. This results in simplified system dynamics without compromising disturbance rejection.
在过去的几年里，完全驱动的空中操纵器已经出现来解决这些问题。几个平台通过固定倾斜传统MAV的螺旋桨组产生内力，优化相互作用[17,18,19,20,11]的全驱动。这些平台在滚动和俯仰方面都很有限，在机械臂中需要额外的自由度。在[12]中，通过优化螺旋桨方向和使用固定的端执行器进行交互，实现了完全的姿态-全向性。虽然平台显示出较高的向下力，但由于全向性所需的内力，侧向和向上力的发挥受到限制。最近的出版物已经证明了推动和滑动的相互作用和干扰抑制，以及各种工业应用[12,19,20,11]。我们的方法结合了全方位性和高力和扭矩能力，以消除对驱动机械臂的需要。这导致了简化的系统动力学，而不影响扰动抑制。
Control approaches for fully actuated systems with pushand-slide capabilities vary in implementation: One approach uses a cascaded proportional-integral-derivative (PID) controller in free flight, switching to an angular rate stabilizing control when in contact [20], another implements a dislocated proportional-derivative (PD) control law for an elastic jointed manipulator model, with integral action in all directions except along the tool’s axis of contact [19], and a further approach uses a pose trajectory tracker in SE(3) in free flight, which switches to a hybrid pose/wrench control when in contact [12]. Impedance control has been implemented on underactuatedbase aerial manipulators [10, 13], without omnidirectional force capabilities. The selective impedance control strategy presented in this paper seeks to advance this concept to address omnidirectional interaction with a single model-based controller. The proposed controller is used for all situations without reliance on transition handling, and using a planner for orientation and movement relative to the local surface normal.
对于具有推滑动能力的完全驱动系统的控制方法实现不同：一种方法在自由飞行中使用级联比例积分导数(PID)控制器，在接触[20]时切换到角速率稳定控制，另一种方法实现弹性连接机械手模型的错位比例导数(PD)控制律，除了沿着接触[19]的工具轴外的所有方向的积分作用，另一种方法在自由飞行中使用SE(3)的姿态轨迹跟踪器，在接触[12]时切换到混合姿态/扳手控制。阻抗控制已在欠驱动基地空中操纵器[10,13]上实现，没有全向力的能力。本文提出的选择性阻抗控制策略旨在推进这一概念，以解决与基于单一模型的控制器的全向交互问题。所提出的控制器用于所有情况，而不依赖于过渡处理，并使用一个相对于局部表面法线的方向和运动的规划器。
A major challenge of porting such a system from a laboratory context to the real world is the need for good state estimation close to the environment. While many of the aforementioned systems operate in controlled environments that harness the precise and reliable capabilities of motioncapture state estimation, this approach is not viable in the field. In the presented platform, an on-board visual-inertial (VI) sensor enables state estimation in complex environments. Precise position and orientation relative to the environment are achieved with a 3D time-of-flight (ToF) camera.
将这样的系统从实验室环境移植到现实世界的一个主要挑战是需要对接近环境的环境进行良好的状态估计。虽然上述许多系统在受控环境中利用运动捕获状态估计的精确和可靠能力的环境中运行，但这种方法在该领域是不可行的。在所提出的平台中，一个车载视觉惯性(VI)传感器可以在复杂的环境中进行状态估计。通过三维飞行时间(ToF)相机实现了相对于环境的精确位置和方向。
The omnidirectional platform used in this work takes the form of a traditional hexarotor with equally spaced arms about the zb-axis. Each propeller group is independently tilted (αi) by a dedicated servomotor located in the body, allowing for various rotor thrust combinations. Double rotor groups provide additional thrust for a compact system. Symmetrically placed rotors balance rotational inertia about the tilt axis to reduce effort of the tilt motors. Processing occurs on an on-board computer and flight controller. Lithium-polymer batteries are mounted to the system base for on-board power. Major system parameters are listed in table I.
