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

Autonomous unmanned aerial vehicles (UAVs) that can execute aggressive (i.e., high-speed and high-acceleration) maneuvers have attracted significant attention in the past few years. This paper focuses on accurate tracking of aggressive quadcopter trajectories. We propose a novel control law for tracking of position and yaw angle and their derivatives of up to fourth order, specifically, velocity, acceleration, jerk, and snap along with yaw rate and yaw acceleration. Jerk and snap are tracked using feedforward inputs for angular rate and angular acceleration based on the differential flatness of the quadcopter dynamics. Snap tracking requires direct control of body torque, which we achieve using closed-loop motor speed control based on measurements from optical encoders attached to the motors. The controller utilizes incremental nonlinear dynamic inversion (INDI) for robust tracking of linear and angular accelerations despite external disturbances, such as aerodynamic drag forces. Hence, prior modeling of aerodynamic effects is not required. We rigorously analyze the proposed control law through response analysis, and we demonstrate it in experiments. The controller enables a quadcopter UAV to track complex 3D trajectories, reaching speeds up to 12.9 m/s and accelerations up to 2.1g, while keeping the root-mean-square tracking error down to 6.6 cm, in a flight volume that is roughly 18 m by 7 m and 3 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.Comment: To be published in IEEE Transactions on Control Systems Technology. Revision: new set of experiments at increased speed (up to 12.9 m/s), updated controller design using quaternion representation, new video available at https://youtu.be/K15lNBAKDC

FlightGoggles: A Modular Framework for Photorealistic Camera, Exteroceptive Sensor, and Dynamics Simulation

FlightGoggles is a photorealistic sensor simulator for perception-driven robotic vehicles. The key contributions of FlightGoggles are twofold. First, FlightGoggles provides photorealistic exteroceptive sensor simulation using graphics assets generated with photogrammetry. Second, it provides the ability to combine (i) synthetic exteroceptive measurements generated in silico in real time and (ii) vehicle dynamics and proprioceptive measurements generated in motio by vehicle(s) in a motion-capture facility. FlightGoggles is capable of simulating a virtual-reality environment around autonomous vehicle(s). While a vehicle is in flight in the FlightGoggles virtual reality environment, exteroceptive sensors are rendered synthetically in real time while all complex extrinsic dynamics are generated organically through the natural interactions of the vehicle. The FlightGoggles framework allows for researchers to accelerate development by circumventing the need to estimate complex and hard-to-model interactions such as aerodynamics, motor mechanics, battery electrochemistry, and behavior of other agents. The ability to perform vehicle-in-the-loop experiments with photorealistic exteroceptive sensor simulation facilitates novel research directions involving, e.g., fast and agile autonomous flight in obstacle-rich environments, safe human interaction, and flexible sensor selection. FlightGoggles has been utilized as the main test for selecting nine teams that will advance in the AlphaPilot autonomous drone racing challenge. We survey approaches and results from the top AlphaPilot teams, which may be of independent interest.Comment: Initial version appeared at IROS 2019. Supplementary material can be found at https://flightgoggles.mit.edu. Revision includes description of new FlightGoggles features, such as a photogrammetric model of the MIT Stata Center, new rendering settings, and a Python AP

A Systems Immunology Approach to the Host-Tumor Interaction: Large-Scale Patterns of Natural Autoantibodies Distinguish Healthy and Tumor-Bearing Mice

Traditionally, immunology has considered a meaningful antibody response to be marked by large amounts of high-affinity antibodies reactive with the specific inciting antigen; the detection of small amounts of low-affinity antibodies binding to seemingly unrelated antigens has been considered to be beneath the threshold of immunological meaning. A systems-biology approach to immunology, however, suggests that large-scale patterns in the antibody repertoire might also reflect the functional state of the immune system. To investigate such global patterns of antibodies, we have used an antigen-microarray device combined with informatic analysis. Here we asked whether antibody-repertoire patterns might reflect the state of an implanted tumor. We studied the serum antibodies of inbred C57BL/6 mice before and after implantation of syngeneic 3LL tumor cells of either metastatic or non-metastatic clones. We analyzed patterns of IgG and IgM autoantibodies binding to over 300 self-antigens arrayed on slides using support vector machines and genetic algorithm techniques. We now report that antibody patterns, but not single antibodies, were informative: 1) mice, even before tumor implantation, manifest both individual and common patterns of low-titer natural autoantibodies; 2) the patterns of these autoantibodies respond to the growth of the tumor cells, and can distinguish between metastatic and non-metastatic tumor clones; and 3) curative tumor resection induces dynamic changes in these low-titer autoantibody patterns. The informative patterns included autoantibodies binding to self-molecules not known to be tumor-associated antigens (including insulin, DNA, myosin, fibrinogen) as well as to known tumor-associated antigens (including p53, cytokeratin, carbonic anhydrases, tyrosinase). Thus, low-titer autoantibodies that are not the direct products of tumor-specific immunization can still generate an immune biomarker of the body-tumor interaction. System-wide profiling of autoantibody repertoires can be informative

