11,779 research outputs found
Stochastic model predictive control for constrained networked control systems with random time delay
In this paper the continuous time stochastic constrained optimal control problem is formulated for the class of networked control systems assuming that time delays follow a discrete-time, finite Markov chain . Polytopic overapproximations of the system's trajectories are employed to produce a polyhedral inner approximation of the non-convex constraint set resulting from imposing the constraints in continuous time. The problem is cast in a Markov jump linear systems (MJLS) framework and a stochastic MPC controller is calculated explicitly, oine, coupling dynamic programming with parametric piecewise quadratic (PWQ) optimization. The calculated control law leads to stochastic stability of the closed loop system, in the mean square sense and respects the state and input constraints in continuous time
Domain Decomposition for Stochastic Optimal Control
This work proposes a method for solving linear stochastic optimal control
(SOC) problems using sum of squares and semidefinite programming. Previous work
had used polynomial optimization to approximate the value function, requiring a
high polynomial degree to capture local phenomena. To improve the scalability
of the method to problems of interest, a domain decomposition scheme is
presented. By using local approximations, lower degree polynomials become
sufficient, and both local and global properties of the value function are
captured. The domain of the problem is split into a non-overlapping partition,
with added constraints ensuring continuity. The Alternating Direction
Method of Multipliers (ADMM) is used to optimize over each domain in parallel
and ensure convergence on the boundaries of the partitions. This results in
improved conditioning of the problem and allows for much larger and more
complex problems to be addressed with improved performance.Comment: 8 pages. Accepted to CDC 201
A Distributed Model Predictive Control Framework for Road-Following Formation Control of Car-like Vehicles (Extended Version)
This work presents a novel framework for the formation control of multiple
autonomous ground vehicles in an on-road environment. Unique challenges of this
problem lie in 1) the design of collision avoidance strategies with obstacles
and with other vehicles in a highly structured environment, 2) dynamic
reconfiguration of the formation to handle different task specifications. In
this paper, we design a local MPC-based tracking controller for each individual
vehicle to follow a reference trajectory while satisfying various constraints
(kinematics and dynamics, collision avoidance, \textit{etc.}). The reference
trajectory of a vehicle is computed from its leader's trajectory, based on a
pre-defined formation tree. We use logic rules to organize the collision
avoidance behaviors of member vehicles. Moreover, we propose a methodology to
safely reconfigure the formation on-the-fly. The proposed framework has been
validated using high-fidelity simulations.Comment: Extended version of the conference paper submission on ICARCV'1
Feedback MPC for Torque-Controlled Legged Robots
The computational power of mobile robots is currently insufficient to achieve
torque level whole-body Model Predictive Control (MPC) at the update rates
required for complex dynamic systems such as legged robots. This problem is
commonly circumvented by using a fast tracking controller to compensate for
model errors between updates. In this work, we show that the feedback policy
from a Differential Dynamic Programming (DDP) based MPC algorithm is a viable
alternative to bridge the gap between the low MPC update rate and the actuation
command rate. We propose to augment the DDP approach with a relaxed barrier
function to address inequality constraints arising from the friction cone. A
frequency-dependent cost function is used to reduce the sensitivity to
high-frequency model errors and actuator bandwidth limits. We demonstrate that
our approach can find stable locomotion policies for the torque-controlled
quadruped, ANYmal, both in simulation and on hardware.Comment: Paper accepted to IEEE/RSJ International Conference on Intelligent
Robots and Systems (IROS 2019
Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach
We introduce a real-time, constrained, nonlinear Model Predictive Control for
the motion planning of legged robots. The proposed approach uses a constrained
optimal control algorithm known as SLQ. We improve the efficiency of this
algorithm by introducing a multi-processing scheme for estimating value
function in its backward pass. This pass has been often calculated as a single
process. This parallel SLQ algorithm can optimize longer time horizons without
proportional increase in its computation time. Thus, our MPC algorithm can
generate optimized trajectories for the next few phases of the motion within
only a few milliseconds. This outperforms the state of the art by at least one
order of magnitude. The performance of the approach is validated on a quadruped
robot for generating dynamic gaits such as trotting.Comment: 8 page
Reformulation and decomposition of integer programs
In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe column generation and the resulting branch-and-price algorithms. This is followed by an examination of Benders’ type algorithms based on projection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.Integer program, Lagrangean relaxation, column generation, branch-and-price, extended formulation, Benders' algorithm
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