Tactile Ergodic Control using Diffusion and Geometric Algbra
Cem Bilaloglu*, Tobias Löw* and Sylvain Calinon
Continuous physical interaction between robots and their environment is a requirement in many industrial and household tasks, such as sanding and cleaning. Due to the complex tactile information, these tasks are notoriously difficult to model and to sense. Thus, planning open-loop trajectories is extremely challenging and likely to fail. In this article, we introduce a closed-loop control method that is constrained to surfaces. The applications that we target have in common that they can be represented by probability distributions on the surface that correlate to the time the robot should spend in a region. These surfaces can easily be captured jointly with the target distributions using coloured pointclouds. Hence, we present the extension of an ergodic control approach that can be used with pointclouds, based on heat equation-driven area coverage (HEDAC). Our method enables closed-loop exploration by measuring the actual coverage using vision. Unlike existing approaches, we approximate the potential field from non-stationary diffusion using spectral acceleration, which does not require complex preprocessing steps and achieves real-time closed-loop control frequencies. We exploit geometric algebra to stay in contact with the target surface by tracking a line while simultaneously exerting a desired force along that line, for which we are using a wrist-mounted force-torque sensor. Our approach is suitable for fully autonomous and human-robot interaction settings where the robot can either directly measure the coverage of the target with its sensors or by being guided online by markings or annotations of a human expert. We tested the performance of our approach in kinematic simulation using pointclouds, ranging from the Stanford bunny to a variety of kitchen utensils. Our real-world experiments demonstrate that the proposed approach can successfully be used to wash kitchenware with curved surfaces, by cleaning the dirt detected by vision in an online manner. We release all our source codes, experiment data and videos as open access at https://geometric-algebra.tobiloew.ch/tactile_ergodic_control/.
These interactive plots contain data corresponding to different initializations you can switch between them by clicking on the legend.
Influence of the Parameters
In this plot, we are keeping the number of eigenfunctions constant and we are only modifying the alpha value. Increasing alpha results in smoother trajectories and a more global exploration behaviour, as can be seen by the frequent switching of the modes.
In this plot, we are keeping alpha constant at 100 and we are only modiyfying the number of eigenfunctions. It can be seen that by increasing the number of eigenfunctions, it eventually converges to the exact solution. Hence, the solutions for 100 and 200 eigenfunctions are very similiar.