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We present a continuous-time collision detection algorithm for quickly detecting whether certain polynomial trajectories in time intersect with convex obstacles. The algorithm is used in conjunction with an existing multicopter trajectory…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
In order for automated mobile vehicles to navigate in the real world with minimal collision risks, it is necessary for their planning algorithms to consider uncertainties from measurements and environmental disturbances. In this paper, we…
Avoiding collisions between obstacles and vehicles such as cars, robots or aircraft is essential to the development of automation and autonomy. To simplify the problem, many collision avoidance algorithms and proofs consider vehicles to be…
This paper proposes a new set of conditions for exactly representing collision avoidance constraints within optimization-based motion planning algorithms. The conditions are continuously differentiable and therefore suitable for use with…
In this paper we study a multi-robot path planning problem for persistent monitoring of an environment. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum time…
We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of…
We present a method for guaranteed collision detection with toleranced motions. The basic idea is to consider the motion as a curve in the 12-dimensional space of affine displacements, endowed with an object-oriented Euclidean metric, and…
An autonomous robot with a limited vision range finds a path to the goal in an unknown environment in 2D avoiding polygonal obstacles. In the process of discovering the environmental map, the robot has to return to some positions marked…
The collision avoidance constraints are prominent as non-convex, non-differentiable, and challenging when defined in optimization-based motion planning problems. To overcome these issues, this paper presents a novel non-conservative…
This paper proposes vehicle motion planning methods with obstacle avoidance in tight spaces by incorporating polygonal approximations of both the vehicle and obstacles into a model predictive control (MPC) framework. Representing these…
Autonomous mobile robots must maintain safety, but should not sacrifice performance, leading to the classical reach-avoid problem: find a trajectory that is guaranteed to reach a goal and avoid obstacles. This paper addresses the near…
Path planning in dynamic environments is essential to high-risk applications such as unmanned aerial vehicles, self-driving cars, and autonomous underwater vehicles. In this paper, we generate collision-free trajectories for a robot within…
We study the problem of determining coordinated motions, of minimum total length, for two arbitrary convex centrally-symmetric (CCS) robots in an otherwise obstacle-free plane. Using the total path length traced by the two robot centres as…
Collision detection is a critical functionality for robotics. The degree to which objects collide cannot be represented as a continuously differentiable function for any shapes other than spheres. This paper proposes a framework for…
Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded constraint. Algorithmically, we introduce a new differentiable…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
Estimating collision probabilities between robots and environmental obstacles or other moving agents is crucial to ensure safety during path planning. This is an important building block of modern planning algorithms in many application…
We present a fully distributed collision avoidance algorithm based on convex optimization for a team of mobile robots. This method addresses the practical case in which agents sense each other via measurements from noisy on-board sensors…