Closed-loop nonlinear optimal control design for flapping-wing flying robot (1.6 m wingspan) in indoor confined space: Prototyping, modeling, simulation, and experiment

This is an open access article under the CC BY license (http://creativecommons.org/ licenses/by/4.0/).The flapping-wing technology has emerged recently in the application of unmanned aerial robotics for autonomous flight, control, inspection, monitoring, and manipulation. Despite the advances in applications and outdoor manual flights (open-loop control), closed-loop control is yet to be investigated. This work presents a nonlinear optimal closed-loop control design via the state-dependent Riccati equation (SDRE) for a flapping-wing flying robot (FWFR). Considering that the dynamic modeling of the flapping-wing robot is complex, a proper model for the implementation of nonlinear control methods is demanded. This work proposes an alternative approach to deliver an equivalent dynamic for the translation of the system and a simplified model for orientation, to find equivalent dynamics for the whole system. The objective is to see the effect of flapping (periodic oscillation) on behavior through a simple model in simulation. Then the SDRE controller is applied to the derived model and implemented in simulations and experiments. The robot bird is a 1.6 m wingspan flapping-wing system (six-degree-of-freedom robot) with four actuators, three in the tail, and one as the flapping input. The underactuated system has been controlled successfully in position and orientation. The control loop is closed by the motion capture system in the indoor test bed where the experiments of flight have been successfully done

A search algorithm for constrained engineering optimization and tuning the gains of controllers

In this work, the application of an optimization algorithm is investigated to optimize static and dynamic engineering problems. The methodology of the approach is to generate random solutions and find a zone for the initial answer and keep reducing the zones. The generated solution in each loop is independent of the previous answer that creates a powerful method. Simplicity as its main advantage and the interlaced use of intensification and diversification mechanisms--to refine the solution and avoid local minima/maxima--enable the users to apply that for a variety of problems. The proposed approach has been validated by several previously solved examples in structural optimization and scored good results. The method is also employed for dynamic problems in vibration and control. A modification has also been done on the method for high-dimensional test functions (functions with very large search domains) to converge fast to the global minimum or maximum; simulated for several well-known benchmarks successfully. For validation, a number of 9 static and 4 dynamic constrained optimization benchmark applications and 32 benchmark test functions are solved and provided, 45 in total. All the codes of this work are available as supplementary material in the online version of the paper on the journal website

Gravity compensation and optimal control of actuated multibody system dynamics

This work investigates the gravity compensation topic, from a control perspective. Thegravity could be levelled by a compensating mechanical system or in the control law, suchas proportional derivative (PD) plus gravity, sliding mode control, or computed torquemethod. The gravity compensation term is missing in linear and nonlinear optimal con-trol, in both continuous- and discrete-time domains. The equilibrium point of the controlsystem is usually zero and this makes it impossible to perform regulation when the desiredcondition is not set at origin or in other cases, where the gravity vector is not zero at theequilibrium point. The system needs a steady-state input signal to compensate for the grav-ity in those conditions. The stability proof of the gravity compensated control law basedon nonlinear optimal control and the corresponding deviation from optimality, with proof,are introduced in this work. The same concept exists in discrete-time control since it usesanalog to digital conversion of the system and that includes the gravity vector of the sys-tem. The simulation results highlight two important cases, a robotic manipulator and atilted-rotor hexacopter, as an application to the claimed theoretical statements.GRIFFIN ERC-2017-Advanced Grant, Action: 788247EU H2020 AERIAL-CORE project contract 871479EU H2020 HYFLIERS project 77941

Experimental method for perching flapping-wing aerial robots

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, 202

A benchmark mechatronics platform to assess the inspection around pipes with variable pitch quadrotor for industrial sites

