A multiphase DMOC‐based trajectory optimization method

Abstract

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...

Ascent trajectory optimization for air‐breathing vehicles in consideration of launch window

“…Even though straightforward in implementation, simplification‐based methods cannot fully reflect the characteristics of the air‐breathing vehicle or obtain the optimality of the optimal solution. These drawbacks are overcome by the optimal control theory, which has been widely applied in trajectory optimization problems . Lu et al demonstrated that the finite difference method is well suited for calculating optimal ascent trajectories.…”

“…These drawbacks are overcome by the optimal control theory, which has been widely applied in trajectory optimization problems. [14][15][16][17][18] Lu et al 19 demonstrated that the finite difference method is well suited for calculating optimal ascent trajectories. In the work of Murillo and Lu,20 the original problem is reduced to a series of root-finding problems and solved by a finite difference algorithm.…”