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Discrete-Time differential dynamic programming on SO(3) With Pose Constraints

IEEE ACCESS 2022年 10卷 112921-112933页

作者： Liu, Shu Liu, Dongpo China Acad Informat & Commun Technol Beijing 100191 Peoples R China

The motion of many robotics systems, such as the rotation of unmanned aerial vehicles, can be modeled by SO(3). However, the difficulties in the parameterization of the SO(3) makes it hard to implement the state-of-the-art collision avoidance algorithm. In this paper, we present a new method for control on SO(3) via the combination of the nonlinear state constraints and geometric control technique. We first define the nonlinear constraints for trajectory optimization on SO(3). Then we solve the trajectory optimization problem by constrained differential dynamic programming (DDP) in a Riemannian geometry framework. The first and second-order expansion of the cost function and dynamics are derived in a coordinate-free manner. The safety condition represented by nonlinear constraints is incorporated into the DDP via an active set method, where we find the active set in the backward path to obtain the optimal control policy. We validated our methods on motion planning of rigid model on SO(3) manifold where pose constraints are imposed. Our methods outperform the baseline methods in terms of convergence speed and numerical robustness to disturbance. The numerical robustness is essential when the system is initialized far from the local optimum.

关键词： Trajectory optimization Manifolds Convergence Motion planning Robot kinematics Geometry Collision avoidance Geometric control motion planning differential dynamic programming nonlinear programming

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A multiple-shooting differential dynamic programming algorithm. Part 1: Theory

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ACTA ASTRONAUTICA 2020年 170卷 686-700页

作者： Pellegrini, Etienne Russell, Ryan P. Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA

Multiple-shooting benefits a wide variety of optimal control algorithms by alleviating large sensitivities present in highly nonlinear problems, improving robustness to initial guesses, and increasing the potential for parallel implementation. In this paper series, motivated by the challenges of optimizing highly sensitive spacecraft trajectories, the multiple-shooting approach is embedded for the first time in the formulation of a differential dynamic programming algorithm. Contrary to traditional nonlinear programming methods which necessitate minimal modification of the formulation in order to incorporate multiple-shooting principles, DDP requires novel non-trivial derivations, in order to include the initial conditions of the multiple-shooting subintervals and track their sensitivities. The initial conditions are updated in a necessary additional algorithmic step. A nullspace trust-region method is used for the solution of the quadratic subproblems, and equality and inequality path and terminal constraints are handled through a general augmented Lagrangian approach. The propagation of the trajectory and the optimization of its controls are decoupled through the use of State-Transition Matrices. Part 1 of the paper series provides the necessary theoretical developments and implementation details for the algorithm. Part 2 contains validation and application cases.

关键词： Optimal control Trajectory optimization differential dynamic programming Multiple-shooting Augmented Lagrangian

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FORWARD differential dynamic-programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1977年第4期21卷 487-504页

作者： VIT, K UNIV SALFORD DEPT ELECT ENGNSALFORD M5 4WTLANCASHIREENGLAND

The dynamic programming formulation of the forward principle of optimality in the solution of optimal control problems results in a partial differential equation with initial boundary condition whose solution is independent of terminal cost and terminal constraints. Based on this property, two computational algorithms are described. The first-order algorithm with minimum computer storage requirements uses only integration of a system of differential equations with specified initial conditions and numerical minimization in finite-dimensional space. The second-order algorithm is based on the differential dynamic programming approach. Either of the two algorithms may be used for problems with nondifferentiable terminal cost or terminal constraints, and the solution of problems with complicated terminal conditions (e.g., with free terminal time) is greatly simplified.

关键词： Optimal control forward dynamic programming differential dynamic programming

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Newton's Method, Bellman Recursion and differential dynamic programming for Unconstrained Nonlinear dynamic Games

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dynamic GAMES AND APPLICATIONS 2022年第2期12卷 394-442页

作者： Di, Bolei Lamperski, Andrew 200 Union St SE Minneapolis MN 55455 USA

dynamic games arise when multiple agents with differing objectives control a dynamic system. They model a wide variety of applications in economics, defense, energy systems and etc. However, compared to single-agent control problems, the computational methods for dynamic games are relatively limited. As in the single-agent case, only specific dynamic games can be solved exactly, so approximation algorithms are required. In this paper, we show how to extend the Newton step algorithm, the Bellman recursion and the popular differential dynamic programming (DDP) for single-agent optimal control to the case of fullinformation nonzero sum dynamic games. We show that the Newton's step can be solved in a computationally efficient manner and inherits its original quadratic convergence rate to open-loop Nash equilibria, and that the approximated Bellman recursion and DDP methods are very similar and can be used to find local feedback O(e(2))-Nash equilibria. Numerical examples are provided.

