scholarly journals ScottyActivity: Mixed Discrete-Continuous Planning with Convex Optimization

2018 ◽  
Vol 62 ◽  
pp. 579-664 ◽  
Author(s):  
Enrique Fernandez-Gonzalez ◽  
Brian Williams ◽  
Erez Karpas
Keyword(s):  
Convex Optimization ◽  
Continuous Time ◽  
Trajectory Optimization ◽  
State Of The Art ◽  
Optimization Techniques ◽  
Mixed Integer ◽  
State Variables ◽  
Control Variables ◽  
Model Complex ◽  
And Control

The state of the art practice in robotics planning is to script behaviors manually, where each behavior is typically generated using trajectory optimization. However, in order for robots to be able to act robustly and adapt to novel situations, they need to plan these activity sequences autonomously. Since the conditions and effects of these behaviors are tightly coupled through time, state and control variables, many problems require that the tasks of activity planning and trajectory optimization are considered together. There are two key issues underlying effective hybrid activity and trajectory planning: the sufficiently accurate modeling of robot dynamics and the capability of planning over long horizons. Hybrid activity and trajectory planners that employ mixed integer programming within a discrete time formulation are able to accurately model complex dynamics for robot vehicles, but are often restricted to relatively short horizons. On the other hand, current hybrid activity planners that employ continuous time formulations can handle longer horizons but they only allow actions to have continuous effects with constant rate of change, and restrict the allowed state constraints to linear inequalities. This is insufficient for many robotic applications and it greatly limits the expressivity of the problems that these approaches can solve. In this work we present the ScottyActivity planner, that is able to generate practical hybrid activity and motion plans over long horizons by employing recent methods in convex optimization combined with methods for planning with relaxed plan graphs and heuristic forward search. Unlike other continuous time planners, ScottyActivity can solve a broad class of robotic planning problems by supporting convex quadratic constraints on state variables and control variables that are jointly constrained and that affect multiple state variables simultaneously. In order to support planning over long horizons, ScottyActivity does not resort to time, state or control variable discretization. While straightforward formulations of consistency checks are not convex and do not scale, we present an efficient convex formulation, in the form of a Second Order Cone Program (SOCP), that is very fast to solve. We also introduce several new realistic domains that demonstrate the capabilities and scalability of our approach, and their simplified linear versions, that we use to compare with other state of the art planners. This work demonstrates the power of integrating advanced convex optimization techniques with discrete search methods and paves the way for extensions dealing with non-convex disjoint constraints, such as obstacle avoidance.

A Probabilistic Theory for Balance Dynamics

2008 ◽  
Vol 65 (9) ◽  
pp. 2949-2960 ◽  
Author(s):  
Gregory J. Hakim
Keyword(s):  
Gravity Wave ◽  
Potential Vorticity ◽  
Joint Probability ◽  
The State ◽  
State Variables ◽  
Control Variables ◽  
Height Control ◽  
Gaussian Statistics ◽  
And Control ◽  
Balance Dynamics

Abstract Balance dynamics are proposed in a probabilistic framework, assuming that the state variables and the master, or control, variables are random variables described by continuous probability density functions. Balance inversion, defined as recovering the state variables from the control variables, is achieved through Bayes’ theorem. Balance dynamics are defined by the propagation of the joint probability of the state and control variables through the Liouville equation. Assuming Gaussian statistics, balance inversion reduces to linear regression of the state variables onto the control variables, and assuming linear dynamics, balance dynamics reduces to a Kalman filter subject to perfect observations given by the control variables. Example solutions are given for an elliptical vortex in shallow water having unity Rossby and Froude numbers, which produce an outward-propagating pulse of inertia–gravity wave activity. Applying balance inversion to the potential vorticity reveals that, because potential vorticity and divergence share well-defined patterns of covariability, the inertia–gravity wave field is recovered in addition to the vortical field. Solutions for a probabilistic balance dynamics model applied to the elliptical vortex reveal smaller errors (“imbalance”) for height control compared to potential vorticity control. Important attributes of the probabilistic balance theory include quantification of the concept of balance manifold “fuzziness,” and clear state-independent definitions of balance and imbalance in terms of the range of the probabilistic inversion operators. Moreover, the theory provides a generalization of the notion of balance that may prove useful for problems involving moist physics, chemistry, and tropical circulations.

