Related papers: Constraint-Aware Mesh Refinement Method by Reachab…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…
An adaptive mesh refinement and error estimation method for numerically solving optimal control problems is developed using Legendre-Gauss-Radau direct collocation. In regions of the solution where the desired accuracy tolerance has not…
This paper presents an optimisation-based approach for an obstacle avoidance problem within an autonomous vehicle racing context. Our control regime leverages online reachability analysis and sensor data to compute the maximal safe…
This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded…
Inactive constraints do not contribute to the solution of an optimal control problem, but increase the problem size and burden the numerical computations. We present a novel strategy for handling inactive constraints efficiently by…
Interval refinement is a technique for reducing the conservatism of traditional interval based reachability methods by lifting the system to a higher dimension using new auxiliary variables and exploiting the introduced structure through a…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…
A mesh refinement method is described for solving optimal control problems using Legendre-Gauss-Radau collocation. The method detects discontinuities in the control solution by employing an edge detection scheme based on jump function…
In this paper, we propose a reachable set based collision avoidance algorithm for unmanned aerial vehicles (UAVs). UAVs have been deployed for agriculture research and management, surveillance and sensor coverage for threat detection and…
We present a real-time-capable set-based framework for closed-loop predictive control of autonomous systems using tools from computational geometry, dynamic programming, and convex optimization. The control architecture relies on the…
Deep neural networks can be trained to be efficient and effective controllers for dynamical systems; however, the mechanics of deep neural networks are complex and difficult to guarantee. This work presents a general approach for providing…
Intercepting dynamic objects in uncertain environments involves a significant unresolved challenge in modern robotic systems. Current control approaches rely solely on estimated information, and results lack guarantees of robustness and…
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…
Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…
This article introduces a new transcription, change point localization, and mesh refinement scheme for direct optimization-based solutions and for uniform approximation of optimal control trajectories associated with a class of nonlinear…
The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these…
This paper presents a method for incorporating control analysis into design optimization for highly-maneuverable aircraft. By studying reachable sets for aircraft dynamics, we ensure that the optimizer will take the aircraft's controlled…