Algorithms for Generation and Tracking of Fast and Agile Flight Trajectories

High-speed flight through cluttered environments is essential to many time-sensitive robotics applications. It requires motion planning and flight control algorithms that enable highly accurate maneuvering at the edge of the vehicle’s capability. These algorithms must overcome challenges particular to fast and agile flight, such as complex dynamics effects including significant unsteady aerodynamics and challenging conditions like post-stall and uncoordinated flight. We propose trajectory generation and tracking algorithms that address these challenges for a quadcopter aircraft and for a fixed-wing transitioning aircraft that combines vertical take-off and landing (VTOL) with efficient forward flight. This thesis contains several contributions. First, we show that robust control based on incremental nonlinear dynamic inversion (INDI) enables fast and agile flight without depending on an accurate dynamics model. Based on the INDI technique, we design a comprehensive quadcopter flight control algorithm that achieves accurate trajectory tracking without relying on any vehicle aerodynamics model. Second, we show differential flatness of a global nonlinear six-degree-of-freedom (6DOF) flight dynamics model for a tailsitter flying wing transitioning aircraft. We leverage the flat transform to design an INDI flight control algorithm capable of tracking agile aerobatics maneuvers that exploit the entire flight envelope, including post-stall and sideways knife-edge flight. Third, we present a trajectory generation algorithm that aims to identify the actual dynamic feasibility boundary by efficiently combining analytical, numerical, and experimental evaluations in trajectory optimization. Finally, we demonstrate our contributions in fast and agile flight through elaborate experiments.Ph.D

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

IEEE Autonomous unmanned aerial vehicles (UAVs) that can execute aggressive (\ie, high-speed and high-acceleration) maneuvers have attracted significant attention in the past few years. This article focuses on accurate tracking of aggressive quadcopter trajectories. We propose a novel control law for tracking of position and yaw angle and their derivatives of up to fourth order, specifically velocity, acceleration, jerk, and snap along with yaw rate and yaw acceleration. Jerk and snap are tracked using feedforward inputs for angular rate and angular acceleration based on the differential flatness of the quadcopter dynamics. Snap tracking requires direct control of body torque, which we achieve using closed-loop motor speed control based on measurements from optical encoders attached to the motors. The controller utilizes incremental nonlinear dynamic inversion (INDI) for robust tracking of linear and angular accelerations despite external disturbances, such as aerodynamic drag forces. Hence, prior modeling of aerodynamic effects is not required. We rigorously analyze the proposed control law through response analysis and demonstrate it in experiments. The controller enables a quadcopter UAV to track complex 3-D trajectories, reaching speeds up to 12.9 m/s and accelerations up to 2.1 g, while keeping the root-mean-square tracking error down to 6.6 cm, in a flight volume that is roughly 18 m x 7 m and 3-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

Continuous Tensor Train-Based Dynamic Programming for High-Dimensional Zero-Sum Differential Games

© 2018 AACC. Zero-sum differential games constitute a prominent research topic in several fields ranging from economics to motion planning. Unfortunately, analytical techniques for differential games can address only simple, illustrative problem instances, and most existing computational methods suffer from the curse of dimensionality, i.e., the computational requirements grow exponentially with the dimensionality of the state space. In order to alleviate the curse of dimensionality for a certain class of two-player pursuit-evasion games, we propose a novel dynamic-programming-based algorithm that uses a continuous tensor-train approximation to represent the value function. In this way, the algorithm can represent high-dimensional tensors using computational resources that grow only polynomially with dimensionality of the state space and with the rank of the value function. The proposed algorithm is shown to converge to optimal solutions. It is demonstrated in several problem instances; in case of a seven-dimensional game, the value function representation was obtained with seven orders of magnitude savings in computational and memory cost, when compared to standard value iteration

Aerobatic Trajectory Generation for a VTOL Fixed-Wing Aircraft Using Differential Flatness

This paper proposes a novel algorithm for aerobatic trajectory generation for a vertical take-off and landing (VTOL) tailsitter flying wing aircraft. The algorithm differs from existing approaches for fixed-wing trajectory generation, as it considers a realistic six-degree-of-freedom (6DOF) flight dynamics model, including aerodynamics equations. Using a global dynamics model enables the generation of aerobatics trajectories that exploit the entire flight envelope, enabling agile maneuvering through the stall regime, sideways uncoordinated flight, inverted flight etc. The method uses the differential flatness property of the global tailsitter flying wing dynamics, which is derived in this work. By performing snap minimization in the differentially flat output space, a computationally efficient algorithm, suitable for online motion planning, is obtained. The algorithm is demonstrated in extensive flight experiments encompassing six aerobatics maneuvers, a time-optimal drone racing trajectory, and an airshow-like aerobatic sequence for three tailsitter aircraft.Comment: 14 pages, 17 figures, video of experiments available at https://aera.mit.edu/projects/TailsitterAerobatic

Multi-fidelity black-box optimization for time-optimal quadrotor maneuvers

We consider the problem of generating a time-optimal quadrotor trajectory for highly maneuverable vehicles, such as quadrotor aircraft. The problem is challenging because the optimal trajectory is located on the boundary of the set of dynamically feasible trajectories. This boundary is hard to model as it involves limitations of the entire system, including complex aerodynamic and electromechanical phenomena, in agile high-speed flight. In this work, we propose a multi-fidelity Bayesian optimization framework that models the feasibility constraints based on analytical approximation, numerical simulation, and real-world flight experiments. By combining evaluations at different fidelities, trajectory time is optimized while the number of costly flight experiments is kept to a minimum. The algorithm is thoroughly evaluated for the trajectory generation problem in two different scenarios: (1) connecting predetermined waypoints; (2) planning in obstacle-rich environments. For each scenario, we conduct both simulation and real-world flight experiments at speeds up to 11 m/s. Resulting trajectories were found to be significantly faster than those obtained through minimum-snap trajectory planning. </jats:p