2,492 research outputs found
Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints
This paper presents a trajectory generation method that optimizes a quadratic
cost functional with respect to linear system dynamics and to linear input and
state constraints. The method is based on continuous-time flatness-based
trajectory generation, and the outputs are parameterized using a polynomial
basis. A method to parameterize the constraints is introduced using a result on
polynomial nonpositivity. The resulting parameterized problem remains
linear-quadratic and can be solved using quadratic programming. The problem can
be further simplified to a linear programming problem by linearization around
the unconstrained optimum. The method promises to be computationally efficient
for constrained systems with a high optimization horizon. As application, a
predictive torque controller for a permanent magnet synchronous motor which is
based on real-time optimization is presented.Comment: Proceedings of the American Control Conference (ACC), pp. 1904-1909,
San Francisco, USA, June 29 - July 1, 201
Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design
We describe an elementary algorithm to build convex inner approximations of
nonconvex sets. Both input and output sets are basic semialgebraic sets given
as lists of defining multivariate polynomials. Even though no optimality
guarantees can be given (e.g. in terms of volume maximization for bounded
sets), the algorithm is designed to preserve convex boundaries as much as
possible, while removing regions with concave boundaries. In particular, the
algorithm leaves invariant a given convex set. The algorithm is based on
Gloptipoly 3, a public-domain Matlab package solving nonconvex polynomial
optimization problems with the help of convex semidefinite programming
(optimization over linear matrix inequalities, or LMIs). We illustrate how the
algorithm can be used to design fixed-order controllers for linear systems,
following a polynomial approach
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
Non-linear estimation is easy
Non-linear state estimation and some related topics, like parametric
estimation, fault diagnosis, and perturbation attenuation, are tackled here via
a new methodology in numerical differentiation. The corresponding basic system
theoretic definitions and properties are presented within the framework of
differential algebra, which permits to handle system variables and their
derivatives of any order. Several academic examples and their computer
simulations, with on-line estimations, are illustrating our viewpoint
Safe Learning of Quadrotor Dynamics Using Barrier Certificates
To effectively control complex dynamical systems, accurate nonlinear models
are typically needed. However, these models are not always known. In this
paper, we present a data-driven approach based on Gaussian processes that
learns models of quadrotors operating in partially unknown environments. What
makes this challenging is that if the learning process is not carefully
controlled, the system will go unstable, i.e., the quadcopter will crash. To
this end, barrier certificates are employed for safe learning. The barrier
certificates establish a non-conservative forward invariant safe region, in
which high probability safety guarantees are provided based on the statistics
of the Gaussian Process. A learning controller is designed to efficiently
explore those uncertain states and expand the barrier certified safe region
based on an adaptive sampling scheme. In addition, a recursive Gaussian Process
prediction method is developed to learn the complex quadrotor dynamics in
real-time. Simulation results are provided to demonstrate the effectiveness of
the proposed approach.Comment: Submitted to ICRA 2018, 8 page
LTV controller flatness-based design for MIMO systems
In this paper, a flatness-based control strategy for multi-input multi-output linear time-varying systems is proposed in order to track desired trajectories. The control design, based on the use of an exact observer, leads to a polynomial two-degree-of-freedom controller without resolving Bézout’s equation in a time-varying framework. The proposed approach is illustrated with the control of a nonlinear model of the satellite SPOT-5
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