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Online trajectory planning enables robot manipulators to react quickly to changing environments or tasks. Many robot trajectory planners exist for known environments but are often too slow for online computations. Current methods in online…

With the increasing integration of robots into human life, their role in architectural spaces where people spend most of their time has become more prominent. While motion capabilities and accurate localization for automated robots have…

Navigating an arbitrary-shaped ground robot safely in cluttered environments remains a challenging problem. The existing trajectory planners that account for the robot's physical geometry severely suffer from the intractable runtime. To…

Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…

In this paper, we consider a robot navigation problem in environments populated by humans. The goal is to determine collision-free and dynamically feasible trajectories that also maximize human satisfaction. This is because they may drive…

This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport…

In recent times, an increasing number of researchers have been devoted to utilizing deep neural networks for end-to-end flight navigation. This approach has gained traction due to its ability to bridge the gap between perception and…

In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…

If we give a robot the task of moving an object from its current position to another location in an unknown environment, the robot must explore the map, identify all types of obstacles, and then determine the best route to complete the…

For enabling efficient, large-scale coordination of unmanned aerial vehicles (UAVs) under the labeled setting, in this work, we develop the first polynomial time algorithm for the reconfiguration of many moving bodies in three-dimensional…

In this article, a formulation of a point-collocation method in which the unknown function is approximated using global expansion in tensor product Bernstein polynomial basis is presented. Bernstein polynomials used in this study are…

Design optimisation offers the potential to develop lightweight aircraft structures with reduced environmental impact. Due to the high number of design variables and constraints, these challenges are typically addressed using gradient-based…

Navigating mobile robots through environments shared with humans is challenging. From the perspective of the robot, humans are dynamic obstacles that must be avoided. These obstacles make the collision-free space nonconvex, which leads to…

Our research introduces a modular motion planning framework for autonomous vehicles using a sampling-based trajectory planning algorithm. This approach effectively tackles the challenges of solution space construction and optimization in…

This paper presents a computationally efficient model predictive control formulation that uses an integral Chebyshev collocation method to enable rapid operations of autonomous agents. By posing the finite-horizon optimal control problem…

As robotic systems continue to address emerging issues in areas such as logistics, mobility, manufacturing, and disaster response, it is increasingly important to rapidly generate safe and energy-efficient trajectories. In this article, we…

The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning,…

Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…

We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level…

Orthogonal collocation methods are direct approaches for solving optimal control problems (OCP). A high solution accuracy is achieved with few optimization variables, making it more favorable for embedded and real-time NMPC applications.…