论文标题
轮式移动机器人的能源时间最佳控制
Energy-Time Optimal Control of Wheeled Mobile Robots
论文作者
论文摘要
本文着重于在障碍空间中进行点对点过渡的轮式移动机器人的能源时间最佳控制。两种可互换的型号用于达到必要条件以实现最佳性。第一个配方利用了哈密顿量，而第二配方则考虑了增强成本的第一个变化，以得出最佳的必要条件。雅各比椭圆函数显示出对状态，控制和成果的封闭形式解决方案的参数化。对最佳控制的分析表明，它们被限制为躺在圆形横截面的圆柱上，这是重量惩罚时间和能量成本的函数。第二种配方的最佳成果显示出显示在两个圆柱体的交汇处。在线性速度被限制为时间不变的情况下，还会开发出对插入点运动的车轮移动机器人的最佳控制。结果表明，成腐烂的木材被限制在圆柱体和挤压抛物线的交汇处。提出了各种点对点操作的数值结果，以说明最佳轨迹的结构的变化，这是终端和初始状态相对位置的函数。
This paper focuses on the energy-time optimal control of wheeled mobile robots undergoing point-to-point transitions in an obstacles free space. Two interchangeable models are used to arrive at the necessary conditions for optimality. The first formulation exploits the Hamiltonian, while the second formulation considers the first variation of the augmented cost to derive the necessary conditions for optimality. Jacobi elliptic functions are shown to parameterize the closed form solutions for the states, control and costates. Analysis of the optimal control reveal that they are constrained to lie on a cylinder whose circular cross-section is a function of the weight penalizing the relative costs of time and energy. The evolving optimal costates for the second formulation are shown to lie on the intersection of two cylinders. The optimal control for the wheeled mobile robot undergoing point-to-point motion is also developed where the linear velocity is constrained to be time-invariant. It is shown that the costates are constrained to lie on the intersection of a cylinder and an extruded parabola. Numerical results for various point-to-point maneuvers are presented to illustrate the change in the structure of the optimal trajectories as a function of the relative location of the terminal and initial states.