在这项工作中使用的全向平台采用了传统的六轴梁的形式，围绕zb轴的臂。每个螺旋桨组由位于阀体内的专用伺服电机独立倾斜(αi)，允许各种转子推力组合。双转子组为一个紧凑的系统提供了额外的推力。对称放置的转子平衡围绕倾斜轴的转动惯性，以减少倾斜电机的努力。处理发生在机载计算机和飞行控制器上。锂-聚合物电池被安装在系统底座上，用于车载供电。主要系统参数见表一。
A manipulator arm is rigidly mounted to the platform body, with a tool frame at the tip of the arm. The zt-axis intersects the body origin, Ob, and lies on the yb-plane. The arm orientation is fully defined by an angular declination of ϕt from the negative zb axis. A ToF camera is rigidly mounted near the base of the arm, its frame orientation aligned with the tool frame. A VI sensor is oriented opposite to the tool to ensure reliable feature detection for state estimation during interaction. Table II gives an overview of the frames used throughout this work.
机械臂刚性地安装在平台主体上，在机械臂的顶端有一个工具框架。zt轴与身体原点Ob相交，位于yb平面上。臂的方向完全由ϕt从负zb轴开始的角偏角来定义。ToF相机刚性安装在手臂的底部，其框架方向与工具框架对齐。VI传感器与工具相反，以确保交互时状态估计的可靠特征检测。表二给出了在整个工作中使用的框架的概述。
This section describes the system model, selective impedance controller, external wrench estimator, and trajectory generator.
本节介绍了系统模型、选择性阻抗控制器、外部扳手估计器和轨迹发生器。
参考文献13
《Impedance control of VToL UAVs with a momentum-based external generalized forces estimator》
参考书籍16
《Robotics: modelling, planning and control》
Impedance control indirectly regulates a wrench exerted by the system on its environment, without the drawbacks of contact detection and controller switching that accompany direct force control
阻抗控制间接地调节了系统对其环境施加的扳手，而没有伴随直接力控制而来的接触检测和控制器切换的缺点
The same controller can account for interaction, as well as for stable flight in free space. We can take advantage of the system’s full actuation to implement an impedance controller with selective apparent inertia, to reject disturbances in some directions while exhibiting compliant behavior in others.
同样的控制器可以解释交互作用，以及在自由空间中的稳定飞行。我们可以利用系统的全驱动来实现一个具有选择性表观惯性的阻抗控制器，在某些方向上抑制干扰，而在其他方向上表现出顺应性行为。
We take the simplified dynamics of the system as (1) and choose the desired closed loop dynamics of the system to be
我们将简化的系统动力学视为（1），并选择所需的系统闭环动力学
where Mv, Dv, and Kv ∈ R6×6 are positive-definite matrices representing the desired apparent inertia, desired damping, and desired stiffness of the system. Position and velocity errors are represented by e x and e v ∈ R6×1 , respectively. We can then derive the applied control wrench by substituting ˙v from (4) into (1) as follows:
其中，Mv、Dv和Kv∈R6×6是正定矩阵，表示系统的期望表观惯性、期望阻尼和期望刚度。位置误差和速度误差分别用ex和ev∈R6×1表示。然后，我们可以通过将（4）中的˙v代入（1）来推导出所应用的控制扳手如下：
Since the stiffness and damping properties of interaction depend highly on the apparent inertia, we first normalize these matrices with respect to the system mass as ˜Mv = M−1Mv, then express stiffness and damping as ˜Dv = ˜M−1 v Dv and ˜Kv = ˜M−1 v Kv. In addition, the selective impedance can be rotated into a desired frame, in this case the fixed endeffector frame, using R = blockdiag{Rbt, Rbt}, where Rbt is a rotation matrix expressing the orientation of the tool frame in the body-fixed frame.
