Accelerometer and Force/Torque Sensor Measurements for Parameter and State Estimation of an Unknown Robot End Effector

Introduction This dataset was created as part of a study on the development of an estimator for the contact wrench (force and torque) of an unknown robot end effector. A conference paper from this study has been submitted and accepted for the 2024 IEEE International Conference on Real-time Computing and Robotics (RCAR 2024) [1]. A force/torque sensor (FTS) was attached to the robot wrist, and the unknown end effector was attached to the FTS. An inertial measurement unit (IMU) was in turn attached to the end effector. The FTS measurement can be decomposed into the (1) sensor bias, (2) contact wrench, and the effects from (3) gravity, (4) inertia, (5) vibrations, and (6) noise. Estimation of the contact wrench requires that the remaining effects are compensated for. The FTS and IMU sensor biases, as well as mass and mass center of the unknown end effector, were estimated as described by Vougioukas [2]. His method requires FTS and IMU samples from 24 specific orientations of the sensors. See his paper for a description of this calibration method. The hardware used to generate this dataset were: KUKA LBR Med 14 serial robot (KUKA AG, Germany) ATI Gamma FTS (ATI Industrial Automation, Inc., USA) ATI Netbox (ATI Industrial Automation, Inc., USA) MPU6886 IMU (M5Stack, China) Arduino Mega 2580 with a W5500 Ethernet Shield Method The robot was used to move the end effector, FTS, and IMU such that a trajectory could be replicated with high precision and accuracy. The trajectory was a simple rotation about the FTS y-axis. This trajectory and the resulting measurements were performed three times. The sensor signals were sampled during each iteration when: The robot moved freely without any kind of disturbance (basline). The robot moved freely with gentle taps to the robot body, using a rubber hammer (vibrations). The robot moved with gentle taps to the body using the hammer, and with a manual force exerted on the end effector (vibrations and contact). The IMU signal was obtained by the Arduino Mega using I2C, and the signal was sent from the Arduino to the external PC using the ethernet shield. This setup resulted in a phase of the IMU signal by 8416 μs. This was compensated for in the offline analysis of the study on the contact wrench estimator [1]. The sensor samplig rates were different for each sensor; they were approximately 100 Hz for the robot controller (FTS orientation measurements), 700 Hz for the FTS, and 254 Hz for the IMU. The frequency for each signal can be obtained through the timestamps in the dataset. Dataset Each CSV file has a row which serves as the header, which labels the columns of each file. The following nomenclature of the column labels were used: t - Timestep in microseconds. Epoch time. fx, fy, fz - The force components as measured by the FTS. tx, ty, tz - The torque components as measured by the FTS. ax, ay, az - The acceleration components measured by the IMU. gx,gy,gz - The direction of the gravitational vector in the FTS frame. r11, r12, r13, r21, r22, r23, r31, r32, r33 - The components of the rotation matrix that represents the FTS orientation in the world frame. (R_wf) The measurements from the FTS and IMU signals from the 24 orientations (as required for the calibration method described by Vougioukas [2]), are stored in 0-calibration_fts-accel.csv. Additionally, the files 0-steady-state_wrench.csv and 0-steady-state_accel.csv contains the continuous sensor signal from the FTS and IMU, respectively, while they were at rest; these two files can be used to calculate the sensor signal variances. After calibration, each sensor signal was recorded independently and stored in a separate file from the other sensors. The raw (biased) values were stored. Each test iteration produced