Dynamical systems with a distributed yet interconnected structure, like multi-rigid-body robots or large-scale multi-agent systems, introduce valuable sparsity into the system dynamics that can be exploited in an optimal control setting for speeding
up computation and improving numerical conditioning. Conventional approaches for solving the Optimal Control Problem (OCP) rarely capitalize on such structural sparsity, and hence suffer from a cubic computational complexity growth as the dimensionality of the system scales. In this paper, we present an OCP formulation that relies on graphical models to capture the sparsely-interconnected nature of the system dynamics. Such a representational choice allows the use of contemporary graphical inference algorithms that enable our solver to achieve a linear time complexity in the state and control dimensions as well as the time horizon. We demonstrate the numerical and computational advantages of our approach on a canonical dynamical system in simulation.
We present a novel continuous time trajectory representation based on a Chebyshev polynomial basis, which when governed by known dynamics models, allows for full trajectory and robot dynamics estimation, particularly useful for high-performance robot
ics applications such as unmanned aerial vehicles. We show that we can gracefully incorporate model dynamics to our trajectory representation, within a factor-graph based framework, and leverage ideas from pseudo-spectral optimal control to parameterize the state and the control trajectories as interpolating polynomials. This allows us to perform efficient optimization at specifically chosen points derived from the theory, while recovering full trajectory estimates. Through simulated experiments we demonstrate the applicability of our representation for accurate flight dynamics estimation for multirotor aerial vehicles. The representation framework is general and can thus be applied to a multitude of high-performance applications beyond multirotor platforms.
Besides the COVID-19 pandemic and political upheaval in the US, 2020 was also the year in which neural volume rendering exploded onto the scene, triggered by the impressive NeRF paper by Mildenhall et al. (2020). Both of us have tried to capture this
excitement, Frank on a blog post (Dellaert, 2020) and Yen-Chen in a Github collection (Yen-Chen, 2020). This note is an annotated bibliography of the relevant papers, and we posted the associated bibtex file on the repository.
In this paper, we explore the task of robot sculpting. We propose a search based planning algorithm to solve the problem of sculpting by material removal with a multi-axis manipulator. We generate collision free trajectories for a manipulator using b
est-first search in voxel space. We also show significant speedup of our algorithm by using octrees to decompose the voxel space. We demonstrate our algorithm on a multi-axis manipulator in simulation by sculpting Michelangelos Statue of David, evaluate certain metrics of our algorithm and discuss future goals for the project.