关键词： Noncooperative dynamic games Open-loop Nash equilibrium Feedback Nash equilibrium Newton's method differential dynamic programming

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A Hybrid differential dynamic programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2012年第2期154卷 382-417页

作者： Lantoine, Gregory Russell, Ryan P. Georgia Inst Technol Sch Aerosp Engn Atlanta GA 30318 USA Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA

A new algorithm is presented to solve constrained nonlinear optimal control problems, with an emphasis on highly nonlinear dynamical systems. The algorithm, called HDDP, is a hybrid variant of differential dynamic programming, a proven second-order technique that relies on Bellman's Principle of Optimality and successive minimization of quadratic approximations. The new hybrid method incorporates nonlinear mathematical programming techniques to increase efficiency: quadratic programming subproblems are solved via trust region and range-space active set methods, an augmented Lagrangian cost function is utilized, and a multiphase structure is implemented. In addition, the algorithm decouples the optimization from the dynamics using first- and second-order state transition matrices. A comprehensive theoretical description of the algorithm is provided in this first part of the two paper series. Practical implementation and numerical evaluation of the algorithm is presented in Part 2.

关键词： Optimal control differential dynamic programming Nonlinear optimization Large-scale problem Trust region Augmented Lagrangian

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Computational Guidance Using Sparse Gauss-Hermite Quadrature differential dynamic programming 21

Computational Guidance Using Sparse Gauss-Hermite Quadrature...

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21st International-Federation-of-Automatic-Control (IFAC) Symposium on Automatic Control in Aerospace (ACA)

作者： He, Shaoming Shin, Hyo-Sang Tsourdos, Antonios Cranfield Univ Sch Aerosp Transport & Mfg Cranfield MK43 0AL Beds England

This paper proposes a new computational guidance algorithm using differential dynamic programming and sparse Gauss-Hermite quadrature rule. By the application of sparse Gauss-Hermite quadrature rule, numerical differentiation in the calculation of Hessian matrices and gradients in differential dynamic programming is avoided. Based on the new differential dynamic programming approach developed, a three-dimensional computational algorithm is proposed to control the impact angle and impact time for an air-to-surface interceptor. Extensive numerical simulations are performed to show the effectiveness of the proposed approach. Copyright (C) 2019. The Authors. Published by Elsevier Ltd. All rights reserved.

关键词： Computational guidance differential dynamic programming Sparse Gauss-Hermite quadrature Impact angle Impact time

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Jumping Motion Based on Momentum Optimization Control and differential dynamic programming for a Multilocomotion Robot

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ADVANCED THEORY AND SIMULATIONS 2022年第5期5卷

作者： Liu, Guoshuai Lu, Zhiguo Wang, Ruchao Zhao, Haibin Liu, Chong Shi, Xinhao Northeastern Univ Sch Mech Engn & Automat Shenyang 110819 Peoples R China

Jumping motion is an indispensable motion mode for a multilocomotion robot, which will improve the crossing ability of the robot. This paper proposes a novel jumping control scheme for an MLR to perform jumping motion. The control strategy divides the whole jumping motion into three phases: the launch phase, the flight phase, and the landing phase. In the launch and landing phases, the controller is designed based on the centroid dynamics. By controlling the centroid momentum, the robot can achieve the desired centroid trajectory to obtain the initial take-off speed in the launch phase and to maintain stability and reduce impact in the landing phase. In the flight phase, differential dynamic programming algorithm is used to adjust the posture of the robot to further improve the jumping height and prepare for a smooth landing. Finally, the effectiveness of the proposed method is evaluated through simulations.