scholarly journals A New Approach for Solving Optimal Nonlinear Control Problems Using Decriminalization and Rationalized Haar Functions

2011 ◽  
Vol 1 ◽  
pp. 387-394 ◽  
Author(s):  
Zhen Yu Han ◽  
Shu Rong Li
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Nonlinear Optimal Control ◽  
Control Problems ◽  
State Variables ◽  
Linear Quadratic ◽  
Control Variables ◽  
Linear Quadratic Optimal Control ◽  
Haar Functions ◽  
And Control

This paper presents a numerical method based on quasilinearization and rationalized Haar functions for solving nonlinear optimal control problems including terminal state constraints, state and control inequality constraints. The optimal control problem is converted into a sequence of quadratic programming problems. The rationalized Haar functions with unknown coefficients are used to approximate the control variables and the derivative of the state variables. By adding artificial controls, the number of state and control variables is equal. Then the quasilinearization method is used to change the nonlinear optimal control problems with a sequence of constrained linear-quadratic optimal control problems. To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented.

Mathematical approaches for optimization of dengue fever dynamics

2019 ◽  
Vol 10 (02) ◽  
pp. 1950006
Author(s):  
Didar Murad ◽  
Noor Badshah ◽  
Muhammad Ali Syed
Keyword(s):  
Optimal Control ◽  
Dengue Fever ◽  
Low Cost ◽  
State Variables ◽  
Control Variables ◽  
Vector Population ◽  
Existence Of Optimal Control ◽  
And Control

Background and Objective: For dengue outbreak prevention and vectors reduction, fundamental role of control parameters like vaccination against dengue virus in human population and insecticide in mosquito population have been addressed theoretically and numerically. For this purpose, an existing model was modified to optimize dengue fever. Methodology: Using Pontryagin’s maximum principle, the dynamics of infection for the optimal control problem was addressed, further, defined cost functional, established existence of optimal control, stated Hamiltonian for characterization of optimization. Results: Numerical simulations for optimal state variables and control variables were performed. Conclusion: Our findings demonstrate that with low cost of control variables, state variable such as recovered population increases gradually and decrease other state variables for host and vector population.

scholarly journals Joint Trajectory and Communication Design for Buffer-Aided Multi-UAV Relaying Networks

2019 ◽  
Vol 9 (24) ◽  
pp. 5524
Author(s):  
Dongju Cao ◽  
Wendong Yang ◽  
Gangyi Xu
Keyword(s):  
Convex Optimization ◽  
Relay Selection ◽  
Rapid Development ◽  
Optimization Techniques ◽  
Mixed Integer ◽  
Rician Fading ◽  
Communication Link ◽  
Average Throughput ◽  
Transmit Power ◽  
Multi Uav

With the rapid development and evolvement of unmanned aerial vehicle (UAV) technology, UAV aided wireless communication technology has been widely studied recently. In this paper, a buffer aided multi-UAV relaying network is investigated to assist blocked ground communication. According to the mobility and implementation flexibility of UAV relays, it is assumed that the communication link between air-to-ground is the Rician fading channel. On the basis of information causality, we derive the state change of the information in the buffer of UAV relays and maximize the end-to-end average throughput by join the relay selection, UAV transmit power, and UAV trajectory optimization. However, the considered problem is a mixed integer non-convex optimization problem, and therefore, it is difficult to solve directly with general optimization methods. In order to make the problem tractable, an efficient iterative algorithm based on the block coordinate descent and the successive convex optimization techniques is proposed. The convergence of the proposed algorithm will be verified analytically at the end of this paper. The simulation results show that by alternately optimizing the relay selection, UAV transmit power, and UAV trajectory, the proposed algorithm is able to achieve convergence quickly and significantly improve the average throughput, as compared to other benchmark schemes.

