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Polygonal collision avoidance (PCA) is short for the problem of collision avoidance between two polygons (i.e., polytopes in planar) that own their dynamic equations. This problem suffers the inherent difficulty in dealing with non-smooth…
We propose an output feedback control-based motion planning technique for agents to enable them to converge to a specified polynomial trajectory while imposing a set of safety constraints on our controller to avoid collisions within the…
Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization…
Control barrier functions (CBFs) have been widely applied to safety-critical robotic applications. However, the construction of control barrier functions for robotic systems remains a challenging task. Recently, collision detection using…
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…
Trajectory planning in dense, interactive traffic scenarios presents significant challenges for autonomous vehicles, primarily due to the uncertainty of human driver behavior and the non-convex nature of collision avoidance constraints.…
Online generation of collision free trajectories is of prime importance for autonomous navigation. Dynamic environments, robot motion and sensing uncertainties adds further challenges to collision avoidance systems. This paper presents an…
This paper considers the problem of robot motion planning in a workspace with obstacles for systems with uncertain 2nd-order dynamics. In particular, we combine closed form potential-based feedback controllers with adaptive control…
In fields such as mining, search and rescue, and archaeological exploration, ensuring real-time, collision-free navigation of robots in confined, cluttered environments is imperative. Despite the value of established path planning…
In this paper, we investigate optimal boundary control problems for Cahn-Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator. The cost functional is of…
Multi-modal behaviors exhibited by surrounding vehicles (SVs) can typically lead to traffic congestion and reduce the travel efficiency of autonomous vehicles (AVs) in dense traffic. This paper proposes a real-time parallel trajectory…
Optimal path planning problems for rigid and deformable (bendable) cuboid robots are considered by providing an analytic safety constraint using generalized $L_p$ norms. For regular cuboid robots, level sets of weighted $L_p$ norms generate…
For a nonlinear system (e.g. a robot) with its continuous state space trajectories constrained by a linear temporal logic specification, the synthesis of a low-level controller for mission execution often results in a non-convex…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
This work proposes a novel transformation termed the conformal navigation transformation to achieve collision-free navigation of a robot in a workspace populated with arbitrary polygonal obstacles. The properties of the conformal navigation…
In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
Optimization-based approaches are widely employed to generate optimal robot motions while considering various constraints, such as robot dynamics, collision avoidance, and physical limitations. It is crucial to efficiently solve the…