arXiv subjects

Mark Petersen

Publications and source records attributed to Mark Petersen.

9 recordsLinked to original sources

arXiv2026

Real-Time Thermal-Inertial Odometry on Embedded Hardware for High-Speed GPS-Denied Flight

We present a real-time monocular thermal-inertial odometry system designed for high-velocity, GPS-denied flight on embedded hardware. The system fuses measurements from a FLIR Boson+ 640 longwave infrared camera, a high-rate IMU, a laser range finder, a barometer, and a magnetometer within a fixed-lag factor graph. To sustain reliable feature tracks under motion blur, low contrast, and rapid viewpoint changes, we employ a lightweight thermal-optimized front-end with multi-stage feature filtering. Laser range finder measurements provide per-feature depth priors that stabilize scale during weakly observable motion. High-rate inertial data is first pre-filtered using a Chebyshev Type II infinite impulse response (IIR) filter and then preintegrated, improving robustness to airframe vibrations during aggressive maneuvers. To address barometric altitude errors induced at high airspeeds, we train an uncertainty-aware gated recurrent unit (GRU) network that models the temporal dynamics of static pressure distortion, outperforming polynomial and multi-layer perceptron (MLP) baselines. Integrated on an NVIDIA Jetson Xavier NX, the complete system supports closed-loop quadrotor flight at 30 m/s with drift under 2% over kilometer-scale trajectories. These contributions expand the operational envelope of thermal-inertial navigation, enabling reliable high-speed flight in visually degraded and GPS-denied environments.

cs.RO↗

arXiv2025

SDSO1 is a Shocked Ghost Planetary Nebula in Front of M 31

We present new, deep narrowband imagery and discuss the nature of SDSO 1, the large [O III]-emitting nebula centered 1.5 degrees SE of M 31. We find strong evidence to support the hypothesis that SDSO 1 is unrelated to M 31 and is instead a faded, giant (D = 20 pc), ghost planetary nebula (GPN) expelled by the symbiotic WD binary star EG Andromedae. The associated 45-pc long turbulent tail, seen in projection in front of M 31, yields an estimated age of 400 kyr. The initial hypersonic velocity of 91 km/s drives a strong bow shock into the local interstellar medium and a reverse shock into the GPN. The SDSO 1 GPN has reached the terminal phase in its evolution where its outward expansion and forward motion have been decelerated greatly by ram pressure and the [O III] emission arises primarily from the reverse shock. We establish the shock-powered GPN phase as a new phase of planetary nebula (PN) evolution, and identify 24 candidate GPNe by their large size and shock-tail morphology. This includes several giant halos of younger PNe, possibly expelled by now degenerate binary companions. The interaction of an old, fast-moving GPN with the ISM generates shocks that remain visible long after the photoionized PN shell has faded below the limit of detectability.

astro-ph.GA↗

arXiv2024

High-order Tensor-Train Finite Volume Method for Shallow Water Equations

In this paper, we introduce a high-order tensor-train (TT) finite volume method for the Shallow Water Equations (SWEs). We present the implementation of the $3^{rd}$ order Upwind and the $5^{th}$ order Upwind and WENO reconstruction schemes in the TT format. It is shown in detail that the linear upwind schemes can be implemented by directly manipulating the TT cores while the WENO scheme requires the use of TT cross interpolation for the nonlinear reconstruction. In the development of numerical fluxes, we directly compute the flux for the linear SWEs without using TT rounding or cross interpolation. For the nonlinear SWEs where the TT reciprocal of the shallow water layer thickness is needed for fluxes, we develop an approximation algorithm using Taylor series to compute the TT reciprocal. The performance of the TT finite volume solver with linear and nonlinear reconstruction options is investigated under a physically relevant set of validation problems. In all test cases, the TT finite volume method maintains the formal high-order accuracy of the corresponding traditional finite volume method. In terms of speed, the TT solver achieves up to 124x acceleration of the traditional full-tensor scheme.

math.NA↗

arXiv2023

Non-Euclidean Motion Planning with Graphs of Geodesically-Convex Sets

Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent nonconvexities in the optimization landscape. The use of mixed-integer programming to encapsulate these nonconvexities and find globally optimal trajectories has recently shown great promise, thanks in part to tight convex relaxations and efficient approximation strategies that greatly reduce runtimes. These approaches were previously limited to Euclidean configuration spaces, precluding their use with mobile bases or continuous revolute joints. In this paper, we handle such scenarios by modeling configuration spaces as Riemannian manifolds, and we describe a reduction procedure for the zero-curvature case to a mixed-integer convex optimization problem. We demonstrate our results on various robot platforms, including producing efficient collision-free trajectories for a PR2 bimanual mobile manipulator.

