We present an evolved steerable version of the single-tail Fish-&-Ribbon–Inspired Small Swimming Harmonic roBot (FRISSHBot), a 59-mg biologically inspired swimmer, which is driven by a new shape-memory alloy (SMA)-based bimorph actuator. The new FRISSHBot is controllable in the two-dimensional (2D) space, which enabled the first demonstration of feedback-controlled trajectory tracking of a single-tail aquatic robot with onboard actuation at the subgram scale. These new capabilities are the result of a physics-informed design with an enlarged head and shortened tail relative to those of the original platform. Enhanced by its design, this new platform achieves forward swimming speeds of up to 13.6 mm/s (0.38 Bl/s), which is over four times that of the original platform. Furthermore, when following 2D references in closed loop, the tested FRISSHBot prototype attains forward swimming speeds of up to 9.1 mm/s, root-mean-square (RMS) tracking errors as low as 2.6 mm, turning rates of up to 13.1 °/s, and turning radii as small as 10 mm.

This paper presents the VLEIBot*(Very Little Eel-Inspired roBot), a 45-mg/23-mm3microrobotic swimmer that is propelled by a bioinspired anguilliform propulsor. The propulsor is excited by a single 6-mg high-work-density (HWD) microactuator and undulates periodically due to wave propagation phenomena generated by fluid-structure interaction (FSI) during swimming. The microactuator is composed of a carbon-fiber beam, which functions as a leaf spring, and shape-memory alloy (SMA) wires, which deform cyclically when excited periodically using Joule heating. The VLEIBot can swim at speeds as high as 15.1 mm • s−1(0.33 Bl • s−1) when driven with a heuristically-optimized propulsor. To improve maneuverability, we evolved the VLEIBot design into the 90-mg/47-mm3VLEIBot+, which is driven by two propulsors and fully controllable in the two-dimensional (2D) space. The VLEIBot+can swim at speeds as high as 16.1 mm • s–1(0.35 Bl • s–1), when driven with heuristically-optimized propulsors, and achieves turning rates as high as 0.28 rad • s–1, when tracking path references. The measured root-mean-square (RMS) values of the tracking errors are as low as 4 mm.

We present model predictive selection (MPS), a new method for selecting the stable closed-loop (CL) equilibrium attitude-error quaternion (AEQ) of an uncrewed aerial vehicle (UAV) during the execution of high-speed yaw maneuvers. In this approach, we minimize the cost of yawing measured with a performance figure of merit (PFM) that takes into account both the aerodynamic-torque control input and attitude-error state of the UAV. Specifically, this method uses a control law with a term whose sign is dynamically switched in real time to select, between two options, the torque associated with the lesser cost of rotation as predicted by a dynamical model of the UAV derived from first principles. This problem is relevant because the selection of the stable CL equilibrium AEQ significantly impacts the performance of a UAV during high-speed rotational flight, from both the power and control-error perspectives. To test and demonstrate the functionality and performance of the proposed method, we present data collected during one hundred real-time high-speed yaw-tracking flight experiments. These results highlight the superior capabilities of the proposed MPS-based scheme when compared to a benchmark controller commonly used in aerial robotics, as the PFM used to quantify the cost of flight is reduced by 60.30 %, on average. To our best knowledge, these are the first flight-test results that thoroughly demonstrate, evaluate, and compare the performance of a real-time controller capable of selecting the stable CL equilibrium AEQ during operation.

We present a new millimeter-scale bimorph actuator for microrobotic applications, driven by feedforward controlled shape-memory alloy (SMA) wires. The device weighs 10 mg, measures 14 mm in length, and occupies a volume of 4.8 mm3, which makes it the lightest and smallest fully functional SMA-based bimorph actuator for microrobotics developed to date. The experimentally measured operational bandwidth is on the order of 20 Hz, and the unimorph and bimorph maximum low-frequency displacement outputs are on the order of 3.5 and 7 mm, respectively. To test and demonstrate the functionality and suitability of the actuator for microrobotics, we developed the Fish-&-Ribbon–Inspired Small Swimming Harmonic roBot (FRISSHBot). Loosely inspired by carangiformes, the FRISSHBot leverages fluid-structure interaction (FSI) phenomena to propel itself forward, weighs 30 mg, measures 34 mm in length, operates at frequencies of up to 4 Hz, and swims at speeds of up to 3.06 mm • s–1(0.09 Bl • s–1). This robot is the lightest and smallest swimmer with onboard actuation developed to date.