因为交互的刚度和阻尼属性高度依赖于表观惯性，我们首先规范化这些矩阵对系统质量˜Mv=M−1Mv，然后表示刚度和阻尼˜Dv=˜M−1vDv和˜Kv=˜M−1vKv。此外，选择性阻抗可以旋转到一个所需的框架，在这种情况下，固定的支架支架框架，使用R=块{Rbt，Rbt}，其中Rbt是一个旋转矩阵，表示工具框架在身体固定框架中的方向。
然后把式子5改写为
Integration of a rigidly attached end-effector to the system simplifies the problem of selective stiffness in impedance control. The apparent mass is lowered along the zt-axis. Orienting the zt-axis normal to the desired contact surface is then sufficient to ensure compliance in the contact direction and stiff behavior in the orthogonal plane, and a stiff response to error in orientation.
将刚性连接的末端执行器与系统的集成简化了阻抗控制中的选择性刚度问题。表观质量沿着zt轴降低。将zt轴垂直于所需的接触面，就足以确保在接触方向上的顺应性和在正交平面上的刚性行为，以及对方向误差的刚性响应。
For surface normal and distance estimation, the desired contact point is defined as the intersection of an observed surface and the zt-axis (Ct0 in fig. 4). In order to estimate the distance to this point and to compute the local surface normal, a point cloud is obtained from the ToF camera and all points within a certain distance to the zt-axis are selected. This subset of 3D points is subsequently called A0t . The 3D contact point location is obtained by an unweighted average of all points in A0t . The local surface normal is obtained by fitting a plane to the set of points A0t in a least-squares sense. If the resulting vector nt points away from the camera (nt · zt > 0), the direction is flipped to ensure consistency.
对于曲面法线和距离估计，所期望的接触点定义为观测曲面与zt轴的交点(图4中的Ct0)。为了估计到这一点的距离并计算局部表面法线，从ToF相机中获得一个点云，并选择与zt轴一定距离内的所有点。这个3D点的子集随后被称为A0t。三维接触点的位置是由a0t中所有点的未加权平均值得到的。局部曲面法线是通过在最小二乘意义上拟合一个平面到点a0t的集而得到的。如果得到的向量nt指向远离相机(nt·zt>0)，则翻转方向以确保一致性。
The MAV is maneuvered to a position relatively close to the surface while maintaining a level orientation. As soon as a stable normal and distance estimate are obtained, the target set point in the tool frame is calculated. The target set point is placed a certain distance behind the estimated contact point. This ensures reliable contact thanks to the impedance controller, even in the presence of small fluctuations in state or distance estimation. The target orientation of the MAV is chosen such that the zt-axis aligns with the estimated surface normal. Rotation is fully defined by requiring the body ybaxis to be aligned with the ground plane, defined by yW /xW , constraining rotation about the zt-axis. A smooth trajectory is generated such that the tool is driven to the estimated target pose.
MAV被操纵到一个相对接近表面的位置，同时保持一个水平方向。一旦得到稳定的法线和距离估计，就计算出工具架中的目标设定点。目标设定点与估计接触点后面一定距离。由于阻抗控制器，即使存在状态或距离估计的小波动。MAV的目标方向的选择使zt轴与估计的表面法线对齐。旋转完全定义为要求物体ybaxis与地平面对齐，由yW/xW定义，同时被zt轴的旋转所限制。生成一个平滑的轨迹，使工具被驱动到估计的目标姿态。
Translation along the surface is achieved by moving the set point tangent to the currently estimated surface in a desired direction (e.g. Ct−x in fig. 4). The set point as well as the surface estimate and generated trajectory are updated at a rate of 5 Hz. Effectively, this corresponds to a pure pursuit path tracking that always maintains contact and orientation with respect to the surface.
