Related papers: Exploiting symmetry for discrete-time reachability…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
To reduce the computational cost of humanoid motion generation, we introduce a new approach to representing robot kinematic reachability: the differentiable reachability map. This map is a scalar-valued function defined in the task space…
Traditional reachability methods provide formal guarantees of safety under bounded disturbances. However, they strictly enforce state constraints as inviolable, which can result in overly conservative or infeasible solutions in complex…
In this study, we propose an algorithmic framework for solving a class of optimal control problems. This class is associated with the minimum-time interception of moving target problems, where a plant with a given state equation must…
Path planning for autonomous vehicles in arbitrary environments requires a guarantee of safety, but this can be impractical to ensure in real-time when the vehicle is described with a high-fidelity model. To address this problem, this paper…
We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction and…
This paper gives convex conditions for synthesis of a distributed control system for large-scale networked nonlinear dynamic systems. It is shown that the technique of control contraction metrics (CCMs) can be extended to this problem by…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
Safe UAV navigation is challenging due to the complex environment structures, dynamic obstacles, and uncertainties from measurement noises and unpredictable moving obstacle behaviors. Although plenty of recent works achieve safe navigation…
We propose control and communication strategies for nonlinear networked control systems subject to state and input constraints. The objective is to steer the state of the system towards a prescribed target set in finite time…
We propose a hierarchical control framework for the synthesis of correct-by-construction controllers for nonlinear control-affine systems with respect to reach-avoid-stay specifications. We first create a low-dimensional continuous…
Robust control problems have significant practical implications since external disturbances can significantly impact the performance of control methods. Existing robust control methods excel at control-affine systems but fail at neural…
This paper presents a reachability-based approach to finite-time transition problem of nonlinear systems between two stationary points (i.e., the point-to-point steering problem). When the target state is reachable, we prove that a solution…
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix $M \in \mathbb{Q}^{d \times d}$, an initial vector…
In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not…
We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…
Autonomous motion planning under unknown nonlinear dynamics presents significant challenges. An agent needs to continuously explore the system dynamics to acquire its properties, such as reachability, in order to guide system navigation…
A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new…
Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main…
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…