three files: The end effector/FTS/IMU orientation in [test_iteration]_orientation.csv The unbiased wrench as measured by the FTS in [test iteration]_wrench.csv The unbiased acceleration as measured by the IMU in [test_iteration]_accel.csv The test iteration prefix for these files are: 1-baseline, 2-vibrations, and 3-vibrations-contact, as described in the previous section "Method". To obtain the relative time between samples across the test iteration files ([]_orientation, []_wrench, and []_accel.csv), load each dataset and determine which has the earliest timestamped sample on the first row. Then, subtract this initial timestamp value from all timestamps across the files for the respective test iteration. Note that the IMU frame does not align with the FTS frame (_accel.csv vs _wrench.csv), the following table describes the rotation matrix R_fa which can be used to transform the acceleration measurements from the IMU frame {a} to the FTS frame {f}. R_fa = 0 0 -1 -1 0 0 0 1 0 References [1] A. Skrede, "A Linear Discrete Kalman Filter to Estimate the Contact Wrench of an Unknown Robot End Effector", Accepted for the 2024 IEEE International Conference on Real-time Computing and Robotics (RCAR), Ålesund, Norway, June 2024 [2] S. Vougioukas, “Bias Estimation and Gravity Compen- sation For Force-Torque Sensors,” in Recent Advances in Simulation, Computational Methods and Soft Computing. WSEAS Press, 2001, pp. 82–85.引言 本数据集为一项针对未知机器人末端执行器接触力扭（contact wrench，即力与力矩组合）估计器开发的研究而构建。该研究的会议论文已被2024年IEEE实时计算与机器人国际会议（IEEE International Conference on Real-time Computing and Robotics, RCAR 2024）接收并录用[1]。 研究中，我们将力扭矩传感器（force/torque sensor, FTS）安装于机器人腕部，未知末端执行器安装于FTS之上，惯性测量单元（inertial measurement unit, IMU）则进一步安装于末端执行器。FTS的测量值可分解为六部分：(1) 传感器偏置、(2) 接触力扭，以及(3) 重力、(4) 惯性、(5) 振动与(6) 噪声带来的影响。要估计接触力扭，需对其余各项影响进行补偿。 如Vougioukas[2]所述，我们对FTS与IMU的传感器偏置，以及未知末端执行器的质量和质心进行了估计。该方法要求获取传感器处于24个特定姿态时的FTS与IMU采样数据，关于该校准方法的细节可参阅其论文。 本数据集采集所用硬件包括：德国库卡（KUKA AG）LBR Med 14串行机器人、美国ATI工业自动化公司的ATI Gamma型FTS、ATI Netbox数据采集模块、中国M5Stack的MPU6886 IMU，以及搭载W5500以太网扩展板的Arduino Mega 2580控制器。 方法 本研究利用机器人移动末端执行器、FTS与IMU，实现轨迹的高精度复现。所采用的轨迹为绕FTS y轴的简单旋转运动，该轨迹与对应测量过程共重复三次。每次迭代过程中，我们在以下三种场景下采集传感器信号： 1. 机器人无任何干扰自由运动（基线场景）； 2. 机器人自由运动，同时使用橡胶锤轻击机器人本体（引入振动）； 3. 机器人运动时，既用橡胶锤轻击本体，同时手动对末端执行器施加外力（同时引入振动与接触力）。 IMU信号通过Arduino Mega经由I2C接口采集，并通过以太网扩展板传输至外部PC。该传输过程导致IMU信号存在8416 μs的相位偏移，该偏移已在本接触力扭估计器研究的离线分析中完成补偿[1]。 各传感器的采样率各不相同：机器人控制器（用于采集FTS姿态测量数据）约为100 Hz，FTS约为700 Hz，IMU约为254 Hz。各信号的具体频率可通过数据集中的时间戳获取。 数据集 每个CSV文件均包含一行表头，用于标注各列的含义。列标签采用如下命名规则： - t：以微秒为单位的时间步长，采用纪元时间格式； - fx, fy, fz：FTS测量得到的三个力分量； - tx, ty, tz：FTS测量得到的三个力矩分量； - ax, ay, az：IMU测量得到的加速度分量； - gx, gy, gz：FTS坐标系下的重力矢量方向； - r11, r12, r13, r21, r22, r23, r31, r32, r33：表示世界坐标系到FTS坐标系的旋转矩阵（R_wf）的各分量。 Vougioukas[2]所述校准方法所需的24个姿态下的FTS与IMU测量数据，存储于0-calibration_fts-accel.csv文件中。此外，0-steady-state_wrench.csv与0-steady-state_accel.csv分别包含FTS与IMU处于静止状态时的连续传感器信号，可用于计算传感器信号的方差。 校准完成后，我们分别记录各传感器的信号，并将其存储于独立的文件中，保存原始（带偏置）的测量值。每个测试迭代生成三个文件： 1. [test_iteration]_orientation.csv：末端执行器/FTS/IMU的姿态数据； 2. [test_iteration]_wrench.csv：FTS测量得到的无偏置力扭数据； 3. [test_iteration]_accel.csv：IMU测量得到的无偏置加速度数据。 上述文件的测试迭代前缀分别为：1-baseline、2-vibrations与3-vibrations-contact，对应前文“方法”部分所述的三种场景。 若要获取同一测试迭代下各文件（[_orientation.csv、_wrench.csv与_accel.csv）中样本的相对时间，可加载各数据集并找到第一行时间戳最早的样本，将该初始时间戳值从对应测试迭代所有文件的时间戳中减去即可。 需注意，IMU坐标系与FTS坐标系并不对齐（_accel.csv与_wrench.csv所用坐标系不同）。下表给出了用于将IMU坐标系{a}下的加速度测量值转换至FTS坐标系{f}的旋转矩阵R_fa： R_fa = [[0, 0, -1], [-1, 0, 0], [0, 1, 0]] 参考文献 [1] A. Skrede, "A Linear Discrete Kalman Filter to Estimate the Contact Wrench of an Unknown Robot End Effector", Accepted for the 2024 IEEE International Conference on Real-time Computing and Robotics (RCAR), Ålesund, Norway, June 2024 [2] S. Vougioukas, "Bias Estimation and Gravity Compensation For Force-Torque Sensors", in Recent Advances in Simulation, Computational Methods and Soft Computing. WSEAS Press, 2001, pp. 82–85.