相关论文: Bezier Reachable Polytopes: Efficient Certificates…
This paper studies tracking of collision-free waypoint paths produced by an offline planner for a planar double-integrator system with bounded speed and acceleration. Because sampling-based planners must route around obstacles, the…
The focus of this thesis is developing a framework for designing correct-by-construction controllers using control certificates. We use nonlinear dynamical systems to model the physical environment (plants). The goal is to synthesize…
Legged robots are increasingly entering new domains and applications, including search and rescue, inspection, and logistics. However, for such systems to be valuable in real-world scenarios, they must be able to autonomously and robustly…
This paper develops a physics-informed scenario approach for safety verification of nonlinear systems using barrier certificates (BCs) to ensure that system trajectories remain within safe regions over an infinite time horizon. Designing…
Learning-based methods provide a promising approach to solving highly non-linear control tasks that are often challenging for classical control methods. To ensure the satisfaction of a safety property, learning-based methods jointly learn a…
Reachability queries ask whether there exists a path from the source vertex to the target vertex on a graph. Recently, several powerful reachability queries, such as Label-Constrained Reachability (LCR) queries and Regular Path Queries…
As a parametric motion representation, B\'ezier curves have significant applications in polynomial trajectory optimization for safe and smooth motion planning of various robotic systems, including flying drones, autonomous vehicles, and…
We consider affine systems defined on polytopes and study the cases where the systems are not in-block controllable with respect to the given polytopes. That are the cases in which we cannot fully control the affine systems within the…
This paper deals with the merging problem of segments of a composite B\'ezier curve, with the endpoints continuity constraints. We present a novel method which is based on the idea of using constrained dual Bernstein polynomial basis (P.…
In this paper, we give novel certificates for triangular equivalence and rank profiles. These certificates enable to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a negligible…
Multi-mobile robot systems show great advantages over one single robot in many applications. However, the robots are required to form desired task-specified formations, making feasible motions decrease significantly. Thus, it is challenging…
We consider reachability decision problems for linear dynamical systems: Given a linear map on $\mathbb{R}^d$ , together with source and target sets, determine whether there is a point in the source set whose orbit, obtained by repeatedly…
Containers as the unit of application delivery are the 'next big thing' in the software development world. They enable developers to create an executable image containing an application bundled with all its dependencies which a user can run…
Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in…
Ensuring safety in cyber-physical systems (CPSs) is a critical challenge, especially when system models are difficult to obtain or cannot be fully trusted due to uncertainty, modeling errors, or environmental disturbances. Traditional…
Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate…
Many computations in robotics can be dramatically accelerated if the robot configuration space is described as a collection of simple sets. For example, recently developed motion planners rely on a convex decomposition of the free space to…
We consider three classification systems for distributed decision tasks: With unbounded computation and certificates, defined by Balliu, D'Angelo, Fraigniaud, and Olivetti [JCSS'18], and with (two flavors of) polynomially bounded local…
Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization…
We introduce a low-memory framework for certifying numerical solutions to polynomial systems which uses solution iterators and spatial partitioning trees to reduce memory requirements. We provide a prototypical algorithm, analyze its…