We present a new unimorph actuator for micro-robotics, which is driven by thin shape-memory alloy (SMA) wires. Using a passive-capillary-alignment technique and existing SMA-microsystem fabrication methods, we developed an actuator that is 7 mm long, has a volume of 0.45 mm3, weighs 0.96 mg, and can achieve operation frequencies of up to 40 Hz as well as lift 155 times its own weight. To demonstrate the capabilities of the proposed actuator, we created an 8-mg crawler, the MiniBug, and a bioinspired 56-mg controllable water-surface-tension crawler, the WaterStrider. The MiniBug is 8.5 mm long, can locomote at speeds as high as 0.76 BL/s (body-lengths per second), and is the lightest fully-functional crawling microrobot of its type ever created. The WaterStrider is 22 mm long, and can locomote at speeds of up to 0.28 BL/s as well as execute turning maneuvers at angular rates on the order of 0.144 rad/s. The WaterStrider is the lightest controllable SMA-driven water-surface-tension crawler developed to date.

We present a new method for synthesizing and implementing high-performancesix-degree-of-freedom($\boldsymbol{6}$-DOF) flight controllers for the Bee$^{++}$, an insect-scale flying robot driven by four independently-actuated flapping wings. Each wing of the Bee$^{++}$is installed with a preset orientation such that the stroke plane generated during flight is inclined, thus enabling reliable roll, pitch, and yaw torque generation. Leveraging this capability, we propose a Lyapunov-based nonlinear control architecture that enables closed-loop position and attitude regulation and tracking. The control algorithms presented in this article simultaneously stabilize position and attitude by independently varying the wingstroke amplitudes of the four flapping wings of the Bee$^{++}$. We use this particular control architecture to exemplify the process of controller synthesis and real-time implementation; however, the aerodynamic design of the Bee$^{++}$is compatible with a great variety of control structures and performance objectives. As a main result, we present the first set of experimental data demonstrating sustained and robust high-performance tracking of a$\boldsymbol{6}$-DOF reference signal during flight at the insect scale, which has been a long-standing control problem in the field of flapping-wing microrobotics. Furthermore, using data obtained through a series of systematic flight tests, we show that the Bee$^{++}$can achieve the highest$\boldsymbol{6}$-DOF performance ever recorded for an insect-scale flapping-wing flying robot during sustained flight.

We present a study of the dynamics and control of a 28-gram quadrotor during the execution of aerobatic maneuvers in the presence of propeller-aerodynamic-coefficient and torque-latency time-variations. First, through a momentum-theory-based analysis of the flow field surrounding the robot during aerobatic flight, we develop a dynamic linear time-varying (LTV) description of the torque acting on the flyer in which both considered effects explicitly appear as distinct mathematical terms. Then, an adaptive control scheme, composed of a backstepping controller and a modified recursive least-squares (RLS) estimator, is designed to counteract the negative effects produced by the time-varying dynamics of the torque that drives the flyer. The suitability and efficacy of the proposed methods are demonstrated through real-time flight experiments in which the quadrotor autonomously performs three different types of aerobatic maneuvers: triple flips, Pugachev's Cobras and mixed flips. Furthermore, analyses of the experimental data compellingly show that the proposed control scheme consistently improves the performance of the aerial vehicle during aerobatic flight, compared to those achieved by using a high-performance linear time-invariant (LTI) controller that does not account for time-varying torque generation.

