scholarly journals Modeling and Simulation of a Point to Point Spherical Articulated Manipulator Using Optimal Control

Author(s):  
Prathamesh Saraf ◽  
R.N. Ponnalagu
Author(s):  
Youngjin Kim ◽  
Tarunraj Singh

Abstract Point-to-point path planning for a kinematic model of a differential-drive wheeled mobile robot (WMR) with the goal of minimizing input energy is the focus of this work. An optimal control problem is formulated to determine the necessary conditions for optimality and the resulting two point boundary value problem is solved in closed form using Jacobi elliptic functions. The resulting nonlinear programming problem is solved for two variables and the results are compared to the traditional shooting method to illustrate that the Jacobi elliptic functions parameterize the exact profile of the optimal trajectory. A set of terminal constraints which lie on a circle in the first quadrant are used to generate a set of optimal solutions. It is noted that for maneuvers where the angle of the vector connecting the initial and terminal point is greater than a threshold, which is a function of the radius of the terminal constraint circle, the robot initially moves into the third quadrant before terminating in the first quadrant. The minimum energy solution is compared to two other optimal control formulations: (1) an extension of the Dubins vehicle model where the constant linear velocity of the robot is optimized for and (2) a simple turn and move solution, both of whose optimal paths lie entirely in the first quadrant. Experimental results are used to validate the optimal trajectories of the differential-drive robot.


Author(s):  
Fouad Yacef ◽  
Nassim Rizoug ◽  
Laid Degaa ◽  
Omar Bouhali ◽  
Mustapha Hamerlain

Unmanned aerial vehicles are used today in many real-world applications. In all these applications, the vehicle endurance (flight time) is an important constraint that affects mission success. This study investigates the limitations of embedded energy for a quadrotor aerial vehicle. We consider a quadrotor simple tasked to travel from an initial hover configuration to a final hover configuration. In order to have a precise approximation of the consumed energy, we propose a power consumption model with battery dynamic, motor dynamic, and rotor efficiency function. We then introduce an optimization algorithm to minimize the energy consumption during quadrotor aerial vehicle mission. The proposed algorithm is based on an optimal control problem formulated for the quadrotor model and solved using nonlinear programming. In the optimal control problem, we seek to find control inputs (rotor velocity) and vehicle trajectory between initial and final configurations that minimize the consumed energy during a point-to-point mission. We extensively test in simulation experiments the proposed algorithm under normal and windy weather conditions. We compare the proposed optimization method with a nonlinear adaptive control approach to highlight the saved amount of energy.


Author(s):  
John Broderick ◽  
Dawn Tilbury ◽  
Ella Atkins

This paper presents a method to compare area coverage paths in the context of energy efficiency. We examine cover-age paths created from the Boustrophedon Decomposition and Spanning Tree methods in an optimal control setting. Our cost function weights the force inputs to drive the robot and the currently uncovered region. We derive an optimal traversal of the path in a point-to-point manner. In particular, we introduce a meas function that represents the percentage of the area that is still to be visited. The effect of meas on the optimal traversal is derived. Trade-offs between area covered versus the time and energy required are presented. A simple trajectory modification allows the vehicle to continue moving through a turn to reduce energy consumption.


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