arXiv subjects

Randall Christensen

Publications and source records attributed to Randall Christensen.

10 recordsLinked to original sources

arXiv2023

Fillet-based RRT: A Rapid Convergence Implementation of RRT for Curvature Constrained Vehicles

Rapidly exploring random trees (RRTs) have proven effective in quickly finding feasible solutions to complex motion planning problems. RRT* is an extension of the RRT algorithm that provides probabilistic asymptotic optimality guarantees when using straight-line motion primitives. This work provides extensions to RRT and RRT* that employ fillets as motion primitives, allowing path curvature constraints to be considered when planning. Two fillets are developed, an arc-based fillet that uses circular arcs to generate paths that respect maximum curvature constraints and a spline-based fillet that uses Bezier curves to additionally respect curvature continuity requirements. Planning with these fillets is shown to far exceed the performance of RRT* using Dubin's path motion primitives, approaching the performance of planning with straight-line path primitives. Path sampling heuristics are also introduced to accelerate convergence for nonholonomic motion planning. Comparisons to established RRT* approaches are made using the Open Motion Planning Library (OMPL).

cs.RO↗

arXiv2022

Path Planning with Uncertainty for Aircraft Under Threat of Detection from Ground-Based Radar

Mission planners for aircraft operating under threat of detection by ground-based radar systems are concerned with the probability of detection. Current path planning methods for such scenarios consider the aircraft pose, radar position, and radar parameters to be deterministic and known. This paper presents a framework for incorporating uncertainty in these quantities into a radar detection model that is used by a path planner. The developed path planner evaluates the radar detection risk in the presence of uncertainties and uses linear covariance analysis to efficiently generate error budgets. The error budgets identify the contribution of each source of uncertainty (e.g., sensor measurement noise, radar position uncertainty) to the overall variability in the probability of detection. The framework is applied to a modified visibility graph path planner that uses the detection risk and its variability to calculate path adjustments, which maintain the detection risk below a specified threshold. The results show that the framework is effective at providing actionable information to the mission planner that improves the final planned path and reduces the detection risk.

eess.SY↗

arXiv2022

Sensitivity of Single-Pulse Radar Detection to Radar State Uncertainty

Mission planners for aircraft operating under threat of detection from ground-based radar systems are often concerned with the probability of detection. Current approaches to path planning in such environments consider the radar state (i.e. radar position and parameters) to be deterministic and known. In practice, there is uncertainty in the radar state which induces uncertainty in the probability of detection. This paper presents a method to incorporate the uncertainty of the radar state in a single-pulse radar detection model. The method linearizes the radar detection model with respect to the the radar state and uses the linearized models to estimate, to the first order, the variance of the probability of detection. The results in this paper validate the linearization using Monte Carlo analysis and illustrate the sensitivity of the probability of detection to radar state uncertainty.

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arXiv2022

Sensitivity of Single-Pulse Radar Detection to Aircraft Pose Uncertainties

Mission planners for aircraft that operate in radar detection environments are often concerned the probability of detection. The probability of detection is a nonlinear function of the aircraft pose and radar position. Current path planning techniques for this application assume that the aircraft pose is deterministic. In practice, however, the aircraft pose is estimated using a navigation filter and therefore contains uncertainty. The uncertainty in the aircraft pose induces uncertainty in the probability of detection, but this phenomenon is generally not considered when path planning. This paper provides a method for combining aircraft pose uncertainty with single-pulse radar detection models to aid mission planning efforts. The method linearizes the expression for the probability of detection and three radar cross section models. The linearized models are then used to determine the variability of the probability of detection induced by uncertainty in the aircraft pose. The results of this paper validate the linearization using Monte Carlo analysis and explore the sensitivity of the probability of detection to aircraft pose uncertainty.

eess.SY↗

arXiv2021

A Closed-Loop Linear Covariance Framework for Vehicle Path Planning in a Static Uncertain Obstacle Fiel