Co-ordination and control of distributed spacecraft systems using convex optimization techniques

2002 ◽  
Vol 12 (2-3) ◽  
pp. 207-242 ◽  
Author(s):  
Michael Tillerson ◽  
Gokhan Inalhan ◽  
Jonathan P. How
Keyword(s):  
Convex Optimization ◽  
Optimization Techniques ◽  
And Control

scholarly journals Learning Mixed-Integer Convex Optimization Strategies for Robot Planning and Control

2020 ◽  
Author(s):  
Abhishek Cauligi ◽  
Preston Culbertson ◽  
Bartolomeo Stellato ◽  
Dimitris Bertsimas ◽  
Mac Schwager ◽  
...  
Keyword(s):  
Convex Optimization ◽  
Mixed Integer ◽  
Planning And Control ◽  
And Control

scholarly journals Energy-Efficient UAV Communication with Multiple GTs Based on Trajectory Optimization

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yu Xu ◽  
Lin Xiao ◽  
Dingcheng Yang ◽  
Laurie Cuthbert ◽  
Yapeng Wang
Keyword(s):  
Trajectory Optimization ◽  
Low Cost ◽  
High Mobility ◽  
Optimization Techniques ◽  
Mixed Integer ◽  
Flight Trajectory ◽  
Special Cases ◽  
Standard Linear ◽  
Standard Linear Programming

Wireless communications with unmanned aerial vehicles (UAVs) is a promising technology offering potential high mobility and low cost. This paper studies a UAV-enabled communication system, in which a fixed-wing UAV is deployed to collect information from a group of distributed ground terminals (GTs). Considering the requirements for quality of service (QoS) (i.e., the throughput of each GT is above a given threshold) and GT scheduling, we maximize the energy efficiency (EE) of the UAV in bits/Joule by optimizing the UAV’s flight trajectory. In this paper, a mixed integer nonconvex optimization problem is formulated. As that is difficult to solve, we divide the formulated problem into two subproblems and apply standard linear programming (LP) and successive convex optimization techniques. We further propose an efficient iterative algorithm that jointly optimizes GT scheduling and the UAV’s trajectory. Moreover, we set two special cases as benchmarks to measure the performance of the proposed design. The numerical results show that our proposed design achieves much better performance than the other two benchmark designs.

Dealing with various sources of uncertainty in the operational control of water systems using ensemble based MPC with convex optimization

2020 ◽  
Author(s):  
Klaudia Horvath ◽  
Maarten Smoorenburg ◽  
Diederik Vreeken ◽  
Ruben Sinnige ◽  
Rodolfo Alvarado Montero ◽  
...  
Keyword(s):  
Convex Optimization ◽  
Open Source ◽  
Goal Programming ◽  
Control Strategy ◽  
Computational Cost ◽  
Water Systems ◽  
Optimal Operation ◽  
Optimization Techniques ◽  
Mixed Integer ◽  
Operational Control

