Accurate Tracking of Aggressive Quadrotor Trajectories Using Incremental Nonlinear Dynamic Inversion and Differential Flatness

Abstract

Autonomous unmanned aerial vehicles (UAVs) that can execute aggressive (i.e., high-speed and highacceleration) maneuvers have attracted significant attention in the past few years. In this paper, we propose a novel control law for accurate tracking of aggressive quadcopter trajectories. The proposed method tracks position and yaw angle with their derivatives of up to fourth order, specifically, the position, velocity, acceleration, jerk, and snap along with the yaw angle, yaw rate and yaw acceleration. Two key aspects of the proposed method are the following. First, the controller exploits the differential flatness of the quadcopter dynamics to generate feedforward inputs for attitude rate and attitude acceleration in order to track the jerk and snap references. The tracking is enabled by direct control of body torque using closed-loop control of all four propeller speeds based on optical encoders attached to the motors. Second, the controller utilizes the incremental nonlinear dynamic inversion (INDI) method for accurate tracking of linear and angular accelerations despite external disturbances. Hence, no prior modeling of aerodynamic effects is required. We rigorously analyze the proposed controller through response analysis, and we demonstrate it in experiments. The proposed control law enables a 1-kg quadcopter UAV to track complex 3D trajectories, reaching speeds up to 8.2 m/s and accelerations up to 2g, while keeping the root-mean-square tracking error down to 4 cm, in a flight volume that is roughly 6.5 m long, 6.5 m wide, and 1.5 m tall. We also demonstrate the robustness of the controller by attaching a drag plate to the UAV in flight tests and by pulling on the UAV with a rope during hover.

DCAD: Decentralized Collision Avoidance With Dynamics Constraints for Agile Quadrotor Swarms

“…Equation (9) represents the non-linear transformation required to obtain u from the flat input. We observe from Etal et al [34] that we require the third derivative of position (r) and the first derivative of yaw (ψ) to express the state and the control input. Hence, we choose the flat state space z and the flat input ν as…”

“…Eqn. 13 gives the non-linear map that transforms the flat inputs to the quadrotor inputs [34]. We assume the presence of an inner-loop attitude controller that can track the attitude values and takes as input…”

FlightGoggles: Photorealistic Sensor Simulation for Perception-driven Robotics using Photogrammetry and Virtual Reality

“…Figure 7 gives an overview of a VIO flight in FlightGoggles. The quadcopter uses the trajectory tracking controller described in [27] to track a predefined trajectory that was generated using methods from [28]. State estimation is based entirely on the pose estimate from VIO, which is using the virtual imagery from FlightGoggles and real inertial measurements from the quadcopter.…”

Safe, Aggressive Quadrotor Flight via Reachability-Based Trajectory Design

“…Such splines have closed-form solutions for desired position, velocity, and higher derivatives, so they compute quickly [4], and one can prove that they only lie within obstacle-free space [5]. Since these splines are smooth, they can typically be tracked within 0.1 m of tracking error at speeds up to 8 m/s [6]; so, spline-based approaches typically treat tracking This work has been accepted to the 2019 ASME Dynamic Systems and Control Conference. The authors are supported by the Office of Naval Research under award number N00014-18-1-2575, and by the National Science Foundation Award #1751093 * Mechanical Engineering, University of Michigan, Ann Arbor, MI <skousik,pdholmes,ramv>@umich.edu unsafe trajectory parameters safe trajectory parameters trajectory parameter space s t a t e s p a c e Fig.…”

“…These methods then rely on the quadrotor's trajectory-tracking low-level controller to ensure the quadrotor does not crash. Since low-level controllers can compensate for aerodynamic and model disturbances [6], [7], and large orientation deviations from a reference trajectory [1], [8], these approaches have been successful at navigating unknown, cluttered environments. However, it is unclear how these methods can be extended to incorporate trajectory-dependent uncertainty (such as tracking error or aerodynamic disturbance) into online planning without dilating obstacles uniformly.…”