Related papers: Single-Impulse Reachable Set in Arbitrary Dynamics…
Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…
Successive convex programming (SCP) is a powerful class of direct optimization methods, known for its polynomial complexity and computational efficiency, making it particularly suitable for autonomous applications. Direct methods are also…
This paper introduces a hybrid dynamical system methodology for managing impulsive control in spacecraft rendezvous and proximity operations under the Hill-Clohessy-Wiltshire model. We address the control design problem by isolating the…
This paper explores expressing the relative state in the close-proximity satellite relative motion problem in terms of fundamental solution constants. The nominal uncontrolled relative state can be expressed in terms of a weighted sum of…
Orbit determination of spacecraft in orbit has been mostly dependent on either GNSS satellite signals or ground station telemetry. Both methods present their limitations, however: GNSS signals can only be used effectively in earth orbit,…
In this paper, we propose reachability analysis using constrained polynomial logical zonotopes. We perform reachability analysis to compute the set of states that could be reached. To do this, we utilize a recently introduced set…
Polynomial optimization problems (POPs) can be reformulated as geometric convex conic programs, as shown by Kim, Kojima, and Toh (SIOPT 30:1251-1273, 2020), though such formulations remain NP-hard. In this work, we prove that several…
We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic…
This paper shows how to find lower bounds on, and sometimes solve globally, a large class of nonlinear optimal control problems with impulsive controls using semi-definite programming (SDP). This is done by relaxing an optimal control…
The arising application of neural networks (NN) in robotic systems has driven the development of safety verification methods for neural network dynamical systems (NNDS). Recursive techniques for reachability analysis of dynamical systems in…
In this paper we examine how Lagrangian techniques can be used to compute underapproximations and overapproximation of the finite-time horizon, stochastic reach-avoid level sets for discrete-time, nonlinear systems. This approach is…
Navigating the ultrasound (US) probe to the standardized imaging plane (SIP) for image acquisition is a critical but operator-dependent task in conventional freehand diagnostic US. Robotic US systems (RUSS) offer the potential to enhance…
A classical approach to the restricted three-body problem is to analyze the dynamics of the massless body in the synodic reference frame. A different approach is represented by the perturbative treatment: in particular the averaged problem…
This study presents an innovative direct numerical simulation approach for complex particle systems with irregular shapes and large numbers. Using partially saturated methods, it accurately models arbitrary shapes, albeit at considerable…
This paper investigates one-step backward reachability for uncertain max-plus linear systems with additive disturbances. Given a target set, the problem is to compute the set of states from which there exists an admissible control input…
In this paper, we propose a decision procedure of reachability for linear system {\xi}' = A{\xi} + u, where the matrix A's eigenvalues can be arbitrary algebraic numbers and the input u is a vector of trigonometric-exponential polynomials.…
This paper presents a new algorithm for autonomous multitarget tracking of resident space objects using optical angles-only measurements from a spaceborne observer. To enable autonomous angles-only navigation of spacecraft swarms, an…
Vector Addition Systems with States (VASS), equivalent to Petri nets, are a well-established model of concurrency. The central algorithmic challenge in VASS is the reachability problem: is there a run from a given starting state and counter…
This work proposes a safety-critical local reactive controller that enables the robot to navigate in unknown and cluttered environments. In particular, the trajectory tracking task is formulated as a constrained polynomial optimization…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…