沿曲面的平移是通过在期望的方向上移动设定点与当前估计的曲面相切来实现的(例如，图4中的Ct−x)。设定点以及表面估计和生成的轨迹以5Hz的速率更新。实际上，这对应于一个纯粹的追踪路径跟踪，它始终保持着相对于表面的接触和方向。
Experiments are conducted using the tilt-rotor aerial manipulation platform presented in section III with characteristics shown in table I, and specific test parameters shown in table III. All diagonal values of KI for the wrench estimator are set to unity. A safety tether is connected loosely to the robot, and minimally affects results. A supplementary video1 is also available for reference.
实验采用第三节所述的倾斜-转子空中操纵平台进行，其特点见表一，具体试验参数见表三。对于扳手估计器的所有KI的对角线值都被设置为单位。一根安全绳松散地连接到机器人上，并且对结果的影响最小。还有一个补充的视频1也可供参考。
Several experiments fuse Vicon motion capture data sampled at 100 Hz with on-board inertial measurement unit (IMU) measurements sampled at 250 Hz for state estimation
有几个实验将100Hz采样的Vicon运动捕获数据与250Hz采样的车载惯性测量单元(IMU)测量数据相结合，以进行状态估计
For viability in industrial environments, however, on-board sensing is preferred. In section V-D, only on-board sensor data is processed. The VI state estimation framework Rovio [5] is used to determine position and attitude (henceforth referred to as “on-board state estimation”) in combination with a ToF camera that estimates distance and orientation w.r.t. the contact surface.
然而，为了提高在工业环境中的生存能力，机载传感是首选的。在V-D节中，只处理车载传感器数据。VI状态估计框架Rovio[5]用于确定位置和姿态（以下称为“车载状态估计”），并与估计距离和方向w.r.t.的ToF相机相结合接触面。
The experiments in this section are designed to demonstrate the following:
• System response to an external wrench with selective impedance control, demonstrating disturbance rejection (section V-B).
• Repeatable tracking of position and orientation when interacting with a planar surface, while rejecting disturbances due to surface friction (section V-C).
• Ability to interact with complex surfaces using purely on-board sensing (section V-D).
• Viability as an infrastructure NDT contact testing tool (section V-E).
本节中的实验旨在证明以下内容：
系统对具有选择性阻抗控制的外部扳手的响应，证明干扰抑制（V-B节）。
与平面相互作用时可重复跟踪位置和方向，同时抑制表面摩擦引起的干扰（第V-C节）。
使用纯机载传感与复杂表面交互的能力（V-D节）。
作为一个基础设施的NDT接触测试工具的可行性(第V-E节)。
自由飞行时的绳索拉动
In this experiment, we evaluate the behaviour of the system with different selective apparent inertia values, demonstrating the ability to reject large disturbances in certain directions. The system is commanded to hold a reference pose 1 m above the ground in free flight. A cord is tied to the tool tip of the rigid manipulator arm, which is aligned with the xb-axis. The other end of the cord is pulled manually to generate an external wrench. The test is performed indoors with external state estimation. In tests 1 through 3, with results shown in fig. 5, two pulls of the rope are made for each set of apparent inertia parameters, approximately along the negative xb-axis. In tests 4 and 5, with results shown in fig. 6, a pull force is applied horizontally perpendicular to the fixed arm axis to generate a torque about the zb-axis.
在这个实验中，我们评估了具有不同选择性表观惯性值的系统的行为，证明了在一定方向上拒绝大干扰的能力。系统在自由飞行中保持离地面1米的参考姿态。一根绳子绑在刚性机械臂的工具尖端，与xb轴对齐。手动拉紧电源线的另一端，以产生一个外部扳手。该测试在室内进行，采用外部状态估计。在测试1至3中，结果如图5所示，对每组表观惯性参数进行两次拉绳，近似沿负xb轴。在试验4和试验5中，结果如图6所示，通过垂直于固定臂轴水平施加拉力，以产生围绕zb轴的扭矩。
Tests 1 and 2 show similar results: a compliant response to a disturbance force in the direction of pull. Apparent mass values in xb and yb are lower than the actual system mass, meaning that force disturbances in these directions will be tracked in the controller, while the PD component simultaneously tracks the reference trajectory.
