Gabriele M. T. D'Eleuterio

Timothy D. Barfoot, James R. Forbes, Gabriele M. T. D'Eleuterio

Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation - together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of a vector space are surjectively mapped to a matrix Lie group. For example, these vectorial representations can be employed for optimization as well as uncertainty representation on groups. The most common mapping is the matrix exponential, which maps elements of a Lie algebra onto the associated Lie group. However, this choice is not unique. It has been previously shown how to characterize all such vectorial parameterizations for SO(3), the group of rotations. Some results are also known for the group of poses, where it is possible to build a family of vectorial mappings that includes the matrix exponential as well as the Cayley transformation. We extend what is known for these pose mappings to the 4 x 4 representation common in robotics, and also demonstrate three different examples of the proposed pose mappings: (i) pose interpolation, (ii) pose servoing control, and (iii) pose estimation in a pointcloud alignment problem. In the pointcloud alignment problem our results lead to a new algorithm based on the Cayley transformation, which we call CayPer.

Timothy D. Barfoot, Gabriele M. T. D'Eleuterio

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense 'closest' to the full Bayesian posterior. Closeness is typically defined through the selection of an appropriate loss functional such as the Kullback-Leibler (KL) divergence. In this paper, we explore a new formulation of variational inference by exploiting the fact that (most) PDFs are members of a Bayesian Hilbert space under careful definitions of vector addition, scalar multiplication and an inner product. We show that, under the right conditions, variational inference based on KL divergence can amount to iterative projection, in the Euclidean sense, of the Bayesian posterior onto a subspace corresponding to the selected approximation family. We work through the details of this general framework for the specific case of the Gaussian approximation family and show the equivalence to another Gaussian variational inference approach. We furthermore discuss the implications for systems that exhibit sparsity, which is handled naturally in Bayesian space, and give an example of a high-dimensional robotic state estimation problem that can be handled as a result. We provide some preliminary examples of how the approach could be applied to non-Gaussian inference and discuss the limitations of the approach in detail to encourage follow-on work along these lines.

Jekanthan Thangavelautham, Kenneth Law, Terence Fu et al.

In this paper, a control approach called Artificial Neural Tissue (ANT) is applied to multirobot excavation for lunar base preparation tasks including clearing landing pads and burying of habitat modules. We show for the first time, a team of autonomous robots excavating a terrain to match a given 3D blueprint. Constructing mounds around landing pads will provide physical shielding from debris during launch/landing. Burying a human habitat modules under 0.5 m of lunar regolith is expected to provide both radiation shielding and maintain temperatures of -25 $^{o}$C. This minimizes base life-support complexity and reduces launch mass. ANT is compelling for a lunar mission because it doesn't require a team of astronauts for excavation and it requires minimal supervision. The robot teams are shown to autonomously interpret blueprints, excavate and prepare sites for a lunar base. Because little pre-programmed knowledge is provided, the controllers discover creative techniques. ANT evolves techniques such as slot-dozing that would otherwise require excavation experts. This is critical in making an excavation mission feasible when it is prohibitively expensive to send astronauts. The controllers evolve elaborate negotiation behaviors to work in close quarters. These and other techniques such as concurrent evolution of the controller and team size are shown to tackle problem of antagonism, when too many robots interfere reducing the overall efficiency or worse, resulting in gridlock. While many challenges remain with this technology our work shows a compelling pathway for field testing this approach.