15,993 research outputs found
Mobile Formation Coordination and Tracking Control for Multiple Non-holonomic Vehicles
This paper addresses forward motion control for trajectory tracking and
mobile formation coordination for a group of non-holonomic vehicles on SE(2).
Firstly, by constructing an intermediate attitude variable which involves
vehicles' position information and desired attitude, the translational and
rotational control inputs are designed in two stages to solve the trajectory
tracking problem. Secondly, the coordination relationships of relative
positions and headings are explored thoroughly for a group of non-holonomic
vehicles to maintain a mobile formation with rigid body motion constraints. We
prove that, except for the cases of parallel formation and translational
straight line formation, a mobile formation with strict rigid-body motion can
be achieved if and only if the ratios of linear speed to angular speed for each
individual vehicle are constants. Motion properties for mobile formation with
weak rigid-body motion are also demonstrated. Thereafter, based on the proposed
trajectory tracking approach, a distributed mobile formation control law is
designed under a directed tree graph. The performance of the proposed
controllers is validated by both numerical simulations and experiments
Shape and Trajectory Tracking of Moving Obstacles
This work presents new methods and algorithms for tracking the shape and
trajectory of moving reflecting obstacles with broken rays, or rays reflecting
at an obstacle. While in tomography the focus of the reconstruction method is
to recover the velocity structure of the domain, the shape and trajectory
reconstruction procedure directly finds the shape and trajectory of the
obstacle. The physical signal carrier for this innovative method are ultrasonic
beams. When the speed of sound is constant, the rays are straight line segments
and the shape and trajectory of moving objects will be reconstructed with
methods based on the travel time equation and ellipsoid geometry. For variable
speed of sound, we start with the eikonal equation and a system of differential
equations that has its origins in acoustics and seismology. In this case, the
rays are curves that are not necessarily straight line segments and we develop
algorithms for shape and trajectory tracking based on the numerical solution of
these equations. We present methods and algorithms for shape and trajectory
tracking of moving obstacles with reflected rays when the location of the
receiver of the reflected ray is not known in advance. The shape and trajectory
tracking method is very efficient because it is not necessary for the reflected
signal to traverse the whole domain or the same path back to the transmitter.
It could be received close to the point of reflection or far away from the
transmitter. This optimizes the energy spent by transmitters for tracking the
object, reduces signal attenuation and improves image resolution. It is a safe
and secure method. We also present algorithms for tracking the shape and
trajectory of absorbing obstacles. The new methods and algorithms for shape and
trajectory tracking enable new applications and an application to one-hop
Internet routing is presented.Comment: 22 pages, 2 figures, 2 table
Optimal Trajectory Tracking for an Autonomous UAV
The aim of the present project is the design of optimal flight trajectories for an automomous aerial vehicle which is expected to reach the desired locations in the operational environment expressed in terms of planned waypoints. The navigation must be performed with the vehicle's best effort, i.e. with the lowest cost. Hence, we want to minimize the input energy, a function of the inputs for the mathematical model which describes the dynamics of the vehicle. The trajectory must satisfy all the constraints and pass through all the planned waypoints. Assuming the vehicle as a point mass model, the best solution has been investigated through a genetic algorithm search procedure. The optimisation problem has been solved by modifying a micro-genetic algorithm software which was initially developed by D.L. Carroll. Between all the possible trajectories we select the more "realistic" connections among the waypoints. First of all, we have left out the trajectories with discontinuity in the derivatives as these are not feasible by the real aircraft. The polynomial spline is a suitable candidate to solve our problem. The algorithm splits the trajectory in sub-trajectories which join a sequence of three waypoints. Starting from the first three waypoints, the following sub-trajectories are superimposed keeping the first waypoint coincident with the last of the previous sub-trajectory. The sequence of polynomials is initialized assuming that jumps in the direction of flight are avoided pointing the heading angle in the presumed direction of flight. The optimal trajectory is a trade-off amongst three factors: the required energy cost, the minimum distance from the required waypoint and the feasibility of the trajectory. Results obtained with this optimization procedure are presente
Gaussian Process Model Predictive Control of An Unmanned Quadrotor
The Model Predictive Control (MPC) trajectory tracking problem of an unmanned
quadrotor with input and output constraints is addressed. In this article, the
dynamic models of the quadrotor are obtained purely from operational data in
the form of probabilistic Gaussian Process (GP) models. This is different from
conventional models obtained through Newtonian analysis. A hierarchical control
scheme is used to handle the trajectory tracking problem with the translational
subsystem in the outer loop and the rotational subsystem in the inner loop.
Constrained GP based MPC are formulated separately for both subsystems. The
resulting MPC problems are typically nonlinear and non-convex. We derived 15 a
GP based local dynamical model that allows these optimization problems to be
relaxed to convex ones which can be efficiently solved with a simple active-set
algorithm. The performance of the proposed approach is compared with an
existing unconstrained Nonlinear Model Predictive Control (NMPC). Simulation
results show that the two approaches exhibit similar trajectory tracking
performance. However, our approach has the advantage of incorporating
constraints on the control inputs. In addition, our approach only requires 20%
of the computational time for NMPC.Comment: arXiv admin note: text overlap with arXiv:1612.0121
Discrete-time adaptive control of robot manipulators
A discrete-time model reference adaptive control scheme is developed for trajectory tracking of robot manipulators. Hyperstability theory is utilized to derive the adaptation laws for the controller gain matrices. It is shown that asymptotic trajectory tracking is achieved despite gross robot parameter variation and uncertainties. The method offers considerable design flexibility and enables the designer to improve the performance of the control system by adjusting free design parameters. The discrete-time adaptation algorithm is extremely simple and is therefore suitable for real-time implementation
Optimal trajectory tracking
This thesis investigates optimal trajectory tracking of nonlinear dynamical
systems with affine controls. The control task is to enforce the system state
to follow a prescribed desired trajectory as closely as possible. The concept
of so-called exactly realizable trajectories is proposed. For exactly
realizable desired trajectories exists a control signal which enforces the
state to exactly follow the desired trajectory. For a given affine control
system, these trajectories are characterized by the so-called constraint
equation. This approach does not only yield an explicit expression for the
control signal in terms of the desired trajectory, but also identifies a
particularly simple class of nonlinear control systems. Based on that insight,
the regularization parameter is used as the small parameter for a perturbation
expansion. This results in a reinterpretation of affine optimal control
problems with small regularization term as singularly perturbed differential
equations. The small parameter originates from the formulation of the control
problem and does not involve simplifying assumptions about the system dynamics.
Combining this approach with the linearizing assumption, approximate and partly
linear equations for the optimal trajectory tracking of arbitrary desired
trajectories are derived. For vanishing regularization parameter, the state
trajectory becomes discontinuous and the control signal diverges. On the other
hand, the analytical treatment becomes exact and the solutions are exclusively
governed by linear differential equations. Thus, the possibility of linear
structures underlying nonlinear optimal control is revealed. This fact enables
the derivation of exact analytical solutions to an entire class of nonlinear
trajectory tracking problems with affine controls. This class comprises
mechanical control systems in one spatial dimension and the FitzHugh-Nagumo
model.Comment: 240 pages, 36 figures, PhD thesi
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