测试1和2显示了类似的结果：对拉动方向的扰动力的顺应响应。xb和yb中的表观质量值低于实际系统质量，这意味着控制器将跟踪这些方向上的力扰动，而PD组件同时跟踪参考轨迹。
The remaining degrees of freedom have high apparent inertia values, actively rejecting detected disturbances to track the reference trajectory. In test 3, apparent mass in xb and yb are set to 5 times the system mass and inertia. Results show positional movement of less than 0.3 m under a lateral disturbance force of 25 N, demonstrating an ability to actively reject large force disturbances.
剩余的自由度具有较高的表观惯性值，主动拒绝检测到的干扰来跟踪参考轨迹。在测试3中，xb和yb中的表观质量被设置为系统质量和惯性的5倍。结果表明，在25N的横向扰动力下，位置运动小于0.3m，具有主动抑制大力扰动的能力。
Tests 4 and 5 compare the response to a torque disturbance about the zb-axis with apparent rotational inertia less than, and greater than the system inertia. In test 4, three pulls are made, targeting rotation about the zb-axis, and rotational compliance is clearly shown in yaw in the attitude tracking plot. While some additional torques are generated around the remaining axes, these are actively rejected by the controller. In test 5, the system counteracts a rotational torque of 3 N m magnitude, reducing the yaw deviation to 0.5 rad. High apparent mass in all directions successfully rejects forces up to 8 N with a translational deviation of less than 0.1 m. These results motivate impedance parameters chosen for the remaining experiments
测试4和5比较了明显转动惯量小于和大于系统惯量的在zb轴周围的扭矩扰动的响应。在测试4中，进行三次拉，围绕zb轴旋转，姿态跟踪图偏航中清晰地显示旋转顺应性。虽然围绕剩余的轴产生一些额外的力矩，但这些力矩会被控制器主动拒绝。在测试5中，系统抵消了3Nm量级的旋转扭矩，将偏航偏差降低到0.5rad。所有方向的高表观质量成功地拒绝了高达8N的力，平移偏差小于0.1m。这些结果激发了为其余实验所选择的阻抗参数
In this experiment, we evaluate the ability of the system to maintain a normal orientation to a whiteboard, rejecting disturbances from friction forces when interacting, as well as the ability to accurately and repeatably draw a defined pattern on the surface
在这个实验中，我们评估了系统保持对白板的正常方向的能力，在相互作用时拒绝来自摩擦力的干扰，以及在表面上准确和重复地绘制一个确定的图案的能力
The whiteboard is positioned in a known location, and a trajectory traces a drawing with the tool point 10 cm behind the surface of the whiteboard. The end-effector is equipped with a standard whiteboard marker, with no additional compliance. Apparent mass is set high in all directions, except for the zt-axis, where it is set to be compliant. Refer to table III for apparent impedance parameters. The experiment uses external state estimation, and takes place in an indoor environment.
白板被放置在一个已知的位置，并且一个轨迹跟踪了一个带有工具点在白板表面后面10厘米处的图形。末端执行器配备了一个标准的白板标记器，没有额外的合规性。表观质量在所有方向上都被设置为高的，除了zt轴，其中它被设置为服从。表观阻抗参数见表三。该实验采用了外部状态估计的方法，并在室内环境中进行。
Tracking results for position and orientation in the top two plots of fig. 7 show ground truth measurements from the motion capture system of two trials drawing the same shape on a whiteboard, compared to the reference trajectory, marked with subscript sp, for set point. In the time interval between (a) and (b), the tool is in contact with the whiteboard, maintaining a consistent force while completing a trajectory.