The dynamics of quadrotors are affected by time-varying torque latency, which can greatly alter the stability robustness and performance of the closed-loop control schemes employed for flight; this issue is especially relevant during the execution of aerobatic maneuvers such as high-speed multi-flips. To address this problem, we propose two controller synthesis methods associated with two different modeling approaches. In the first approach, we describe torque latency with a linear time-invariant (LTI)model, identified through ground experiments, which is then used to design a backstepping-based nonlinear controller. In the second approach, we employ an improved linear time-varying (LTV)model with a priori unknown parameters, which is used to synthesize and implement a novel nonlinear adaptive control scheme updated in real time using the recursive least-squares (RLS)algorithm. Empirical observations suggest that the torque delay affecting the system depends on the time-varying angular speed of the flyer and its derivative. This phenomenon is explained by the fact that the aerodynamic forces produced by, and acting on, the rotating propellers vary with the local velocity of the incident flows. Hence, in the proposed adaptive structure, we define the parameters of the LTV latency model as linear functions of the angular speed reference and its derivative. Experimental results compellingly demonstrate the efficacy of the methods introduced in this paper; compared to the highperformance linear controller in [1]-[3], the backstepping-based control scheme and adaptive controller decrease the average root mean square (RMS)value of the control error by 17.82 % and 38.42 %, respectively.

We present a new experimental method for the generation and real-time implementation of high-speed aerobatic maneuvers, including multiple flips, on a 19-gram autonomous quadrotor. A key element in the proposed approach is the design and experimental tuning of a gain scheduling control strategy in which two linear time-invariant (LTI) controllers are alternatingly activated and deactivated to switch between a normal flight mode and an aerobatic mode, enabling the flyer to perform consecutive multiple flips in a robustly stable manner. The implementation of the controllers is done using on-board power, sensors and computing capabilities, so that the quadrotor remains fully autonomous during flight. Notably, the attainment of autonomy, using real-time control, is made possible by the development of a new method for speed planning based on cubic functions, the geometric generalization of the notion of multi-flip and the empirical identification of the flyer's dynamics, required for trajectory generation and controller synthesis. Compelling experimental results demonstrate the suitability of the proposed approach. In particular, we present maneuvers that include consecutive single, double, and triple flips about the flyer's roll principal axis and a non-principal axis. To the best of our knowledge, to this date, the flyer used in this research is the smallest controlled quadrotor to have autonomously accomplished three consecutive flips while remaining stable.

We present experimental results on the controlled vertical flight of a flapping-wing flying microrobot, in which for the first time an on-board sensing system is used for measuring the microrobot's altitude for feedback control. Both the control strategy and the sensing system are biologically inspired. The control strategy relies on amplitude modulation mediated by optical flow. The research presented here is a key step toward achieving the goal of complete autonomy for flying microrobots, since this demonstrates that strategies for controlling flapping-wing microrobots in vertical flight can rely on optical flow sensors.

The Harvard RoboBee is the first insect-scale cflapping-wing robot weighing less than 100 mg that is able to lift its own weight. However, when flown without guide wires, this vehicle quickly tumbles after takeoff because of instability in its dynamics. Here, we show that by adding aerodynamic dampers, we can can alter the vehicle's dynamics to stabilize its upright orientation. We provide an analysis using wind tunnel experiments and a dynamic model. We demonstrate stable vertical takeoff, and using a marker-based external camera tracking system, hovering altitude control in an active feedback loop. These results provide a stable platform for both system dynamics characterization and unconstrained active maneuvers of the vehicle and represent the first known hovering demonstration of an insect-scale flapping-wing robot.

Abstract — Flapping-wing robots typically include numerous nonlinear elements, such as nonlinear geometric and aerodynamic components. For an insect-sized flapping-wing micro air vehicle (FWMAV), we show that a linearized model is sufficient to predict system behavior with reasonable accuracy over a large operating range, not just locally around the linearization state. The theoretical model is verified against an identified model from a prototype robotic fly and implications for vehicle design are discussed. I.

This paper addresses the issues relating to the enforcement of robust BIBO (l∞) stability when implementing the adaptive inverse control (AIC) scheme for noise cancelation. In this scheme, an adaptive FIR-form filter is added to a closed-loop system in order to reduce the output error caused by external disturbances. A Small-Gain-Theorem-based sufficient stability condition, which accounts for the feedback interaction between the time-varying adaptive filter and the unmodeled dynamics existing in the closed-loop plant, is derived. This condition leads to the formulation of a constrained convex optimization problem solvable recursively using a modified RLS algorithm that preserves the converge properties of the original RLS algorithm.