281 research outputs found
Autonomous docking using direct optimal control
We propose a method for performing autonomous docking of marine vessels using
numerical optimal control. The task is framed as a dynamic positioning problem,
with the addition of spatial constraints that ensure collision avoidance. The
proposed method is an all-encompassing procedure for performing both docking,
maneuvering, dynamic positioning and control allocation. In addition, we show
that the method can be implemented as a real-time MPC-based algorithm on
simulation results of a supply vessel.Comment: 12th IFAC Conference on Control Applications in Marine Systems,
Robotics, and Vehicles (CAMS 2019). IFAC; Daejeon. 2019-09-18 - 2019-09-2
On the integration of singularity-free representations of SO(3) for direct optimal control
In this paper we analyze the performance of different combinations of: (1) parameterization of the rotational degrees of freedom (DOF) of multibody systems, and (2) choice of the integration scheme, in the context of direct optimal control discretized according to the direct multiple-shooting method. The considered representations include quaternions and Direction Cosine Matrices, both having the peculiarity of being non-singular and requiring more than three parameters to describe an element of the Special Orthogonal group SO(3). These representations yield invariants in the dynamics of the system, i.e., algebraic conditions which have to be satisfied in order for the model to be representative of physical reality. The investigated integration schemes include the classical explicit Rungeâ\u80\u93Kutta method, its stabilized version based on Baumgarteâ\u80\u99s technique, which tends to reduce the drift from the underlying manifold, and a structure-preserving alternative, namely the Rungeâ\u80\u93Kutta Munthe-Kaas method, which preserves the invariants by construction. The performances of the combined choice of representation and integrator are assessed by solving thousands of planning tasks for a nonholonomic, underactuated cart-pendulum system, where the pendulum can experience arbitrarily large 3D rotations. The aspects analyzed include success rate, average number of iterations and CPU time to convergence, and quality of the solution. The results reveal how structure-preserving integrators are the only choice for lower accuracies, whereas higher-order, non-stabilized standard integrators seem to be the computationally most competitive solution when higher levels of accuracy are pursued. Overall, the quaternion-based representation is the most efficient in terms of both iterations and CPU time to convergence, albeit at the cost of lower success rates and increased probability of being trapped by higher local minima
Finite Elements with Switched Detection for Direct Optimal Control of Nonsmooth Systems with Set-Valued Step Functions
This paper extends the Finite Elements with Switch Detection (FESD) method
[Nurkanovi\'c et al., 2022] to optimal control problems with nonsmooth systems
involving set-valued step functions. Logical relations and common nonsmooth
functions within a dynamical system can be expressed using linear and nonlinear
expressions of the components of the step function. A prominent subclass of
these systems are Filippov systems. The set-valued step function can be
expressed by the solution map of a linear program, and using its KKT conditions
allows one to transform the initial system into an equivalent dynamic
complementarity system (DCS). Standard Runge-Kutta (RK) methods applied to DCS
have only first-order accuracy. The FESD discretization makes the step sizes
degrees of freedom and adds further constraints that ensure exact switch
detection to recover the high-accuracy properties that RK methods have for
smooth ODEs. All methods and examples in this paper are implemented in the
open-source software package NOSNOC.Comment: submitted to CDC202
Solving Optimal Control with Nonlinear Dynamics Using Sequential Convex Programming
Sequential convex programming (SCP) is a useful tool in obtaining real-time solutions to direct optimal control, but it is unable to adequately model nonlinear dynamics due to the linearization and discretization required. As nonlinear program solvers are not yet functioning
in real-time, a tool is needed to bridge the gap between satisfying the nonlinear dynamics and completing execution fast enough to be useful. This paper presents a real-time control algorithm, sequential convex programming with nonlinear dynamics correction (SCPn), which ameliorates the performance of SCP under nonlinear dynamics. Simulations are presented to validate the efficacy of the method
Large scale direct optimal control applied to the re-entry problem
Projet PROMATHWe present the numerical solution of an atmospheric reentry problem for a space shuttle. We discretize the control and state with the same grid, and use a large-scale successive quadratic programming technique. With the help of sliding horizon and successive refinement of the discretization, we can solve on a workstation a problem with 1600 time step, an unusually large figure for this kind of real world optimal control problem
Optimal Trajectories for Propellant-Free Rendezvous Missions
The paper provides a new approach to utilizing space environmental forces in
time- and energy-optimal, propellant-less spacecraft rendezvous missions.
Considering the nonlinear form of the relative dynamic equations, rendezvous
missions are posed as optimal control problems subject to input saturation. We
conduct a direct optimal control approach to obtain optimal trajectories and
control inputs. Initially, we consider the differential drag only and conduct a
comprehensive analysis of the effect of altitude on the required control input
and achieved cost function. Lorentz forces are then utilized with the
differential drag, reducing the time required for time-optimal missions. For
energy-optimal missions with combined differential drag and Lorentz forces, a
weighting matrix in the cost function is introduced to adjust the relative
contributions of these forces
Optimal Guidance and Control with Nonlinear Dynamics Using Sequential Convex Programming
This paper presents a novel method for expanding the use of sequential convex programming (SCP) to the domain of optimal guidance and control problems with nonlinear dynamics constraints. SCP is a useful tool in obtaining real-time solutions to direct optimal control, but it is unable to adequately model nonlinear dynamics due to the linearization and discretization required. As nonlinear program solvers are not yet functioning in real-time, a tool is needed to bridge the gap between satisfying the nonlinear dynamics and completing execution fast enough to be useful. Two methods are proposed, sequential convex programming with nonlinear dynamics correction (SCPn) and modified SCPn (M-SCPn), which mixes SCP and SCPn to reduce runtime and improve algorithmic robustness. Both methods are proven to generate optimal state and control trajectories that satisfy the nonlinear dynamics. Simulations are presented to validate the efficacy of the methods as compared to SCP
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