cs.RO↗

arXiv2023

Growing Convex Collision-Free Regions in Configuration Space using Nonlinear Programming

One of the most difficult parts of motion planning in configuration space is ensuring a trajectory does not collide with task-space obstacles in the environment. Generating regions that are convex and collision free in configuration space can separate the computational burden of collision checking from motion planning. To that end, we propose an extension to IRIS (Iterative Regional Inflation by Semidefinite programming) [5] that allows it to operate in configuration space. Our algorithm, IRIS-NP (Iterative Regional Inflation by Semidefinite & Nonlinear Programming), uses nonlinear optimization to add the separating hyperplanes, enabling support for more general nonlinear constraints. Developed in parallel to Amice et al. [1], IRIS-NP trades rigorous certification that regions are collision free for probabilistic certification and the benefit of faster region generation in the configuration-space coordinates. IRIS-NP also provides a solid initialization to C-IRIS to reduce the number of iterations required for certification. We demonstrate that IRIS-NP can scale to a dual-arm manipulator and can handle additional nonlinear constraints using the same machinery. Finally, we show ablations of elements of our implementation to demonstrate their importance.

cs.RO↗

arXiv2022

Motion Planning around Obstacles with Convex Optimization

Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous differential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization problem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of B\'ezier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap rounding of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time.

cs.RO↗

arXiv2021

Local time stepping for the shallow water equations in MPAS

We assess the performance of a set of local time-stepping (LTS) schemes for the shallow water equations implemented in the Model for Prediction Across Scales (MPAS). The goal of LTS is to speed up the simulation by allowing different time-steps on different regions of the computational grid. The LTS schemes considered here were originally introduced by Hoang et al. (J. Comput. Phys., Vol. 382, p.152-176, 2019), who laid out the mathematical foundation of the methods. Here, the authors take on the task of presenting a fast, efficient and scalable parallel implementation of these LTS methods on high performance computing machines, with the aim to provide a recipe for other climate modeling groups that may be interested in employing LTS algorithms in their codes. As a matter of fact, even if MPAS is our framework of choice, our approach is general enough and could be of interest to other groups beyond the MPAS community. Due to their nature, LTS methods possess an inherent load imbalance that needs to be carefully addressed in order to obtain efficient scalability. Even more important is the far from trivial task of computing the right-hand side terms only on specific LTS regions during the time-stepping procedure. An inefficient handling of this task causes a drastic decay of the CPU time performance, making the LTS algorithms practically of no use. The emphasis of the present work is therefore on the computational and parallel aspects of the LTS methods, whose proper handling is crucial to make the methods run faster against existing strategies, such as for instance high-order explicit global time-stepping schemes. This is in fact the ultimate goal of using an LTS procedure and it is the one to which we direct all our optimization efforts.

math.NA↗

arXiv2021

On the Spatial and Temporal Order of Convergence of Hyperbolic PDEs

In this work, we determine the full expression for the global truncation error of hyperbolic partial differential equations (PDEs). In particular, we use theoretical analysis and symbolic algebra to find exact expressions for the coefficients of the generic global truncation error. Our analysis is valid for any hyperbolic PDE, be it linear or non-linear, and employing finite difference, finite volume, or finite element discretization in space, and advanced in time with a predictor-corrector, multistep, or a deferred correction method, belonging to the Method of Lines. Furthermore, we discuss the practical implications of this analysis. If we employ a stable numerical scheme and the orders of accuracy of the global solution error and the global truncation error agree, we make the following asymptotic observations: (a) the order of convergence at constant ratio of $\Delta t$ to $\Delta x$ is governed by the minimum of the orders of the spatial and temporal discretizations, and (b) convergence cannot even be guaranteed under only spatial or temporal refinement. An implication of (a) is that it is impractical to invest in a time-stepping method of order higher than the spatial discretization. In addition to (b), we demonstrate that under certain circumstances, the error can even monotonically increase with refinement only in space or only in time, and explain why this phenomenon occurs. To verify our theoretical findings, we conduct convergence studies of linear and non-linear advection equations using finite difference and finite volume spatial discretizations, and predictor-corrector and multistep time-stepping methods. Finally, we study the effect of slope limiters and monotonicity-preserving strategies on the order of accuracy.

math.NA↗

arXiv2015

A Computational Investigation of the Finite-Time Blow-Up of the 3D Incompressible Euler Equations Based on the Voigt Regularization

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for fixed values of the regularization parameter $\alpha>0$. Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be sufficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.

math.AP↗