David E. J. van Wijk

This manuscript introduces the covariance-constrained Kalman filter (CKF), designed to enhance the performance of the traditional Kalman filter (KF) and extended Kalman filter (EKF). The EKF, particularly when applied to highly nonlinear systems, can suffer from significant issues. Large covariance updates may cause rapid convergence, which in turn leads to overconfidence in state estimates. Additionally, large state updates degrade the accuracy of the first-order Taylor series approximation, resulting in linear error covariances that poorly represent the true estimation errors. To mitigate these scenarios, the CKF constrains the Kalman gain to limit the size of both state and covariance updates, preventing overconfidence in the filter's state estimates and improving overall filter stability. The derivation of the CKF, applicable to both linear and nonlinear systems, employs Lagrange multipliers to enforce these constraints analytically. The performance of the covariance-constrained EKF (CEKF) is benchmarked against the standard EKF and partial-update EKF (PEKF) through two numerical simulations: a falling-body tracking problem and an orbit determination problem. Monte Carlo analyses reveal that the CEKF successfully reduces the number of diverging cases, enhances covariance accuracy, and matches the Mahalanobis distance to the expected performance, outperforming the EKF in the scenarios investigated. The CEKF exhibits control over both the state and covariance updates, where the PEKF is only able to control the covariance. The results confirm that the CKF is a robust and efficient alternative for filtering nonlinear systems prone to divergence due to large state and covariance updates.

Obtaining a controlled invariant set is crucial for safety-critical control with control barrier functions (CBFs) but is non-trivial for complex nonlinear systems and constraints. Backup control barrier functions allow such sets to be constructed online in a computationally tractable manner by examining the evolution (or flow) of the system under a known backup control law. However, for systems with unmodeled disturbances, this flow cannot be directly computed, making the current methods inadequate for assuring safety in these scenarios. To address this gap, we leverage bounds on the nominal and disturbed flow to compute a forward invariant set online by ensuring safety of an expanding norm ball tube centered around the nominal system evolution. We prove that this set results in robust control constraints which guarantee safety of the disturbed system via our Disturbance-Robust Backup Control Barrier Function (DR-bCBF) solution. The efficacy of the proposed framework is demonstrated in simulation, applied to a double integrator problem and a rigid body spacecraft rotation problem with rate constraints.

This work examines the closed-loop deployment of spacecraft servicing modules onto an uncontrolled bundle of assembly components as a method of gaining custody during the in-space assembly process. Minimum energy, low-thrust relative trajectories are generated using indirect optimal control on linear dynamics over a finite time search horizon. A line search solves for the minimum energy solution in the closed subset that satisfies a keep out zone constraint. A trajectory tracking linear quadratic regulator is used in conjunction with an extended Kalman filter to closed-loop maneuver the spacecraft under nonlinear relative orbital motion dynamics. Bearing angles, range, and range rate measurements are assumed available. Launch ΔV’s from the servicer spacecraft’s deployment of a module and the ΔV’s seen in the relative frame upon impact on the client are included, and their effect on covariance due to impact site uncertainty is investigated. Discussions regarding these GN&C elements’ importance within the context of the manufacturing/assembly process are included.

While reinforcement learning (RL) offers high-performance solutions to complex tasks, its trial-and-error paradigm presents safety concerns when exploring unsafe states may be unacceptable. Safety filtering or run-time assurance (RTA) approaches can be used to monitor the RL agent’s desired control and prevent the agent from taking unsafe actions by satisfying safety constraints during and after training. This study investigates the problem of on-orbit inspection of a chief spacecraft using a deputy spacecraft controlled by an RL agent with safety constraints. Several constraints on the state space are enforced using discrete control barrier functions and an optimization-based RTA system. This assures the safety of the deputy spacecraft and its sensors even with a neural-network-based primary controller. A detailed analysis of RL agent performance for eight separate experiments is presented, including each safety constraint individually, all constraints simultaneously, and no constraints. Results demonstrate that the RL agent can complete the inspection task while adhering to safety constraints in a simulated RL environment. These results also show that the RTA system can aid the RL agent in learning a successful policy over fewer time steps but may lead to higher fuel usage, depending on the constraint(s) enforced.

Directional sensors, such as video cameras, have become ubiquitous to many autonomous robots applications, such as monitoring and surveillance. The performance of these sensors and processing algorithms, however, may be hindered by the presence of objects that block visibility. This article presents a novel approach for planning the path of a mobile directional sensor deployed to observe multiple targets distributed in an environment populated with multiple obstacles and occlusions. Unlike existing art gallery or watchman’s route methods, the visibility theory and motion planners developed in this article account for both line-of-sight visibility and bounded field-of-view constraints, and can provide obstacle avoidance based on robot geometry and kinodynamic constraints. The computational complexity analysis and experiments on a camera-equipped drone demonstrate that, despite the challenging geometric characteristics of directional C-targets, the approach scales to real-world problems. Furthermore, when compared to algorithms inspired by traveling salesman and target coverage approaches, the directional visibility planners presented in this article are significantly more effective both at guaranteeing complete target visibility and at minimizing distance traveled.