Optimal Motion Planning of Manipulators With Elastic Links and Joints in Generalized Point-to-Point Task

2009 ◽  
Author(s):  
H. N. Rahimi ◽  
M. H. Korayem ◽  
A. Nikoobin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Minimum Principle ◽  
Linear Equations ◽  
Dynamic Modelling ◽  
Lagrange Formulation ◽  
Point Motion ◽  
Optimal Motion Planning ◽  
Point To Point

Finding optimal trajectory is critical in several applications for robots from payload transport between two given states in a prescribed time such that a cost functional is minimized. This paper is concerned with the path planning of flexible robotic arms in point-to-point motion, based on indirect solution of optimal control problem. Dynamic modelling technique based on the combined Euler–Lagrange formulation and assumed modes method is applied, then by implementing the Pontryagin’s minimum principle; necessary conditions for optimality are derived. Nonlinear states and control constraints are treated without any simplifications or transforming them into sequences of systems with linear equations. By these means, the modelling of the complete optimal control problem and the accompanying boundary value problem is automated to a great extent. Finally, the performance of method is illustrated through the computer simulations.

Trajectory optimization of flexible link manipulators in point-to-point motion

Robotica ◽  
2008 ◽  
Vol 27 (6) ◽  
pp. 825-840 ◽  
Author(s):  
M. H. Korayem ◽  
A. Nikoobin ◽  
V. Azimirad
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Trajectory ◽  
Planning Problem ◽  
Flexible Manipulators ◽  
Flexible Link ◽  
Maximum Payload ◽  
Point Motion ◽  
Point To Point

SUMMARYThe aim of this paper is to determine the optimal trajectory and maximum payload of flexible link manipulators in point-to-point motion. The method starts with deriving the dynamic equations of flexible manipulators using combined Euler–Lagrange formulation and assumed modes method. Then the trajectory planning problem is defined as a general form of optimal control problem. The computational methods to solve this problem are classified as indirect and direct techniques. This work is based on the indirect solution of open-loop optimal control problem. Because of the offline nature of the method, many difficulties like system nonlinearities and all types of constraints can be catered for and implemented easily. By using the Pontryagin's minimum principle, the obtained optimality conditions lead to a standard form of a two-point boundary value problem solved by the available command in MATLAB®. In order to determine the optimal trajectory a computational algorithm is presented for a known payload and the other one is then developed to find the maximum payload trajectory. The optimal trajectory and corresponding input control obtained from this method can be used as a reference signal and feedforward command in control structure of flexible manipulators. In order to clarify the method, derivation of the equations for a planar two-link manipulator is presented in detail. A number of simulation tests are performed and optimal paths with minimum effort, minimum effort-speed, maximum payload, and minimum vibration are obtained. The obtained results illustrate the power and efficiency of the method to solve the different path planning problems and overcome the high nonlinearity nature of the problems.

Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn–Hilliard–Navier–Stokes equations

Analysis ◽  
2020 ◽  
Vol 40 (3) ◽  
pp. 127-150
Author(s):  
Tania Biswas ◽  
Sheetal Dharmatti ◽  
Manil T. Mohan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stokes Equations ◽  
Minimum Principle ◽  
Immiscible Fluids ◽  
Second Order ◽  
Navier Stokes ◽  
Distributed Optimal Control ◽  
Navier Stokes Equations

AbstractIn this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two-dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn–Hilliard–Navier–Stokes equations. We describe the first order necessary conditions of optimality via the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.

Energy efficiency path planning for a quadrotor aerial vehicle

2021 ◽  
pp. 014233122110585
Author(s):  
Fouad Yacef ◽  
Nassim Rizoug ◽  
Laid Degaa ◽  
Omar Bouhali ◽  
Mustapha Hamerlain
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Weather Conditions ◽  
Optimization Method ◽  
Control Approach ◽  
Mission Success ◽  
Aerial Vehicle ◽  
Vehicle Trajectory ◽  
Point To Point

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.

Optimal motion planning of juggling by 3-DOF manipulators using adaptive PSO algorithm

Robotica ◽  
2013 ◽  
Vol 32 (6) ◽  
pp. 967-984 ◽  
Author(s):  
Adel Akbarimajd
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Minimum Energy ◽  
Pso Algorithm ◽  
Optimization Method ◽  
Horizontal Distance ◽  
Optimal Motion Planning ◽  
Adaptive Pso ◽  
Joint Motions

SUMMARYThree-DOF manipulators were employed for juggling of polygonal objects in order to have full control over object's configuration. Dynamic grasp condition is obtained for the instances that the manipulators carry the object on their palms. Manipulation problem is modeled as a nonlinear optimal control problem. In this optimal control problem, time of free flight is used as a free parameter to determine throw and catch times. Cost function is selected to get maximum covered horizontal distance using minimum energy. By selecting third-order polynomials for joint motions, the problem is changed to a constrained parameter selection problem. Adaptive particle swarm optimization method is consequently employed to solve the optimization problem. Effectiveness of the optimization algorithm is verified by a set of simulations in MSC. ADAMS.

scholarly journals Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics

2021 ◽  
Author(s):  
Etienne Bertin ◽  
Elliot Brendel ◽  
Bruno Hérissé ◽  
Julien Alexandre dit Sandretto ◽  
Alexandre Chapoutot
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Loop ◽  
Minimum Principle ◽  
Open Loop ◽  
Pontryagin Minimum Principle ◽  
Interval Method ◽  
Bounded Uncertainties ◽  
The Given

