Abstract
We present a novel method for learning from demonstration 6-D tasks that can be modeled as a sequence of linear motions and compliances. The focus of this paper is the learning of a single linear primitive, many of which can be sequenced to perform more complex tasks. The presented method learns from demonstrations how to take advantage of mechanical gradients in in-contact tasks, such as assembly, both for translations and rotations, without any prior information. The method assumes there exists a desired linear direction in 6-D which, if followed by the manipulator, leads the robot’s end-effector to the goal area shown in the demonstration, either in free space or by leveraging contact through compliance. First, demonstrations are gathered where the teacher explicitly shows the robot how the mechanical gradients can be used as guidance towards the goal. From the demonstrations, a set of directions is computed which would result in the observed motion at each timestep during a demonstration of a single primitive. By observing which direction is included in all these sets, we find a single desired direction which can reproduce the demonstrated motion. Finding the number of compliant axes and their directions in both rotation and translation is based on the assumption that in the presence of a desired direction of motion, all other observed motion is caused by the contact force of the environment, signalling the need for compliance. We evaluate the method on a KUKA LWR4+ robot with test setups imitating typical tasks where a human would use compliance to cope with positional uncertainty. Results show that the method can successfully learn and reproduce compliant motions by taking advantage of the geometry of the task, therefore reducing the need for localization accuracy.
Highlights
It is essential that the contact wrenches are managed when interacting with the environment; without suitable compliant interaction, the linear motions depicted by the arrows in Fig. 1 would not result in the alignments shown, but instead would cause jamming, wedging, or breakage of equipment or workpieces
There are multiple methods for encoding the learned skill, such as Stable Estimator of Dynamical Systems (SEDS) (Khansari-Zadeh and Billard 2011), Gaussian Mixture Models (GMM) with Gaussian Mixture Regression (GMR) (Calinon et al 2007), Riemannian Motion Policies (Mukadam et al 2020), and several popular movement primitives, such as Dynamic Movement Primitives (DMP) (Schaal 2006), Kernelized Movement Primitives (KMP) (Huang et al 2019) and Probabilistic Movement Primitives (ProMP) (Paraschos et al 2013). Whereas these methods are perfectly capable of representing free space motions and contact tasks without position uncertainties, they have a tight coupling between force and position trajectories, which makes them susceptible to errors in initial position especially when dealing with multiple demonstrations
Tm = ρ × FN + l × Fμ + Iα wherel and ρ are the lever arm position vectors perpendicular to corresponding applied forces, I the inertia matrix and α the angular acceleration. This model is for a singlepoint contact, we show that the method is robust enough that we can teach multi-point contact tasks as well; considering a thorough contact formation treatment is outside the scope of this paper
Summary
There are multiple methods for encoding the learned skill, such as Stable Estimator of Dynamical Systems (SEDS) (Khansari-Zadeh and Billard 2011), Gaussian Mixture Models (GMM) with Gaussian Mixture Regression (GMR) (Calinon et al 2007), Riemannian Motion Policies (Mukadam et al 2020), and several popular movement primitives, such as Dynamic Movement Primitives (DMP) (Schaal 2006), Kernelized Movement Primitives (KMP) (Huang et al 2019) and Probabilistic Movement Primitives (ProMP) (Paraschos et al 2013) Whereas these methods are perfectly capable of representing free space motions and contact tasks without position uncertainties, they have a tight coupling between force and position trajectories, which makes them susceptible to errors in initial position especially when dealing with multiple demonstrations. Even though recent publications have shown that with certain modifications DMPs can be used to realize unseen trajectories (Abu-Dakka et al 2015), a primitive without the force-position coupling would be more flexible for easy generalization to tasks similar to demonstration
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