Robert Niemiec

Control and Performance of a Reconfigurable Multicopter

This paper presents a concept of a multicopter that can be reconfigured between a quadcopter, hexacopter, octocopter, and decacopter. The controls for each of the configurations are identified, and for the configurations with control redundancy, the power optimal controls are presented. A dynamic simulation model is implemented and used to compare the various configurations. The maximum useful weights of the octocopter, hexacopter, and quadcopter were 76.5%, 53.1%, and 29.7% that of the decacopter, respectively. Over a range of useful weights, the decacopter required the least power when the useful weight was greater than around 23% of its maximum, due to lower induced and profile power requirements of the lighter-loaded, slower-spinning rotors. At lower useful weights, smaller configurations required less power due to their lower empty weight. Increasing the number of rotors increased the maximum hover endurance, cruise endurance, and maximum range. Maximum moments and accelerations produced by each airc...

Multirotor Controls, Trim, and Autonomous Flight Dynamics of Plus- and Cross-Quadcopters

This paper examines a quadcopter operating in the plus and cross configurations. The plus configuration generates a yaw moment when a pitch/roll control input is introduced; but, for the cross configuration, the pitch/roll control is decoupled from yaw. Although the collective revolutions-per-minute control requirement, pitch attitude, and power requirement versus flight speed are identical for both configurations, in forward flight, the plus configuration requires a larger pitch control input because it uses only two rotors and a compensatory yaw control input. Quadcopters display two oscillatory modes in hover, a longitudinal phugoid mode (coupling longitudinal translation and pitch), and a lateral phugoid mode (coupling lateral translation and roll). Both modes are stable, and their poles are coincident in hover. In forward flight, the modes are distinct, and the frequency and damping of both modes increase. The nature of the lateral phugoid mode in forward flight is very similar to hover, but the long...

Design studies on cellular structures with pneumatic artificial muscle inclusions for modulus variation

This article presents a variable modulus cellular structure based on a hexagonal unit cell with pneumatic artificial muscle inclusions. The cell is pin-jointed, loaded in the horizontal direction, with three pneumatic artificial muscles (one vertical pneumatic artificial muscle and two horizontal pneumatic artificial muscles) oriented in an “H” configuration between the vertices of the cell. A method for calculation of the hexagonal cell modulus is introduced, as is an expression for the balance of tensile forces between the horizontal and vertical pneumatic artificial muscles. Simulation is then compared to experimental measurement of the unit cell modulus in the horizontal direction over a pressure range of 682 kPa, and an increase in cell modulus of 200% is demonstrated experimentally. A design study considering parametric variation in cell angle, vertical to inclined wall length ratio, and pneumatic artificial muscle contraction ratios shows that changes in modulus of over 1000% are possible when the pneumatic artificial muscles are pressurized to 1992 kPa. This concept provides a way to create a structural unit cell whose in-plane modulus can be tuned based on the orientation of pneumatic artificial muscles within the cell and the pressure supplied to the individual muscles.

Reversible airfoils for stopped rotors in high speed flight

This study starts with the design of a reversible airfoil rib for stopped-rotor applications, where the sharp trailing-edge morphs into the rounded leading-edge, and vice-versa. A NACA0012 airfoil is approximated in a piecewise linear manner and straight, rigid outer profile links used to define the airfoil contour. The end points of the profile links connect to control links, each set on a central actuation rod via an offset. Chordwise motion of the actuation rod moves the control and the profile links and reverses the airfoil. The paper describes the design methodology and evolution of the final design, based on which two reversible airfoil ribs were fabricated and used to assemble a finite span reversible rotor/wing demonstrator. The profile links were connected by Aluminum strips running in the spanwise direction which provided stiffness as well as support for a pre-tensioned elastomeric skin. An inter-rib connector with a curved-front nose piece supports the leading-edge. The model functioned well and was able to reverse smoothly back-and-forth, on application and reversal of a voltage to the motor. Navier–Stokes CFD simulations (using the TURNS code) show that the drag coefficient of the reversible airfoil (which had a 13% maximum thickness due to the thickness of the profile links) was comparable to that of the NACA0013 airfoil. The drag of a 16% thick elliptical airfoil was, on average, about twice as large, while that of a NACA0012 in reverse flow was 4–5 times as large, even prior to stall. The maximum lift coefficient of the reversible airfoil was lower than the elliptical airfoil, but higher than the NACA0012 in reverse flow operation.