图7前两幅图中位置和方向的跟踪结果显示了两次试验的运动捕捉系统在白板上绘制的相同形状的地面真实测量值，并与用下标sp的参考轨迹进行了比较。在(a)和(b)之间的时间间隔内，工具与白板接触，在完成轨迹时保持一致的力。
This experiment evaluates the ability to use depth servoing to maintain orientation to a local surface normal in unknown environments, using a state estimation strategy that is directly
该实验评估了在未知环境中使用深度伺服测量来保持对局部表面法线的方向的能力，直接使用了一种状态估计策略
deployable in the field. The system is manually positioned to face a start point, then autonomously approaches the structure while orienting the zt-axis to align with the locally observed surface normal (see fig. 8).
可在现场部署。系统被手动定位到面对一个起点，然后自动接近结构，同时定位zt轴与局部观察到的表面法线对齐（见图8）。
Contact is made, a line is traced, and the system leaves the structure. State estimation is achieved using on-board sensing only, and tests are performed without any prior information such as maps or structural information. The test environment is the ceiling vault of a staircase landing that is in daily use (see fig. 1). The maximum altitude of contact is approximately 4 m above the ground.
进行接触，跟踪一条线，然后系统离开结构。状态估计仅使用机载传感实现，测试没有任何先验信息，如地图或结构信息。测试环境为日常使用的楼梯平台的天花板拱顶（见图1）。最大接触高度约为距地面4米。
As visualized in fig. 9, the estimated surface normals and distances are smooth and consistent which subsequently results in a clean set point trajectory and reliable contact. At the initial contact point, the on-board state estimator drifts several centimeters. As the surface normal and distance estimates are drift-free and planning is updated frequently, our system is robust against such drifts. Overall, the tool traverses a distance of 0.53 m on the surface during contact, with an average velocity of 0.17 m s−1 .
如图9所示，估计的表面法线和距离是平滑的和一致的，从而得到了一个干净的设定点轨迹和可靠的接触。在初始接触点处，机载状态估计器会漂移几厘米。由于表面法线和距离估计是无漂移的，规划经常更新，我们的系统对这种漂移是鲁棒的。总体而言，工具在接触时上的距离为0.53m，平均速度为0.17ms−1。
The bottom plot in fig. 9 shows the set point and measured attitude of the tool frame. During the time frame shown, attitude is set based on the estimated surface normal. The change of attitude during translation along the surface only affects rotation about the yt-axis.
图9的底部图显示了工具框架的设定点和测量姿态。在所示的时间范围内，根据估计的表面法线设置姿态。沿表面平移过程中姿态的变化只影响围绕yt轴的旋转。
In this experiment, we evaluate the ability of the system to maintain the positional accuracy and force required for useful measurements with a NDT contact sensor on reinforced concrete structures. The test is performed with external state estimation.
在这个实验中，我们评估了该系统在钢筋混凝土结构上使用NDT接触传感器来保持位置精度和有用测量所需的力的能力。采用外部状态估计的方法进行了测试。
The rigid arm is equipped with a NDT contact sensor that measures both the electrical potential difference between a saturated copper sulfate electrode (CSE) and the embedded steel, and the electrical resistance between the sensor on the concrete surface and the steel reinforcement. Electrical potential and resistance results can be used as an indicator for the corrosion state of the steel [4]. A cable is connected to the reinforcement in the concrete structure, and is routed to the flying system via a physical tether to perform the measurements.
刚性臂配备有NDT接触传感器，可以测量饱和硫酸铜电极(CSE)和预埋钢之间的电位差，以及混凝土表面传感器和钢筋之间的电阻。电势和电阻结果可作为[4]钢腐蚀状态的指标。一根电缆被连接到混凝土结构中的钢筋上，并通过一根物理系绳被连接到飞行系统上，以进行测量。
The concrete specimen used for this experiment has a known corrosion spot at a certain location and a constant cover depth within the block. The corrosion state can therefore be evaluated against this information. The concrete block is positioned at a known location, and a trajectory is defined to contact 9 points at 5 cm intervals along the surface, with the contact point set 10 cm behind the surface of the wall to generate sufficient contact force for meaningful measurements.
