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Given a graph $G$, the optimization version of the graph burning problem seeks for a sequence of vertices, $(u_1,u_2,...,u_p) \in V(G)^p$, with minimum $p$ and such that every $v \in V(G)$ has distance at most $p-i$ to some vertex $u_i$. The length $p$ of the optimal solution is known as the burning number and is denoted by $b(G)$, an invariant that helps quantify the graph's vulnerability to contagion. This paper explores the advantages and limitations of an $\mathcal{O}(mn + pn^2)$ deterministic greedy heuristic for this problem, where $n$ is the graph's order, $m$ is the graph's size, and $p$ is a guess on $b(G)$. This heuristic is based on the relationship between the graph burning problem and the clustered maximum coverage problem, and despite having limitations on paths and cycles, it found most of the optimal and best-known solutions of benchmark and synthetic graphs with up to 102400 vertices. Beyond practical advantages, our work unveils some of the fundamental aspects of graph burning: its relationship with a generalization of a classical coverage problem and compact integer programs. With this knowledge, better algorithms might be designed in the future., Comment: 17 pages; corrected proofs

In this paper, an adaptive nonlinear strategy for the motion and force control of flexible manipulators is proposed. The approach provides robust motion control until contact is detected when force control is then available--without any control switch--, and vice versa. This self-tuning in mixed contact/non-contact scenarios is possible thanks to the unified formulation of force and motion control, including an integral transpose-based inverse kinematics and adaptive-update laws for the flexible manipulator link and contact stiffnesses. Global boundedness of all signals and asymptotic stability of force and position are guaranteed through Lyapunov analysis. The control strategy and its implementation has been validated using a low-cost basic microcontroller and a manipulator with 3 flexible joints and 4 actuators. Complete experimental results are provided in a realistic mixed contact scenario, demonstrating very-low computational demand with inexpensive force sensors., Comment: Preprint submitted to Elsevier (under review)

In this work, we present an experimental setup and guide to enable the perching of large flapping-wing robots. The combination of forward flight, limited payload, and flight oscillations imposes challenging conditions for localized perching. The described method details the different operations that are concurrently performed within the 4 second perching flight. We validate this experiment with a 700 g ornithopter and demonstrate the first autonomous perching flight of a flapping-wing robot on a branch. This work paves the way towards the application of flapping-wing robots for long-range missions, bird observation, manipulation, and outdoor flight., Comment: IROS 2022 Workshop: Agile Robotics: Perception, Learning, Planning, and Control, 2022

An interlaced method to learn and control nonlinear system dynamics from a set of demonstrations is proposed, under a constrained optimization framework for the unsupervised learning process. The nonlinear system is modelled as a mixture of Gaussians and the Sontag's formula together with its associated Control Lyapunov Function is proposed for learning and control. Lyapunov stability and robustness in noisy data environments are guaranteed, as a result of the inclusion of control in the learning-optimization problem. The performances are validated through a well-known dataset of demonstrations with handwriting complex trajectories, succeeding in all of them and outperforming previous methods under bounded disturbances, possibly coming from inaccuracies, imperfect demonstrations or noisy datasets. As a result, the proposed interlaced solution yields a good performance trade-off between reproductions and robustness. The proposed method can be used to program nonlinear trajectories in robotic systems through human demonstrations., Comment: Preprint submitted to journal (under review). 25 pages, 6 figures, font 12pt

Flapping wings are a bio-inspired method to produce lift and thrust in aerial robots, leading to quiet and efficient motion. The advantages of this technology are safety and maneuverability, and physical interaction with the environment, humans, and animals. However, to enable substantial applications, these robots must perch and land. Despite recent progress in the perching field, flapping-wing vehicles, or ornithopters, are to this day unable to stop their flight on a branch. In this paper, we present a novel method that defines a process to reliably and autonomously land an ornithopter on a branch. This method describes the joint operation of a flapping-flight controller, a close-range correction system and a passive claw appendage. Flight is handled by a triple pitch-yaw-altitude controller and integrated body electronics, permitting perching at 3 m/s. The close-range correction system, with fast optical branch sensing compensates for position misalignment when landing. This is complemented by a passive bistable claw design can lock and hold 2 Nm of torque, grasp within 25 ms and can re-open thanks to an integrated tendon actuation. The perching method is supplemented by a four-step experimental development process which optimizes for a successful design. We validate this method with a 700 g ornithopter and demonstrate the first autonomous perching flight of a flapping-wing robot on a branch, a result replicated with a second robot. This work paves the way towards the application of flapping-wing robots for long-range missions, bird observation, manipulation, and outdoor flight.

The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability of a graph to contagion. This paper introduces a simple farthest-first traversal-based approximation algorithm for this problem over general graphs. We refer to this proposal as the Burning Farthest-First (BFF) algorithm. BFF runs in $O(n^3)$ steps and has an approximation factor of $3-2/b(G)$, where $b(G)$ is the size of an optimal solution. Despite its simplicity, BFF tends to generate near-optimal solutions when tested over some benchmark datasets; in fact, it returns similar solutions to those returned by much more elaborated heuristics from the literature.

In this paper, we present a novel estimation and control strategy to balance a formation of discrete-time oscillators on a circle. We consider the case in which each oscillator only gathers noisy proximity measurements, whose range is lower than the desired spacing along the circle, implying total disconnectedness of the balanced formation. These restrictions pose relevant challenges that are overcome through the symbiotic combination of an estimator that borrows tools from interval analysis and a three-level bang-bang controller. We prove that the formation can be balanced, with an accuracy that can be regulated by tuning a controller parameter. The effectiveness of the proposed strategy is further illustrated through a set of numerical simulations., Comment: 9 pages, 2 figures, 2 tables, provisionally accepted in Automatica