The advent of rotor-based hopping robots has created very capable hopping platforms with high agility and efficiency, and similar controllability, as compared to their purely flying quadrotor counterparts. Advances in robot performance have increased the hopping height to greater than 4 meters and opened up the possibility for more complex aerial trajectories (i.e., behaviors). However, currently hopping robots do not directly control their aerial trajectory or transition to flight, eliminating the efficiency benefits of a hopping system. Here we show a real-time, computationally efficiency, non-linear drag compensated, trajectory generation methodology and accompanying Lyapunov-based controller. The combined system can create and follow complex aerial trajectories from liftoff to touchdown on horizontal and vertical surfaces, while maintaining strick control over the orientation at touchdown. The computational efficiency provides broad applicability across all size scales of hopping robots while maintaining applicability to quadrotors in general.

Manipulation of Elasto-Flexible Cables with Single or Multiple UA Vs Chiara Gabellieri 1, Lars Teeuwen 1, Y aolei Shen 1, Antonio Franchi 1, 2 Abstract -- This work considers a large class of systems composed of multiple quadrotors manipulating deformable and extensible cables. The cable is described via a discretized representation, which decomposes it into linear springs interconnected through lumped-mass passive spherical joints. Sets of flat outputs are found for the systems. Numerical simulations support the findings by showing cable manipulation relying on flatness-based trajectories. Eventually, we present an experimental validation of the effectiveness of the proposed discretized cable model for a two-robot example. Moreover, a closed-loop controller based on the identified model and using cable-output feedback is experimentally tested. I NTRODUCTION AND R ELATEDW ORK Deformable object manipulation is an important recent development in aerial robotics with potential applications ranging from fire fighting [1], and in general the manipulation of fluid conduits [2], to waterway maintenance [3], e.g., in case of oil-spill events [4]. Y et, for the challenges it involves [5], deformable object manipulation is still regarded as an open problem.

For autonomous crane lifting, optimal trajectories of the crane are required as reference inputs to the crane controller to facilitate feedforward control. Reducing the unactuated payload motion is a crucial issue for under-actuated tower cranes with spherical pendulum dynamics. The planned trajectory should be optimal in terms of both operating time and energy consumption, to facilitate optimum output spending optimum effort. This article proposes an anti-swing tower crane trajectory planner that can provide time-energy optimal solutions for the Computer-Aided Lift Planning (CALP) system developed at Nanyang Technological University, which facilitates collision-free lifting path planning of robotized tower cranes in autonomous construction sites. The current work introduces a trajectory planning module to the system that utilizes the geometric outputs from the path planning module and optimally scales them with time information. Firstly, analyzing the non-linear dynamics of the crane operations, the tower crane is established as differentially flat. Subsequently, the multi-objective trajectory optimization problems for all the crane operations are formulated in the flat output space through consideration of the mechanical and safety constraints. Two multi-objective evolutionary algorithms, namely Non-dominated Sorting Genetic Algorithm (NSGA-II) and Generalized Differential Evolution 3 (GDE3), are extensively compared via statistical measures based on the closeness of solutions to the Pareto front, distribution of solutions in the solution space and the runtime, to select the optimization engine of the planner. Finally, the crane operation trajectories are obtained via the corresponding planned flat output trajectories. Studies simulating real-world lifting scenarios are conducted to verify the effectiveness and reliability of the proposed module of the lift planning system.

Trajectory generation for quadrotors with limited field-of-view sensors has numerous applications such as aerial exploration, coverage, inspection, videography, and target tracking. Most previous works simplify the task of optimizing yaw trajectories by either aligning the heading of the robot with its velocity, or potentially restricting the feasible space of candidate trajectories by using a limited yaw domain to circumvent angular singularities. In this paper, we propose a novel \textit{global} yaw parameterization method for trajectory optimization that allows a 360-degree yaw variation as demanded by the underlying algorithm. This approach effectively bypasses inherent singularities by including supplementary quadratic constraints and transforming the final decision variables into the desired state representation. This method significantly reduces the needed control effort, and improves optimization feasibility. Furthermore, we apply the method to several examples of different applications that require jointly optimizing over both the yaw and position trajectories. Ultimately, we present a comprehensive numerical analysis and evaluation of our proposed method in both simulation and real-world experiments.

Differential flatness enables efficient planning and control for underactuated robotic systems, but we lack a systematic and practical means of identifying a flat output (or determining whether one exists) for an arbitrary robotic system. In this work, we leverage recent results elucidating the role of symmetry in constructing flat outputs for free-flying robotic systems. Using the tools of Riemannian geometry, Lie group theory, and differential forms, we cast the search for a globally valid, equivariant flat output as an optimization problem. An approximate transcription of this continuum formulation to a quadratic program is performed, and its solutions for two example systems achieve precise agreement with the known closed-form flat outputs. Our results point towards a systematic, automated approach to numerically identify geometric flat outputs directly from the system model, particularly useful when complexity renders pen and paper analysis intractable.

Mechanical systems naturally evolve on principal bundles describing their inherent symmetries. The ensuing factorization of the configuration manifold into a symmetry group and an internal shape space has provided deep insights into the locomotion of many robotic and biological systems. On the other hand, the property of differential flatness has enabled efficient, effective planning and control algorithms for various robotic systems. Yet, a practical means of finding a flat output for an arbitrary robotic system remains an open question. In this work, we demonstrate surprising new connections between these two domains, for the first time employing symmetry directly to construct a flat output. We provide sufficient conditions for the existence of a trivialization of the bundle in which the group variables themselves are a flat output. We call this a geometric flat output, since it is equivariant (i.e. maintains the symmetry) and is often global or almost-global, properties not typically enjoyed by other flat outputs. In such a trivialization, the motion planning problem is easily solved, since a given trajectory for the group variables will fully determine the trajectory for the shape variables that exactly achieves this motion. We provide a partial catalog of robotic systems with geometric flat outputs and worked examples for the planar rocket, planar aerial manipulator, and quadrotor.

This paper presents a two-step algorithm for online trajectory planning in indoor environments with unknown obstacles. In the first step, sampling-based path planning techniques such as the optimal Rapidly exploring Random Tree (RRT*) algorithm and the Line-of-Sight (LOS) algorithm are employed to generate a collision-free path consisting of multiple waypoints. Then, in the second step, constrained quadratic programming is utilized to compute a smooth trajectory that passes through all computed waypoints. The main contribution of this work is the development of a flexible trajectory planning framework that can detect changes in the environment, such as new obstacles, and compute alternative trajectories in real time. The proposed algorithm actively considers all changes in the environment and performs the replanning process only on waypoints that are occupied by new obstacles. This helps to reduce the computation time and realize the proposed approach in real time. The feasibility of the proposed algorithm is evaluated using the Intel Aero Ready-to-Fly (RTF) quadcopter in simulation and in a real-world experiment.