Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userComputationally efficient stochastic MPC: a probabilistic scaling approach
245
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In recent years, the increasing interest in Stochastic model predictive control (SMPC) schemes has highlighted the limitation arising from their inherent computational demand, which has restricted their applicability to slow-dynamics and high-performing systems. To reduce the computational burden, in this paper we extend the probabilistic scaling approach to obtain low-complexity inner approximation of chance-constrained sets. This approach provides probabilistic guarantees at a lower computational cost than other schemes for which the sample complexity depends on the design space dimension. To design candidate simple approximating sets, which approximate the shape of the probabilistic set, we introduce two possibilities: i) fixed-complexity polytopes, and ii) $ell_p$-norm based sets. Once the candidate approximating set is obtained, it is scaled around its center so to enforce the expected probabilistic guarantees. The resulting scaled set is then exploited to enforce constraints in the classical SMPC framework. The computational gain obtained with the proposed approach with respect to the scenario one is demonstrated via simulations, where the objective is the control of a fixed-wing UAV performing a monitoring mission over a sloped vineyard.
rate research
Read More
Quadcopters are increasingly used for applications ranging from hobby to industrial products and services. This paper serves as a tutorial on the design, simulation, implementation, and experimental outdoor testing of digital quadcopter flight controllers, including Explicit Model Predictive Control, Linear Quadratic Regulator, and Proportional Integral Derivative. A quadcopter was flown in an outdoor testing facility and made to track an inclined, circular path at different tangential velocities under ambient wind conditions. Controller performance was evaluated via multiple metrics, such as position tracking error, velocity tracking error, and onboard computation time. Challenges related to the use of computationally limited embedded hardware and flight in an outdoor environment are addressed with proposed solutions.
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of simple-approximating sets of given complexity. A probabilistic scaling procedure then allows to rescale these sets to obtain the desired probabilistic guarantees. The proposed approach is shown to be applicable in several problem in systems and control, such as the design of Stochastic Model Predictive Control schemes or the solution of probabilistic set membership estimation problems.
Developing controllers for obstacle avoidance between polytopes is a challenging and necessary problem for navigation in a tight space. Traditional approaches can only formulate the obstacle avoidance problem as an offline optimization problem. To address these challenges, we propose a duality-based safety-critical optimal control using control barrier functions for obstacle avoidance between polytopes, which can be solved in real-time with a QP-based optimization problem. A dual optimization problem is introduced to represent the minimum distance between polytopes and the Lagrangian function for the dual form is applied to construct a control barrier function. We demonstrate the proposed controller on a moving sofa problem where non-conservative maneuvers can be achieved in a tight space.
Many problems in robotics involve multiple decision making agents. To operate efficiently in such settings, a robot must reason about the impact of its decisions on the behavior of other agents. Differential games offer an expressive theoretical framework for formulating these types of multi-agent problems. Unfortunately, most numerical solution techniques scale poorly with state dimension and are rarely used in real-time applications. For this reason, it is common to predict the future decisions of other agents and solve the resulting decoupled, i.e., single-agent, optimal control problem. This decoupling neglects the underlying interactive nature of the problem; however, efficient solution techniques do exist for broad classes of optimal control problems. We take inspiration from one such technique, the iterative linear-quadratic regulator (ILQR), which solves repeated approximations with linear dynamics and quadratic costs. Similarly, our proposed algorithm solves repeated linear-quadratic games. We experimentally benchmark our algorithm in several examples with a variety of initial conditions and show that the resulting strategies exhibit complex interactive behavior. Our results indicate that our algorithm converges reliably and runs in real-time. In a three-player, 14-state simulated intersection problem, our algorithm initially converges in < 0.25s. Receding horizon invocations converge in < 50 ms in a hardware collision-avoidance test.
In this paper, we consider a stochastic Model Predictive Control able to account for effects of additive stochastic disturbance with unbounded support, and requiring no restrictive assumption on either independence nor Gaussianity. We revisit the rather classical approach based on penalty functions, with the aim of designing a control scheme that meets some given probabilistic specifications. The main difference with previous approaches is that we do not recur to the notion of probabilistic recursive feasibility, and hence we do not consider separately the unfeasible case. In particular, two probabilistic design problems are envisioned. The first randomization problem aims to design textit{offline} the constraint set tightening, following an approach inherited from tube-based MPC. For the second probabilistic scheme, a specific probabilistic validation approach is exploited for tuning the penalty parameter, to be selected textit{offline} among a finite-family of possible values. The simple algorithm here proposed allows designing a textit{single} controller, always guaranteeing feasibility of the online optimization problem. The proposed method is shown to be more computationally tractable than previous schemes. This is due to the fact that the sample complexity for both probabilistic design problems depends on the prediction horizon in a logarithmic way, unlike scenario-based approaches which exhibit linear dependence. The efficacy of the proposed approach is demonstrated with a numerical example.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
