Sensors play an important role in robotics, since they are needed by robots in order for them to perceive the environment and interact with it. It is therefore essential that the sensor readings are as accurate as possible. Achieving a high accuracy makes it necessary to perform a good calibration of the sensors.

Calibration usually means determining either the intrinsic or extrinsic parameters of the sensor. In this particular case we are interested in finding the extrinsic parameters of an array of time of flight sensors that is attached to a Franka Emika serial manipulator. While it is possible to roughly determine the position of the array by taking measurements, the position and orientation of the sensors on the array cannot be measured accurately due to possible deformations during attaching or manufacturing the array. The challenge therefore lies in finding the exact positions and orientations of all sensors by refining a rough initial estimate.

There are various ways to tackle this problem, however in its essence it always is a geometric problem. Hence, the idea to solve this problem is to use an algebra that is made for geometry, namely geometric algebra. It is formalism that is currently resurfacing and gaining popularity in robotics. Its strength lies among other things in the possiblity to represent geometric primitives such as lines, planes and circles and their intersections in a parameterization and exception free way. This property makes it the ideal tool for the calibration of sensors that take distance measurements along a line or more generally a cone.

Thus, the goal of this project is the derivation of an algorithm for the fast and reliable extrinsic calibration of an array of time of flight sensors on a kinematic chain, as well as investigating the usage of geometric algebra as a tool for solving this problem. The expected outcome will include an implementation of the algorithm that has been tested thoroughly on the hardware that is provided in our lab, i.e. the sensor array and the robot.

Keywords: geometric algebra, model-based optimization, time of flight sensors, parameters identification, robot manipulation

In contact-rich robotics tasks, it is crucial to have an accurate measurement of forces and torques exchanged between the robot and its environment to feed those measurements back in a control loop. However, force/torque sensors placed between the tip of the robot and the end-effector measure not only those interaction forces, but also static (e.g. due to gravity) and dynamic (e.g. inertial, Coriolis and centrifugal) effects of the end-effector due to its non-negligible mass. In order to compensate for those measurement errors, the dynamic parameters of the end-effector such as mass, inertia and center-of-mass offset have to be known to be able to predict the resulting forces/torques corrupting the sensor measurement. Typically, those parameters are unknown or inaccurate, such that a model identification procedure is required. For the identification procedure, data has to be collected by moving the robot such that trajectories of motion and reaction forces can be recorded.

In this project, a load inertial parameter estimation algorithm will be implemented that (1) autonomously excites the robot sufficiently to collect dynamic motion/force data, (2) applies derivation filters (offline) to compute high-quality robot joint acceleration signals, and (3) solves an optimization problem to obtain an estimate of the inertial parameters of the robots end-effector.

The algorithm will be implemented (Python or C++) and tested on a 7-axis Franka Emika robot equipped with 6-axis force/torque sensor from Bota systems. Potentially, the work can be extended by using IMU measurements online to have a better estimate of the current acceleration of the robot, which will improve the prediction quality when using the learned dynamics model.

Keywords: parameters identification, force-torque sensing, robot manipulation

Reference:

Hollerbach, J., Khalil, W. and Gautier, M. (2008) Model Identification. Springer Handbook of Robotics, pp. 321-344.