Related papers: Graph-Theoretic B\'ezier Curve Optimization over S…
Graph-structured data are central to many scientific and industrial applications where the goal is to optimize expensive black-box objectives defined over graph structures or node configurations -- as seen in molecular design, supply…
In the automation of many kinds of processes, the observable outcome can often be described as the combined effect of an entire sequence of actions, or controls, applied throughout its execution. In these cases, strategies to optimise…
We derive a variational model to fit a composite B\'ezier curve to a set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the…
This research addresses the increasing demand for advanced navigation systems capable of operating within confined surroundings. A significant challenge in this field is developing an efficient planning framework that can generalize across…
Trajectory retiming is the task of computing a feasible time parameterization to traverse a path. It is commonly used in the decoupled approach to trajectory optimization whereby a path is first found, then a retiming algorithm computes a…
Safe corridor-based Trajectory Optimization (TO) presents an appealing approach for collision-free path planning of autonomous robots, offering global optimality through its convex formulation. The safe corridor is constructed based on the…
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…
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…
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
In this paper, we focus on non-conservative collision avoidance between robots and obstacles with control affine dynamics and convex shapes. System safety is defined using the minimum distance between the safe regions associated with robots…
Optimization based motion planning provides a useful modeling framework through various costs and constraints. Using Graph of Convex Sets (GCS) for trajectory optimization gives guarantees of feasibility and optimality by representing…
Industrial robots are increasingly deployed in applications requiring an end effector tool to closely track a specified path, such as in spraying and welding. Performance and productivity present possibly conflicting objectives: tracking…
We propose a general framework for geometric approximation of circular arcs by parametric polynomial curves. The approach is based on constrained uniform approximation of an error function by scalar polynomials. The system of nonlinear…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
This paper presents a method for optimal motion planning of continuum robots by employing Bernstein surfaces to approximate the system's dynamics and impose complex constraints, including collision avoidance. The main contribution is the…
In the coordinated motion planning problem, we are given a graph together with the starting and destination vertices of $k$ robots. At each time step, any subset of robots may move, each traversing an edge of the graph, provided that no two…
Bearing-based distributed formation control is attractive because it can be implemented using vision-based measurements to achieve a desired formation. Gradient-descent-based controllers using bearing measurements have been shown to have…
Distributed consensus has been intensively studied in recent years as a means to mitigate state differences among dynamic nodes on a graph. It has been successfully employed in various applications, e.g., formation control of multi-robots,…
This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is…
Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…