Path planning in an uncertain environment is a key enabler of true vehicle autonomy. Over the past two decades, numerous approaches have been developed to account for errors in the vehicle path while navigating complex and often uncertain environments. An important capability of such planning is the prediction of vehicle dispersion covariances about a candidate path. This work develops a new closed-loop linear covariance (CL-LinCov) framework applicable to a wide range of autonomous system architectures. Important features of the developed framework include the (1) separation of high-level guidance from low-level control, (2) support for output-feedback controllers with internal states, dynamics, and output, and (3) multi-use continuous sensors for navigation state propagation, guidance, and feedback control. The closed-loop nature of the framework preserves the important coupling between the system dynamics, exogenous disturbances, and the guidance, navigation, and control algorithms. The developed framework is applied to a simplified model of an unmanned aerial vehicle and validated by comparison via Monte Carlo analysis. The utility of the CL-LinCov information is illustrated by its application to path planning in a static, uncertain obstacle field via a modified version of the Rapidly Exploring Random Tree algorithm.

cs.RO↗

arXiv2021

Sensitivity Study of Fiducial-Aided Navigation of Unmanned Aerial Vehicles

The possible applications and benefits of autonomous Unmanned Aerial Vehicle (UAV) use in urban areas are gaining considerable attention. Before these possibilities can be realized, it is essential that UAVs be able to navigate reliably and precisely in urban environments. The most common means of determining the location of a UAV is to utilize position measurements from Global Navigation Satellite Systems (GNSS). In urban environments, however, GNSS measurements are significantly degraded due to occlusions and multipath. This research analyzes the use of camera Line-of-Sight (LOS) measurements to self-describing fiducials as a replacement for conventional GNSS measurements. An extended Kalman filter (EKF) is developed and validated for the purpose of combining continuous measurements from an Inertial Measurement Unit (IMU) with the discrete LOS measurements to accurately estimate the states of a UAV. The sensitivity of the estimation error covariance to various system parameters is assessed, including IMU grade, fiducial placement, vehicle altitude, and image processing frequency.

cs.RO↗

arXiv2021

Analytical Aircraft State and IMU Signal Generator from Smoothed Reference Trajectory

This work presents a method for generating position, attitude, and velocity states for an aircraft following a smoothed reference trajectory. The method also generates accelerometer and gyro measurements consistent with the aircraft states. This work describes three corner smoothing algorithms for generating a smoothed reference trajectory from a series waypoints that accounts for limitations in the physical system. The smoothed reference trajectory, and curvilinear motion theory are used to generate the lower-order states. A coordinated turn maneuver is then applied to generate accelerometer and gyro measurement estimates.

eess.SY↗

arXiv2020

GPS-Denied Navigation Using SAR Images and Neural Networks

Unmanned aerial vehicles (UAV) often rely on GPS for navigation. GPS signals, however, are very low in power and easily jammed or otherwise disrupted. This paper presents a method for determining the navigation errors present at the beginning of a GPS-denied period utilizing data from a synthetic aperture radar (SAR) system. This is accomplished by comparing an online-generated SAR image with a reference image obtained a priori. The distortions relative to the reference image are learned and exploited with a convolutional neural network to recover the initial navigational errors, which can be used to recover the true flight trajectory throughout the synthetic aperture. The proposed neural network approach is able to learn to predict the initial errors on both simulated and real SAR image data.

cs.CV↗

arXiv2020

Sensitivity of BPA SAR Image Formation to Initial Position, Velocity, and Attitude Navigation Errors

The Back-Projection Algorithm (BPA) is a time domain matched filtering technique to form synthetic aperture radar (SAR) images. To produce high quality BPA images, precise navigation data for the radar platform must be known. Any error in position, velocity, or attitude results in improperly formed images corrupted by shifting, blurring, and distortion. This paper develops analytical expressions that characterize the relationship between navigation errors and image formation errors. These analytical expressions are verified via simulated image formation and real data image formation.

eess.SP↗

arXiv2020

Zero-Error Tracking for Autonomous Vehicles through Epsilon-Trajectory Generation

This paper presents a control method and trajectory planner for vehicles with first-order nonholonomic constraints that guarantee asymptotic convergence to a time-indexed trajectory. To overcome the nonholonomic constraint, a fixed point in front of the vehicle can be controlled to track a desired trajectory, albeit with a steady-state error. To eliminate steady state error, a sufficiently smooth trajectory is reformulated for the new reference point such that, when tracking the new trajectory, the vehicle asymptotically converges to the original trajectory. The resulting zero-error tracking law is demonstrated through a novel framework for creating time-indexed Clothoids. The Clothoids can be planned to pass through arbitrary waypoints using traditional methods yet result in trajectories that can be followed with zero steady-state error. The results of the control method and planner are illustrated in simulation wherein zero-error tracking is demonstrated.

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