<p>Model Predictive Control (MPC) can be an effective tool for the operational control of water systems, but there are still many open questions about how this technique can effectively take into uncertainties of forecasts, initial states or the model setup. Moreover, computational cost and robustness often prohibit the use of existing methods in practice. We here report recent developments in the open source RTC-Tools software framework that allow representing these uncertainties through ensembles and computing the optimal control strategy with convex optimization techniques in combination with lexicographical goal programming. Convex optimization is required to have robust mathematical solutions within the short computation times that are feasible in operational practice. Goal programming is here used to facilitate straightforward optimization of competing objectives with results understandable for end-users. Adaptations of Raso’s Tree-Based MPC (e.g. Raso et al., 2014) are used to represent the possibilities offered in future control steps, permitting a realistic moving horizon control strategy while not being excessively conservative.</p><p>The developments are illustrated with applications in different water systems using methods for convex optimization of linear Mixed Integer problems as well as quadratically constrained problems with both open source and commercial solvers. We also demonstrate how RTC-Tools build-in methods can be used for linearization of system equations and objectives. The applications were evaluated in controlled experiments to learn about strengths and weaknesses in comparison with other ensemble and deterministic MPC methods.</p><p>Exploration of the added value of selected uncertainty representation techniques within MPC solutions is presented in a separate contribution (Smoorenburg et al. 2020, session HS4.3 “Ensemble hydrological forecasting: Decision making under uncertainty”).</p><p>Raso, L., D. Schwanenberg, N. C. van de Giesen, and P. J. van Overloop. 2014. “Short-Term Optimal Operation of Water Systems Using Ensemble Forecasts.” Advances in Water Resources 71 (September): 200–208.</p>

scholarly journals Cable tree wiring - benchmarking solvers on a real-world scheduling problem with a variety of precedence constraints

Constraints ◽  
2021 ◽  
Author(s):  
Jana Koehler ◽  
Josef Bürgler ◽  
Urs Fontana ◽  
Etienne Fux ◽  
Florian Herzog ◽  
...  
Keyword(s):  
State Of The Art ◽  
Precedence Constraints ◽  
Traveling Salesman ◽  
Mixed Integer ◽  
Automated Manufacturing ◽  
Scheduling Problem ◽  
Tasks Scheduling ◽  
Optimization Modulo Theories ◽  
Coupled Tasks ◽  
Np Hardness

AbstractCable trees are used in industrial products to transmit energy and information between different product parts. To this date, they are mostly assembled by humans and only few automated manufacturing solutions exist using complex robotic machines. For these machines, the wiring plan has to be translated into a wiring sequence of cable plugging operations to be followed by the machine. In this paper, we study and formalize the problem of deriving the optimal wiring sequence for a given layout of a cable tree. We summarize our investigations to model this cable tree wiring problem (CTW). as a traveling salesman problem with atomic, soft atomic, and disjunctive precedence constraints as well as tour-dependent edge costs such that it can be solved by state-of-the-art constraint programming (CP), Optimization Modulo Theories (OMT), and mixed-integer programming (MIP). solvers. It is further shown, how the CTW problem can be viewed as a soft version of the coupled tasks scheduling problem. We discuss various modeling variants for the problem, prove its NP-hardness, and empirically compare CP, OMT, and MIP solvers on a benchmark set of 278 instances. The complete benchmark set with all models and instance data is available on github and was included in the MiniZinc challenge 2020.

scholarly journals A Multi-Timescale Bilinear Model for Optimization and Control of HVAC Systems with Consistency

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 400 ◽  
Author(s):  
Zelin Nie ◽  
Feng Gao ◽  
Chao-Bo Yan
Keyword(s):  
Optimization Model ◽  
Air Conditioning ◽  
State Of The Art ◽  
Hvac Systems ◽  
Practical Significance ◽  
Hvac System ◽  
Bilinear Model ◽  
Optimization And Control ◽  
And Control ◽  
Slow Timescale

Reducing the energy consumption of the heating, ventilation, and air conditioning (HVAC) systems while ensuring users’ comfort is of both academic and practical significance. However, the-state-of-the-art of the optimization model of the HVAC system is that either the thermal dynamic model is simplified as a linear model, or the optimization model of the HVAC system is single-timescale, which leads to heavy computation burden. To balance the practicality and the overhead of computation, in this paper, a multi-timescale bilinear model of HVAC systems is proposed. To guarantee the consistency of models in different timescales, the fast timescale model is built first with a bilinear form, and then the slow timescale model is induced from the fast one, specifically, with a bilinear-like form. After a simplified replacement made for the bilinear-like part, this problem can be solved by a convexification method. Extensive numerical experiments have been conducted to validate the effectiveness of this model.

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