Variable modulus cellular structures using pneumatic artificial muscles

This paper presents a novel variable modulus cellular structure based on a hexagonal unit cell with pneumatic artificial muscle (PAM) inclusions. The cell considered is pin-jointed, loaded in the horizontal direction, with three PAMs (one vertical PAM and two horizontal PAMs) oriented in an “H” configuration between the vertices of the cell. A method for calculation of the hexagonal cell modulus is introduced, as is an expression for the balance of tensile forces between the horizontal and vertical PAMs. An aluminum hexagonal unit cell is fabricated and simulation of the hexagonal cell with PAM inclusions is then compared to experimental measurement of the unit cell modulus in the horizontal direction with all three muscles pressurized to the same value over a pressure range up to 758 kPa. A change in cell modulus by a factor of 1.33 and a corresponding change in cell angle of 0.41° are demonstrated experimentally. A design study via simulation predicts that differential pressurization of the PAMs up to 2068 kPa can change the cell modulus in the horizontal direction by a factor of 6.83 with a change in cell angle of only 2.75°. Both experiment and simulation show that this concept provides a way to decouple the length change of a PAM from the change in modulus to create a structural unit cell whose in-plane modulus in a given direction can be tuned based on the orientation of PAMs within the cell and the pressure supplied to the individual muscles.

Trim Analysis of a Classical Octocopter After Single-Rotor Failure

The performance of an octocopter with single rotor failure is examined in hover and forward flight conditions. The aircraft model uses blade element theory coupled with a finite-state dynamic inflow model to determine rotor aerodynamic forces (thrust, drag, and side-force) and moments (rolling moment, pitching moment, and torque). Failure of various rotors is considered in both flight conditions and an understanding is developed of how the aircraft trims post-failure in terms of multirotor controls defined for the aircraft. In hover, the baseline octocopter trims with all rotors operating at the same rotational speed. When a rotor fails, trim solutions exist that utilize the original reactionless controls of the aircraft to drive the commanded thrust of the failed rotor to zero. The combination of reactionless controls used varies depending on the position of the failed rotor. Post-failure, the primary and reactionless multirotor controls are redefined for each rotor in terms of the original multirotor controls. In forward flight, rotor failure is recovered in a similar manner to the hover case, with additional inputs required to compensate for the rotor hub moments and in-plane forces that were not present in hover. Overall, trim solutions exist for any single rotor failure in both hover and forward flight at 10 m/s. In hover, rotor failure requires an additional 10.7% increase in power to trim, in forward flight this penalty is found to range between 7.7 and 13% depending on the rotor that has failed.

Leading- and Trailing-Edge Reversal of a Cambered Airfoil for Stopped Rotors

For helicopters in very high-speed flight there is interest in stopping the rotor and having it operate as a fixed-wing. However, with conventional airfoils, one half of the stopped rotor/wing would be in reverse flow. To overcome this challenge, this paper focuses on airfoil reversal, where the sharp trailing-edge morphs into the rounded leading-edge, and vice-versa. Extending on a previous study that reversed symmetric airfoils, the current paper presents a design methodology and solution for reversal of a cambered airfoil. Navier Stokes CFD simulation results show that rather than using straight links to approximate a reference airfoil profile, curved links that exactly represent the nose to mid-chord section reduce aerodynamic penalties considerably despite the “bumps” they produce over the trailing-edge region. The aerodynamic performance of a curved-link reversible NACA 23012 was seen to be close to that of the reference NACA 23012. A curved-link reversible NACA 4-digit airfoil, with the same thickness and camber as the Fairchild Reverse Velocity Rotor (RVR) airfoil performed significantly better, aerodynamically, than the RVR airfoil in reverse flow. The study examined actuator force requirement, and showed that both the magnitude and direction of the actuator force required to resist the aerodynamic loads vary depending on the airfoil angle of attack and the internal mechanism design.