Article number 102641This paper investigates the inspection-of-pipe topic in a new framework, by rotation around a pipe, peculiar to industrial sites and refineries. The evolution of the ultimate system requires prototype design and preliminary tests. A new benchmark has been designed and built to mimic the rotation around a pipe, with the main purpose of assessing the different types of rotors and control systems. The benchmark control system presents a mechatronics package including mechanical design and machining, electronics and motor drive, motor-blade installation, computer programming, and control implementation. The benchmark is also modular, working with two modes of one- and two-degree-of-freedom (DoF), easily interchangeable. To cover a full rotation, conventional fixed-pitch drones fail to provide negative thrusts; nonetheless, variable-pitch (VP) rotor quad- copters can produce that in both directions. A closed-loop nonlinear optimal method is chosen as a controller, so- called, “the state-dependent Riccati equation (SDRE)” approach. Optimal control policies are challenging for experimentation though it has been successfully done in this report. The advantage of the VP is also illustrated in a rotation plus radial motion in comparison with fixed-pitch rotors while a wind gust disturbs the inspection task. The proposed VP system compensated the disturbance while the fixed pitch was pushed away by the wind gust. The solution methods to the SDRE were mixed, a closed-form exact solution for the one-DoF system, and a numerical one for the two-DoF. Solving the Riccati online in each time step is a critical issue that was effectively solved by the implementation approach, through online communication with MATLAB software. Both simula- tions and experiments have been performed along with a discussion to prove the application of VP systems in rotary-motion pipe inspectionEuropean Union (UE). H2020 779411Agencia Estatal de Investigación española RTI2018-102224-B-I0

A 79.7g Manipulator Prototype for E-Flap Robot: A Plucking-Leaf Application

The manipulation capabilities of flapping-wing flying robots (FWFRs) is a problem barely studied. This is a direct consequence of the load-carrying capacity limitation of the flapping-wing robots. Ornithopters will improve the existent multirotor unmanned aerial vehicles (UAVs) since they could perform longer missions and offer a safe interaction in proximity to humans. This technology also opens the possibility to perch in some trees and perform tasks such as obtaining samples from nature, enabling biologists to collect samples in remote places, or assisting people in rescue missions by carrying medicines or first-aid kits. This paper presents a very lightweight manipulator (79.7g) prototype to be mounted on an ornithopter. The distribution of the mass on the flapping-wing robot is sensitive and an extra lumped mass far from the center-of-mass (CoM) of the robot deteriorates the flight stability. A configuration was proposed to avoid changing the CoM. Flight experiments show that adding the arm to the robot only moved the CoM 6mm and the performance of the flight with the manipulator has been satisfactory. Plucking leaf is chosen as an application to the designed system and several experimental tests confirmed successful sampling of leaves by the prototype

How ornithopters can perch autonomously on a branch

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

Equivalent Vertical Dynamics of Flapping-Wing Flying Robot in Regulation Control: Displacement Transmissibility Ratio

This paper presents an equivalent dynamic model for vertical regulation control of a flapping-wing flying robot. The model is presented based on the data of a series of flight experiments for an available platform. The system shows oscillations in motion in all experiments with an approximate frequency between [3. 5, 4. 5](Hz), changing within a limited range. The behavior of the equivalent model represents a system with base excitation. The displacement transmissibility ratio (TR) is found for the model to investigate the oscillatory behavior in the system during the flight. Reduction of the oscillations through the transmissibility ratio will decrease the uncertainty in flight and consequently, that could increase the success rate of perching on a branch (now it has a 10 - 15(cm) uncertain periodic motion); perching needs precision on the last meter approaching phase. An analytical expression for TR is presented which is used for parameter selection, tuning, and selection of the flapping frequency, as the base excitation source. The study shows that the robot works in a proper zone of the frequency ratio, and also, the sensitivity of the TR is high concerning the changes in the stiffness constant

A proportional closed-loop control for equivalent vertical dynamics of flapping-wing flying robot

The closed-loop position control of a flapping-wing flying robot (FWFR) is a challenging task. A complete six-degree-of-freedom (DoF) modeling and control design is preferable though that imposes complexity on the procedure and analysis of the oscillations in the trajectory. Another approach could be studying independent state variables of the system and designing a controller for them. This will provide the possibility of a better understanding of the dynamic, comparing to experimental data, then use this information for moving forward to complete 6-DoF modeling. In this work, a simple linear proportional closed-loop controller is proposed and analyzed for an equivalent dynamic model of the flapping-wing flying robot. The equivalent dynamic modeling considers the flapping motion as a base excitation that disturbs the system in oscillatory behavior. The frequency of the oscillation and data of the motion was obtained from previous experimental results and used in the modeling. The designed controller performed the regulation task easily and regulated the system to a series of set-point control successfully. The motivation for the selection of a proportional control is to keep the design as simple as possible to analyze the excitation and behavior of the flapping more precisely. A discussion on the transient and steady-state flight and the role of control design on them have been presented in this work