本实验所用的混凝土试样在一定位置有一个已知的腐蚀点，在砌块内有一个恒定的覆盖深度。因此，可以根据这些信息来评估腐蚀状态。混凝土块位于已知位置，轨迹定义为沿表面每5cm间隔接触9个点，接触点设置在墙表面后10cm，以产生足够的接触力进行有意义的测量。
Tracking results in the top plot of fig. 10 show precise trajectory tracking along all translational axes, except during shaded contact regions, where the xW position is blocked by the concrete specimen. A low apparent inertia in the ztdirection allows for compliant behaviour of the system. The second plot shows forces that arise in the direction of the concrete surface, achieving a value of 1.8 N in the contact phase.
图10上图的跟踪结果显示了沿所有平移轴的精确轨迹跟踪，除了在阴影接触区域，其中xW位置被混凝土试样阻挡。在zt方向上的低表观惯性允许系统的兼容行为。第二个图显示了在混凝土表面的方向上产生的力，在接触阶段达到了1.8N的值。
A constant offset in zb-force can be seen, and is attributed to an error in the system mass and the center of mass offset estimates. Tracking results demonstrate that the controller is robust to this model error in directions with high apparent inertia.
可以看到zb力的一个恒定的偏移，这归因于系统质量和质心偏移估计的误差。跟踪结果表明，该控制器在高表观惯性方向上对该模型误差具有较强的鲁棒性。
Data collected from the NDT sensor are shown in fig. 11, where corrosion implications are deduced according to [8], and correspond with corrosion at contact points 2 and 3.
从NDT传感器收集的数据如图11所示，其中腐蚀影响根据[8]推导出来，与接触点2和3处的腐蚀相对应。
Additional tests were performed to evaluate on-board state estimation as a viable alternative to a motion capture system
进行了额外的测试来评估机载状态估计作为一个可行的替代运动捕获系统
and to determine the accuracy of estimated force measurements. On-board state estimation is used in flight, with data from a Vicon motion capture system as ground truth. Estimated force is computed using on-board state estimation as an input to the generalized momentum approach. Force ground truth data was collected from a 6-axis Rokubi 210 force sensor with its surface aligned with the zW -plane, rigidly mounted to a wall.
并确定估计的力测量的准确性。机上状态估计，以Vicon运动捕捉系统的数据作为地面真实。估计力的计算使用车载状态估计作为广义动量方法的输入。力的地面真实数据是从一个6轴的Rokubi210力传感器中收集的，其表面与zw平面对齐，刚性地安装在一面墙上。
The force sensor records measurements at 800 Hz, with a resolution of 0.1 N. The system follows a trajectory along the xW -axis which goes in and out of contact with the force sensor. Apparent mass in the direction of contact is changed between contact events.
力传感器记录800hz的测量值，分辨率为0.1n。系统沿xw轴遵循轨迹，与力传感器接触。接触方向上的表面质量在接触事件之间发生改变。
The first plot in fig. 12 compares positional on-board state estimation to ground truth, as the system tracks a trajectory along the xW -axis. At contact points (1) and (2), movement along x is blocked by the force sensor. The system remains stable under impedance control despite a set point offset of 0.6 m. Error in on-board state estimation is presented in the second plot, showing error growth when the system is in motion versus small error in quasi-static hovering.
图12中的第一个图比较了位置车载状态估计和地面真相，因为系统沿着xw轴跟踪一个轨迹。在接触点（1）和（2）处，沿着x的运动被力传感器阻塞。该系统在阻抗控制下保持稳定，尽管设定点偏移量为0.6m。第二幅图中显示了车载状态估计的误差，显示了系统运动时误差增长，而准静态悬停时误差较小。
Root mean squared error (RMSE) of all 6 positional and rotational measurements are presented in table IV. Roll and pitch errors are higher due to a bias, which we can attributed to a center of mass offset. Results show that on-board state estimation can adequately replace an external motion capture system for interactive flights of short duration.