An interval method based on the Pontryagin Minimum Principle is proposed to enclose the solutions of an optimal control problem with embedded bounded uncertainties. This method is used to compute an enclosure of all optimal trajectories of the problem, as well as open loop and closed loop enclosures meant to enclose a concrete system using an optimal control regulator with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, as well as some applications. For instance guaranteeing that the given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties or on the contrary that the problem is unsuitable and needs to be adjusted.

scholarly journals A bilevel optimal motion planning (BOMP) model with application to autonomous parking

2019 ◽  
Vol 3 (4) ◽  
pp. 370-382 ◽  
Author(s):  
Shenglei Shi ◽  
Youlun Xiong ◽  
Jiankui Chen ◽  
Caihua Xiong
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Motion Planning ◽  
Control Problem ◽  
Control Method ◽  
Significant Feature ◽  
Optimal Motion ◽  
Optimal Control Method ◽  
Optimal Motion Planning ◽  
Upper Level

Abstract In this paper, we present a bilevel optimal motion planning (BOMP) model for autonomous parking. The BOMP model treats motion planning as an optimal control problem, in which the upper level is designed for vehicle nonlinear dynamics, and the lower level is for geometry collision-free constraints. The significant feature of the BOMP model is that the lower level is a linear programming problem that serves as a constraint for the upper-level problem. That is, an optimal control problem contains an embedded optimization problem as constraints. Traditional optimal control methods cannot solve the BOMP problem directly. Therefore, the modified approximate Karush–Kuhn–Tucker theory is applied to generate a general nonlinear optimal control problem. Then the pseudospectral optimal control method solves the converted problem. Particularly, the lower level is the $$J_2$$J2-function that acts as a distance function between convex polyhedron objects. Polyhedrons can approximate objects in higher precision than spheres or ellipsoids. As a result, a fast high-precision BOMP algorithm for autonomous parking concerning dynamical feasibility and collision-free property is proposed. Simulation results and experiment on Turtlebot3 validate the BOMP model, and demonstrate that the computation speed increases almost two orders of magnitude compared with the area criterion based collision avoidance method.

Trajectory Planning of Quadrotor Systems for Various Objective Functions

Robotica ◽  
2020 ◽  
Vol 39 (1) ◽  
pp. 137-152
Author(s):  
Hamidreza Heidari ◽  
Martin Saska
Keyword(s):  
Optimal Control ◽  
Path Planning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Planning ◽  
Minimum Principle ◽  
Optimal Path ◽  
Necessary Condition ◽  
Objective Functions ◽  
Wide Range

SUMMARYQuadrotors are unmanned aerial vehicles with many potential applications ranging from mapping to supporting rescue operations. A key feature required for the use of these vehicles under complex conditions is a technique to analytically solve the problem of trajectory planning. Hence, this paper presents a heuristic approach for optimal path planning that the optimization strategy is based on the indirect solution of the open-loop optimal control problem. Firstly, an adequate dynamic system modeling is considered with respect to a configuration of a commercial quadrotor helicopter. The model predicts the effect of the thrust and torques induced by the four propellers on the quadrotor motion. Quadcopter dynamics is described by differential equations that have been derived by using the Newton–Euler method. Then, a path planning algorithm is developed to find the optimal trajectories that meet various objective functions, such as fuel efficiency, and guarantee the flight stability and high-speed operation. Typically, the necessary condition of optimality for a constrained optimal control problem is formulated as a standard form of a two-point boundary-value problem using Pontryagin’s minimum principle. One advantage of the proposed method can solve a wide range of optimal maneuvers for arbitrary initial and final states relevant to every considered cost function. In order to verify the effectiveness of the presented algorithm, several simulation and experiment studies are carried out for finding the optimal path between two points with different objective functions by using MATLAB software. The results clearly show the effect of the proposed approach on the quadrotor systems.

Vehicle Trajectory Specification in Presence of Traffic Lights with Known or Uncertain Switching Times

2020 ◽  
Vol 2674 (8) ◽  
pp. 53-66
Author(s):  
Panagiotis Typaldos ◽  
Ioanna Kalogianni ◽  
Kyriakos Simon Mountakis ◽  
Ioannis Papamichail ◽  
Markos Papageorgiou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Real Time ◽  
Switching Time ◽  
Minimum Principle ◽  
Stochastic Dynamic ◽  
Traffic Lights ◽  
Switching Times ◽  
Optimal Approach

The main purpose of this work is to generate optimal trajectories for vehicles crossing a signalized junction, with traffic signals operated in either fixed-time or real-time (adaptive) mode. In the latter case, the next switching time is decided in real time based on the prevailing traffic conditions and is therefore uncertain in advance. The GLOSA (Green Light Optimal Speed Advisory) problem is addressed by using traffic lights information and calculating a trajectory and velocity profile for the vehicle based on the vehicle’s initial state (position and speed) and a fixed final destination state. At first, an appropriate optimal control problem is formulated and solved analytically via Pontryagin’s minimum principle (PMP) for the case of known switching times. Subsequently, for the case of real-time signals, availability of a time-window of possible signal switching times, along with the corresponding probability distribution, is assumed, and the problem is cast in the format of a stochastic optimal control problem and is solved numerically using stochastic dynamic programming (SDP) techniques. Application results, for various driving scenarios, of the deterministic approach, which considers the case of known switching times, and a comprehensive comparison of the stochastic GLOSA approach with a sub-optimal approach are presented. In particular, it is demonstrated that the proposed SDP approach achieves better average performance compared with the sub-optimal approach because of the better (probabilistic) information on the traffic light switching time.

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