Mark W. Mueller

Stability and control of a quadrocopter despite the complete loss of one, two, or three propellers

This paper presents periodic solutions for a quadrocopter maintaining a height around a position in space despite having lost a single, two opposing, or three propellers. In each case the control strategy consists of the quadrocopter spinning about a primary axis, fixed with respect to the vehicle, and tilting this axis for translational control. A linear, timeinvariant description of deviations from the attitude equilibrium is derived, allowing for a convenient cascaded control design. The results for the cases of losing one and two propellers are validated in experiment, while the case of losing three propellers is validated in a nonlinear simulation. These results have application in multicopter fault-tolerant control design, and also point to possible design directions for novel flying vehicles.

A computationally efficient algorithm for state-to-state quadrocopter trajectory generation and feasibility verification

An algorithm is proposed allowing for the rapid generation and evaluation of quadrocopter state interception trajectories. These trajectories are from arbitrary initial states to final states defined by the vehicle position, velocity and acceleration with a specified end of time. Sufficient criteria are then derived allowing trajectories to be tested for feasibility with respect to thrust and body rates. It is also shown that the range of a linear combination of the vehicle state can be solved for in closed form, useful e.g. for testing that the position remains within a box. The algorithm is applied by revisiting the problem of finding a trajectory to hit a ball towards a target with a racket attached to a quadrocopter. The trajectory generator is used in a model predictive control like strategy, where thousands of trajectories are generated and evaluated at every controller update step, with the first input of the optimal trajectory being sent to the vehicle. It is shown that the method can generate and evaluate on the order of one million trajectories per second on a standard laptop computer.

Fusing ultra-wideband range measurements with accelerometers and rate gyroscopes for quadrocopter state estimation

A state estimator for a quadrocopter is presented, using measurements from an accelerometer, angular rate gyroscope, and a set of ultra-wideband ranging radios. The estimator uses an extended aerodynamic model for the quadrocopter, where the full 3D airspeed is observable through accelerometer measurements. The remaining quadrocopter states, including the yaw orientation, are rendered observable by fusing ultra-wideband range measurements, under the assumption of no wind. The estimator is implemented on a standard microcontroller using readily-available, low-cost sensors. Performance is experimentally investigated in a variety of scenarios, where the quadrocopter is flown under feedback control using the estimator output.

Relaxed hover solutions for multicopters

This paper presents a relaxed definition of hover for multicopters with propellers pointing in a common direction. These solutions are found by requiring that the multicopter remain substantially in one position, and that the solutions be constant when expressed in a coordinate system attached to the vehicle. The vehicle’s angular velocity is then shown to be either zero or parallel to gravity. The controllability of a vehicle’s attitude about these solutions is then investigated. These relaxed hover solutions may be applied as an algorithmic failsafe, allowing, for example, a quadrocopter to fly despite the complete loss of one, two, or three of its propellers. Experimental results validate the quadrocopter failsafe for two types of failure (a single propeller and two opposing propellers failing), and a nonlinear simulation validates the remaining two types of failure (two adjacent and three propellers failing). The relaxed hover solutions are also shown to allow a multicopter to maintain flight in spite of extreme center of mass offsets. Finally, the design and experimental validation of three novel vehicles is presented.

A Computationally Efficient Motion Primitive for Quadrocopter Trajectory Generation

A method is presented for the rapid generation and feasibility verification of motion primitives for quadrocopters and similar multirotor vehicles. The motion primitives are defined by the quadrocopters initial state, the desired motion duration, and any combination of components of the quadrocopters position, velocity, and acceleration at the motions end. Closed-form solutions for the primitives are given, which minimize a cost function related to input aggressiveness. Computationally efficient tests are presented to allow for rapid feasibility verification. Conditions are given under which the existence of feasible primitives can be guaranteed a priori . The algorithm may be incorporated in a high-level trajectory generator, which can then rapidly search over a large number of motion primitives which would achieve some given high-level goal. It is shown that a million motion primitives may be evaluated and compared per second on a standard laptop computer. The motion primitive generation algorithm is experimentally demonstrated by tasking a quadrocopter with an attached net to catch a thrown ball, evaluating thousands of different possible motions to catch the ball.

Covariance Correction Step for Kalman Filtering with an Attitude

Redundant attitude representations are often used in Kalman filters for estimating dynamic states that include an attitude. A minimal three-element attitude deviation is combined with a reference attitude, where the deviation is included in the filter state and has an associated covariance estimate. This paper derives a reset step that adjusts the covariance matrix when information is moved from the attitude deviation to the reference attitude. When combined with the extended or unscented Kalman filter prediction and measurement steps, the reset allows one to easily construct a Kalman filter for a system for which the state includes an attitude. This algorithm is closely related to (and a correction to) the multiplicative extended Kalman filter or the unscented quaternion estimator, depending on whether the reset is combined with an extended or unscented Kalman filter. In comparison to the multiplicative extended Kalman filter, it is more general and includes a reset after the measurement update, as well ...

A controllable flying vehicle with a single moving part

This paper presents the “monospinner”: a mechanically simple flying vehicle with only one moving part. The vehicle is shown to be controllable in three translational degrees of freedom and two rotational degrees of freedom. The vehicle has a single scalar control input, the thrust magnitude, and is controlled by a cascaded control strategy with an inner attitude controller and an outer position controller. The vehicle design is chosen based on two robustness metrics: the ability to maintain hover under perturbations and the probability of input saturation based on a stochastic model. The resulting mechanical and control designs are experimentally demonstrated, where it is also shown that the vehicle is sufficiently robust to achieve hover after being thrown into the air.