This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.

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Nonlinear Complementary Filters on the Special Orthogonal Group

This paper provides new results for the tracking control of a quadrotor unmanned aerial vehicle (UAV). The UAV has four input degrees of freedom, namely the magnitudes of the four rotor thrusts, that are used to control the six translational and rotational degrees of freedom, and to achieve asymptotic tracking of four outputs, namely, three position variables for the vehicle center of mass and the direction of one vehicle body-fixed axis. A globally defined model of the quadrotor UAV rigid body dynamics is introduced as a basis for the analysis. A nonlinear tracking controller is developed on the special Euclidean group SE(3) and it is shown to have desirable closed loop properties that are almost global. Several numerical examples, including an example in which the quadrotor recovers from being initially upside down, illustrate the versatility of the controller.

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Geometric tracking control of a quadrotor UAV on SE(3)

This paper provides new results for control of complex flight maneuvers for a quadrotor unmanned aerial vehicle (UAV). The flight maneuvers are defined by a concatenation of flight modes or primitives, each of which is achieved by a nonlinear controller that solves an output tracking problem. A mathematical model of the quadrotor UAV rigid body dynamics, defined on the configuration space $\SE$, is introduced as a basis for the analysis. The quadrotor UAV has four input degrees of freedom, namely the magnitudes of the four rotor thrusts; each flight mode is defined by solving an asymptotic optimal tracking problem. Although many flight modes can be studied, we focus on three output tracking problems, namely (1) outputs given by the vehicle attitude, (2) outputs given by the three position variables for the vehicle center of mass, and (3) output given by the three velocity variables for the vehicle center of mass. A nonlinear tracking controller is developed on the special Euclidean group $\SE$ for each flight mode, and the closed loop is shown to have desirable closed loop properties that are almost global in each case. Several numerical examples, including one example in which the quadrotor recovers from being initially upside down and another example that includes switching and transitions between different flight modes, illustrate the versatility and generality of the proposed approach.

Geometric Tracking Control of a Quadrotor UAV on SE(3)

Formation control analysis and design problems for unmanned aerial vehicle (UAV) swarm systems to achieve time-varying formations are investigated. To achieve predefined time-varying formations, formation protocols are presented for UAV swarm systems first, where the velocities of UAVs can be different when achieving formations. Then, consensus-based approaches are applied to deal with the time-varying formation control problems for UAV swarm systems. Necessary and sufficient conditions for UAV swarm systems to achieve time-varying formations are proposed. An explicit expression of the time-varying formation center function is derived. In addition, a procedure to design the protocol for UAV swarm systems to achieve time-varying formations is given. Finally, a quadrotor formation platform, which consists of five quadrotors is introduced. Theoretical results obtained in this brief are validated on the quardrotor formation platform, and outdoor experimental results are presented.

Time-Varying Formation Control for Unmanned Aerial Vehicles: Theories and Applications

This paper presents two types of nonlinear controllers for an autonomous quadrotor helicopter. One type, a feedback linearization controller involves high-order derivative terms and turns out to be quite sensitive to sensor noise as well as modeling uncertainty. The second type involves a new approach to an adaptive sliding mode controller using input augmentation in order to account for the underactuated property of the helicopter, sensor noise, and uncertainty without using control inputs of large magnitude. The sliding mode controller performs very well under noisy conditions, and adaptation can effectively estimate uncertainty such as ground effects.

Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter

In this paper, we propose a new quaternion-based feedback control scheme for exponential attitude stabilization of a four-rotor vertical takeoff and landing aerial robot known as a quadrotor aircraft. The proposed controller is based upon the compensation of the Coriolis and gyroscopic torques and the use of a PD/sup 2/ feedback structure, where the proportional action is in terms of the vector quaternion and the two derivative actions are in terms of the airframe angular velocity and the vector quaternion velocity. We also show that the model-independent PD controller, where the proportional action is in terms of the vector-quaternion and the derivative action is in terms of the airframe angular velocity, without compensation of the Coriolis and gyroscopic torques, provides asymptotic stability for our problem. The proposed controller as well as some other controllers have been tested experimentally on a small-scale quadrotor aircraft.

S. McGilvray

Papers

Attitude stabilization of a VTOL quadrotor aircraft