# Glossary for Pipenberg et al. (2019): Design and Fabrication of the Mars Helicopter

Glossary for Pipenberg et al. (2019): Design and Fabrication of the Mars Helicopter Rotor, Airframe, and Landing Gear Systems

2 degree-of-freedom (DoF)

Degrees of Freedom (DoF) is probably the most important concept in robotics.   It can refer to:

• How many independent values you need to characterize the state of the robot; for example: X, Y, Z (position) and roll, pitch, heading (angles) would be six DoF.
• The number of independent actuators (like joints or motors) onboard the vehicle.  For example, a quadcopter has four motors, each of which must be controlled to keep the vehicle aloft.
• The number of values provided by a sensor.  For example, an IMU is often described as “6 DoF” (gyrometer X, Y, Z; accelerometer X, Y, Z) or “9 DoF” (gyrometer X, Y, Z; accelerometer X, Y, Z, magnetometer X, Y, Z).
• The number of independent mechanisms  you can use to control the robot or vehicle.   For example, most cars have a steering wheel, gas pedal, and break, three DoF control.  For radio-controlled vehicles (like this toy helicopter), control DoF is typically called “channels”.

analytical model: a set of equations (like the ones you learned in high-school physics and calculus) for modeling a system.  Once the system becomes complicated enough, an analytical model may become impractical or impossible to derive.  In this case, some sort of simulation (like a smaller scale model or software simulation) is often used.

avionics: a portmanteau (word combination like cheeseburger) for aviation electronics.

brushless (motor):  an electric motor that provides superior performance and durability by minimizing contact between the moving parts and the stationary parts.  The most common type of motor found in drones (see photo)

camber line: a line halfway between the upper and lower parts of a rotor blade or airplane wing, illustrating the curvature of the blade/wing (see illustration)

chord:  the distance between the leading edge (front) and trailing edge (back) of a rotor blade (see illustration)

co-axial: on the same axis (shaft).  Unlike a traditional helicopter that has a tail-rotor to counter spin, or a multi-rotor vehicle (quadcopter / drone), the Mars helicopter has both rotors on the same axis and must therefore spin the rotors in opposite directions.

discretized mass model: the “Lego bricks” approach to modeling a complex physical system like a rotor blade, weather patterns, etc.  Instead of trying to model the whole system, it’s broken down into a manageable set of components (elements) each of which can be modeled individually and related to the behavior of nearby components using Finite Element Analysis.

Finite Element Analysis: see discretized mass model, and check out this half-minute introductory video.

geared DC motor: see servo

gimbal:  a device for mounting a camera that uses motors and an IMU to stabilize the camera and keep it pointing in a desired direction no matter what the vehicle is doing (see image).

high-bandwidth control: as with your internet connection, high-bandwidth simply means fast.  Also called closed-loop control, and specifically PID Control, which we will discuss at length.

high-modulus: stiff, resistant to bending (see Young’s Modulus).

IMU (Inertial Measurement Unit): a device consisting of one or more sensors used for determining the state (orientation, and perhaps altitude) of an aerial vehicle.  A typical IMU consists of a gyrometer (a.ka. gyroscope) measuring the rate of angular rotation and accelerometer measuring the angular orientation).  Many IMUs also provide a magnetometer (compass) for determining heading (direction) and a barometer for determining altitude above sea-level.  Thanks to advances modern semiconductor (MEMS) technology driven by smartphones, a typical IMU is about the size of the fingernail on your little finger (see image).

laminar flow: See Reynolds Number.

lift coefficient: a dimensionless (having no units like meters/second, kilograms, etc.) measurement specifying how much lift is provided by a given rotor, propeller, etc.  For example, this figure shows how the lift coefficient varies with the rotor blade’s angle of attack.  (Question: why does the lift stop going up after a certain angle?)

limiting case: when modeling a system, as in life, it is safer to err on the side of caution; i.e., to prepare for a situation that is more extreme than what you’re actually likely to encounter.  So, for the Mars lander, concrete was used to simulate bedrock, and sand to simulate gravel.

pitch (angle of attack): refers to both (1) the angle (twist) of the blade of a rotor and (2) the nose-down / nose-up orientation of the vehicle.

rangefinder:  Any sensor providing information on the distance between the vehicle and another object.  Typically the other object is the ground, in which case the rangefinder helps determine the vehicle’s AGL (Above-Ground-Level) altitude.  Traditional rangefinders used SONAR (ultrasonic sound waves) like a submarine, which places speed-of-sound limitations on performance.  More modern rangefinders use infrared (light waves) for faster response times.  (See this image for the state-of-the-art).

Reynolds number: a dimensionless (having no units like meters/second, kilograms, etc.) measurement specifying the degree of laminar (smooth) versus turbulent (rough) flow over a surface like an airplane wing, rotor blade, etc.  Specifically, the Reynolds number predicts the point at which the transition from laminar to turbulent flow takes place.  Higher Reynolds number => more turbulent.

rotor: the general term for a pair of blades that spin to provide lift to an aerial vehicle.  Unlike the propellers used on a traditional quadcopter, which consist of a single piece of carbon fiber, nylon, etc., the Mars helicopter has variable-pitch rotors.  Hence, it is considered inaccurate to refer to them as propellers.

servo: a geared motor that can be set to a fixed position for use for controlling a robot’s steering or limbs, or adjusting a swashplate (see photo)

swashplate:  a device mounted below a rotor that can be manipulated to change the pitch (angle)of the rotor blade, enabling forward/back (pitch) and left/right (roll) movement of a helicopter (see animation)

unstable in open-loop: refers to the fact that — unlike a radio-controlled airplane or car — a multi-rotor vehicle will become unstable (flip over and crash) if controlled only by an open-loop controller (human being with a joystick). This instability is what requires the use of an IMU.