所有6个位置和旋转测量值的均方根误差(RMSE)见表4。由于偏差，滚动和音高误差更高，我们可以将其归因于质心偏移。结果表明，机载状态估计可以充分替代短期交互式飞行的外部运动捕捉系统。
The lower plots in fig. 12 compare momentum based force estimation to ground truth. Due to high noise on the raw force sensor data, we process the signal with a 5th order Butterworth filter designed for the 800 Hz measurement frequency with a cutoff of 5 Hz.
图12中的下图比较了基于动量的力估计和地面真相。由于原始力传感器数据的高噪声，我们使用5阶巴特沃斯滤波器处理信号，设计为800赫兹测量频率，截止频率为5Hz。
. The filtered signal is plotted, as well as the raw data, which extends beyond the plot range. In general, force magnitudes match the ground truth measurements well. RMSE of the force estimate compared to filtered ground truth is shown in table IV. In the direction of contact, an error of 1.62 N is due largely to a slow response to a step force, which is influenced by the chosen KI . Further tuning of KI could improve fidelity of the estimator without causing
.绘制了滤波后的信号和原始数据。一般来说，力的大小与地面真实测量值很吻合。力估计与过滤后的地面真相的RMSE如表四所示。在接触方向上，1.62N的误差主要是由于对步进力的反应缓慢，这受到所选择的KI的影响。对KI的进一步调整可以提高估计器的保真度
Torque error was not evaluated due to the lack of a fixed connection to the sensor, and remains as future work. Experimental results have demonstrated that the system is able to interact for inspection tasks with the chosen parameters.
由于与传感器缺乏固定的连接，因此没有评估扭矩误差，这仍然是未来的工作。实验结果表明，该系统能够与所选的参数进行交互。
A practical system for high force and torque aerial contact applications has been achieved in the form of a novel tiltrotor omnidirectional aerial manipulation platform. Various experiments demonstrate the system’s ability to track full pose trajectories with interaction while rejecting disturbances using an impedance controller with selective apparent inertia. We further validate the system’s ability to act as a tool for contactbased inspection through experiments with a NDT sensor.
以一种新型倾斜器全向空中操作平台，实现了一种高力和扭矩空中接触应用的实用系统。各种实验证明，该系统能够通过交互作用跟踪全姿态轨迹，同时使用具有选择性表观惯性的阻抗控制器来抑制干扰。通过NDT传感器的实验，我们进一步验证了系统作为基于接触检查的工具的能力。
This work forms the basis needed for autonomous contact inspection of complete civil structures. Several open issues of the current system motivate future development. Wall and ground effects are not differentiated from contact forces in the momentum-based wrench estimator and may cause difficulty controlling interaction forces. Though counteracted by the impedance controller, estimation of wind disturbance could improve overall system performance. Drift in position and yaw over time of the VI state estimator prompts the additional integration of an absolute localization source, such as a global positioning system (GPS), a total station theodolite or feature-based localization. Future extensions of this work will integrate the control approach with mapping, and generate coverage trajectories for complete structural evaluation.
这项工作构成了对完整土建结构的自主接触检查所需的基础。当前系统的几个未决问题推动了未来的发展。在基于动量的扳手估计器中，墙壁和地面效应与接触力没有区别，可能导致难以控制相互作用力。通过阻抗控制器的估计可以提高系统的整体性能。VI状态估计器随时间变化的位置漂移和偏航促使了绝对定位源的额外集成，如全球定位系统(GPS)、全站经纬仪或基于特征的定位。这项工作的未来扩展将把控制方法与映射相结合，并生成进行完整的结构评估的覆盖轨迹。