关键词： differential dynamic programming jump momentum optimization control multilocomotion robot

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Primal-dual differential dynamic programming: A model-based reinforcement learning for constrained dynamic optimization

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COMPUTERS & CHEMICAL ENGINEERING 2022年 167卷

作者： Kim, Jong Woo Oh, Tae Hoon Son, Sang Hwan Lee, Jong Min Tech Univ Berlin Chair Bioproc Engn Str 17 Juni 135 D-10623 Berlin Germany Incheon Natl Univ Dept Energy & Chem Engn Incheon 22012 South Korea Seoul Natl Univ Inst Chem Proc Sch Chem & Biol Engn 1 Gwanak-ro Seoul 08826 South Korea Kyoto Univ Dept Chem Engn Katsura CampusNishikyo ku Kyoto 6158510 Japan Pusan Natl Univ Sch Chem & Biomol Engn Busan 46241 South Korea

The main objective of this study is to develop primal-dual differential dynamic programming (DDP), a model -based reinforcement learning (RL) framework that can handle constrained dynamic optimization problems. DDP has advantages of being able to provide a closed-loop policy and having computational complexity that grows linearly with respect to the time horizon. To take advantage, the DDP should consider optimality and feasibility for the disturbed state during closed-loop operations. Previous DDPs consider the feasibility only for the nominal state condition and can handle limited types of constraints. In this paper, we propose a primal- dual DDP incorporating modified augmented Lagrangian that can handle general nonlinear constraints. We pay special attention to obtain the feasible policy when active set changes due to the state perturbations, using path-following predictor-corrector approach. The developed framework method was applied to van der Pol oscillator and batch crystallization process, thereby validating the key aspects of this study.

关键词： Reinforcement learning differential dynamic programming Constrained optimization Augmented Lagrangian Path-following

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Learning and ensemble based MPC with differential dynamic programming for nuclear power autonomous control

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EXPERT SYSTEMS WITH APPLICATIONS 2023年 215卷

作者： Li, Wenhuai Cai, Jiejin Duan, Chengjie Chen, Shu Ding, Peng Lin, Jiming Cui, Dawei China Nucl Power Technol Res Inst Co Ltd Shenzhen Peoples R China South China Univ Technol Sch Elect Power Guangzhou Peoples R China Engn Res Ctr Adv Nucl Energy Artificial Intelligen Shenzhen Peoples R China

Reactor autonomous control is one of the key research fields of advanced reactor R&D. Although some basic achievements have been made, it is still an unfinished goal to realize the intelligent autonomous control of the reactor. In this paper, some learning-based and ensemble-based predictive models and some model predictive control strategies combined with ensemble Kalman filter (EnKF) are proposed to realize a feasible path to the reactor autonomous control. For a typical point reactor and the operation target, reactor state space predictions are completed by mechanism-based models and data-driven learning-based models respectively. Mechanism models based on parameter perturbation and the neural network models that have higher accuracy are selected as predictors of model predictive control (MPC). The MPC results show that the model with less precision (e.g. support vector machine and random forest regression) has large oscillation results, while the predictive control based on neural network and mechanism model can effectively achieve the control objectives. To improve the accuracy of MPC, ensemble learning methodologies with a second learner based on linear regression, stacking different predictive models into one model are proposed. The accuracy of MPC with the ensemble model can exceed or be close to the optimal individual results. EnKF is proposed to estimate core state and covariance, which would be helpful to restrain the influence of observation uncertainties and predictive model error. In addition, some limitation of the proposed methodologies is discussed and needed further study.

关键词： Model predictive control Nuclear power control differential dynamic programming Ensemble learning Ensemble Kalman filter

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Rejectable deep differential dynamic programming for real-time integrated generation dispatch and control of micro-grids

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ENERGY 2021年 225卷 120268-120268页

作者： Yin, Linfei Zhao, Lulin Guangxi Univ Coll Elect Engn Nanning 530004 Peoples R China

With the application of renewable energy and distributed power generation in micro-grids, conventional artificial intelligent control strategies have shown deficiencies for the frequency control and economic dispatch of micro-grids. Conventional deep learning controllers could provide outputs although when the predicted probability is not high, which will lead to micro-grid system divergence. This paper proposes a rejectable deep differential dynamic programming for the real-time integrated generation dispatch and control of micro-grids. The rejectable deep differential dynamic programming can provide an action from an analytic control algorithm when the predicted probability is not high enough. The deep differential dynamic programming contains four deep neural networks, i.e., "deep differential prediction network", "deep differential evaluation network 1", "deep differential evaluation network 2" and "deep differential execution network". To verify the feasibility and effectiveness of the proposed rejectable deep differential dynamic programming, a total of 25 combined conventional optimization and control algorithms are compared under a micro-grid based on Hainan Power Grid. The numeric simulation results show that the proposed approach can obtain high control performance for the real-time integrated generation dispatch and control framework, which can replace the conventional combined "economic dispatch thorn automatic generation control thorn droop control" framework of micro-grids. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Rejectable operation Deep neural networks differential dynamic programming Integrated generation dispatch and control framework

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