A tutorial for applying DMOC to solve optimization control problems

This paper proposes a new multi-phase DMOC based trajectory optimization methodology to solve optimal control problems for mechanical systems. DMOC (Discrete Mechanics and Optimal Control) approach directly derives from discrete Lagrange-D'Alembert principle. The constraints for the optimization of a given cost functional are modeled as Euler-Lagrange equations. In addition to the basic requirements of DMOC, a Multi-phase Trajectory Optimization Strategy is proposed to satisfy some specific requirements and help to improve trajectory generation performance when the system should operate in a relatively complex or special environment; To show its advantages, the numerical simulations illustrate the proposed approach by generating the multi-phase optimal trajectory for a quadrotor, and comparison with another state-of-art direct Gauss Pseudo-spectrum Method (GPM) is presented. The experiment results show that our approach is more efficient to generate optimal trajectory for complex nonlinear problems than GPM, and with prospect of wide application in trajectory optimization.

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“…It can solve the linear, nonlinear and integer mathematical programming problem. For detail tutorial for applying DMOC can refer to [16].…”

Section: Discrete Boundary Conditionsmentioning

confidence: 99%

A multi-phase DMOC-based optimal trajectory generation methodology for a quadrotor

Wang

Zhang

Shan

2014

Proceedings of the 33rd Chinese Control Conference

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“…For a detailed tutorial on using DMOC, refer to Zhang and Inanc. 15 3.2 | Multiphase discrete mechanics and optimal control…”

Section: The Forced Del Equationsmentioning

confidence: 99%

A multiphase DMOC‐based trajectory optimization method

Zhang

Wang

Inanc

2017

Optim Control Appl Methods

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SummaryDiscrete mechanics and optimal control (DMOC) is a methodology that takes advantage of variational structure to solve certain optimal control problems for mechanical systems. This paper proposes to combine a multiphase strategy with the original DMOC method, resulting in a new multiphase DMOC (MDMOC) method and making optimal trajectory generation more efficient. The advantages of the proposed method are demonstrated mathematically, and in addition, a quadrotor, unmanned aerial vehicle, simulation example is presented to show its superiority over the DMOC method. Furthermore, to show its potential application, an arbitrarily chosen controller was used to track the desired trajectory generated by MDMOC. This new MDMOC methodology can also be applied to other mechanical systems such as mobile robots and underwater gliders.KEYWORDS discrete mechanics and optimal control, optimal control applications, quadrotor, trajectory optimization | INTRODUCTIONRobotic vehicles are becoming increasingly popular because of their great flexibility and mobility. They are widely used in military, civilian, commercial, and many other fields. Traditionally, robotic vehicles can be categorized into 4 main types: underwater robots, land mobile robots, unmanned aircraft, and space robots. Recently, small unmanned aerial vehicles (UAVs), as a kind of self-propelled aerial robot, have attracted widespread research attention because of their potential applications, including reconnaissance, surveillance, search and rescue, and environmental monitoring.In practice, it is always preferable for UAVs to generate a real-time trajectory, which is the foundation of reconnaissance, exploration, or tracking missions. However, due to their limited payload, it is essential to plan the optimal trajectory to achieve minimum time and/or minimum energy objectives.1 Therefore, an efficient trajectory optimization method and corresponding tracking controller design are indispensable. Generally, trajectory optimization can be considered as an optimal control problem. 2 Many kinds of optimization algorithm have been proposed for different systems. Betts 3 presented a survey showing that numerical methods for solving optimal trajectory problems can normally be classified into 2 categories: indirect and direct. Direct methods have been widely used by transforming a continuous optimal control problem into a nonlinear programming (NLP) problem. 4 Bouktir et al 5 presented a numerical method to generate a minimum-time optimal trajectory for a quadrotor with nonlinear under-actuated properties; Ross et al 2 proposed a guess-free spectral algorithm with several limiting assumptions in which the problem must be reasonably bounded and scaled; Chamseddine et al 6 applied a planning/replanning strategy to a quadrotor and illustrated the simplicity and efficiency of the method. All these approaches can solve the specified problems with relative efficiency. However, they are applicable only to trajectory optimization problems for certain specific simple mechanical...

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“…DMOC Tutorial (62) This section presents a detailed procedure [73] to apply DMOC methodology to solve optimal control problems. language AMPL.…”

Section: Initialmentioning

confidence: 99%

Optimal trajectory generation with DMOC versus NTG : application to an underwater glider and a JPL aerobot.

Zhang¹

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A tutorial for applying DMOC to solve optimization control problems

Cited by 6 publications

References 17 publications

A multi-phase DMOC-based optimal trajectory generation methodology for a quadrotor

A multi-phase DMOC-based optimal trajectory generation methodology for a quadrotor

A multiphase DMOC‐based trajectory optimization method

Optimal trajectory generation with DMOC versus NTG : application to an underwater glider and a JPL aerobot.

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