scholarly journals Path Tracking Algorithms for Non-Convex Waiter Motion Problem

2018 ◽  
Vol 62 (1) ◽  
pp. 16-23
Author(s):  
Ákos Nagy ◽  
Gábor Csorvási ◽  
István Vajk
Keyword(s):  
Motion Planning ◽  
Optimization Problem ◽  
Minimum Energy ◽  
Real Life ◽  
Problem Formulation ◽  
Energy Planning ◽  
Special Area ◽  
Time Optimal ◽  
Motion Problem ◽  
Optimal Approach

Originally, motion planning was concerned with problems such as how to move an object from a start to a goal position without hitting anything. Later, it has extended with complications such as kinematics, dynamics, uncertainties, and also with some optimality purpose such as minimum-time, minimum-energy planning. The paper presents a time-optimal approach for robotic manipulators. A special area of motion planning is the waiter motion problem, in which a tablet is moved from one place to another as fastas possible, avoiding the slip of the object that is placed upon it. The presented method uses the direct transcription approach for the waiter problem, which means a optimization problem is formed in order to obtain a time-optimal control for the robot. Problem formulation is extended with a non-convex jerk constraints to avoid unwanted oscillations during the motion. The possible local and global solver approaches for the presented formulation are discussed, and the waiter motion problem is validated by real-life experimental results with a 6-DoF robotic arm.

Nonconvex Time-Optimal Trajectory Planning for Robot Manipulators

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Ákos Nagy ◽  
István Vajk
Keyword(s):  
Motion Planning ◽  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Robot Manipulator ◽  
Viscous Friction ◽  
Global Optimum ◽  
Convex Optimization Problem ◽  
Optimal Motion Planning ◽  
Time Optimal ◽  
Active Research

Time-optimal motion-planning has been a topic of active research in the literature for a while. This paper presents a new approach for velocity profile generation, which is a subproblem in motion-planning. In the case of simplified constraints, profile generation can be translated to a convex optimization problem. However, some practical constraints (e.g., velocity-dependent torque, viscous friction) destroy the convexity. The proposed method can obtain the global optimum of the nonconvex optimization problem. The experimental results with a three degrees-of-freedom (DOF) robot manipulator are also presented in this paper.

scholarly journals Solution for Nonlinear Three-Dimensional Intercept Problem with Minimum Energy

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Henzeh Leeghim ◽  
Donghoon Kim ◽  
James Turner
Keyword(s):  
Optimization Problem ◽  
Minimum Energy ◽  
Three Dimensional ◽  
Problem Formulation ◽  
Initial Position ◽  
Iteration Algorithm ◽  
Trajectory Design ◽  
Interplanetary Trajectory ◽  
Classical Orbit ◽  
Hohmann Transfer

Classical orbit intercept applications are commonly formulated and solved as Lambert-type problems, where the time-of-flight (TOF) is prescribed. For general three-dimensional intercept problems, selecting a meaningful TOF is often a difficult and an iterative process. This work overcomes this limitation of classical Lambert’s problem by reformulating the intercept problem in terms of a minimum-energy application, which then generates both the desired initial interceptor velocity and the TOF for the minimum-energy transfer. The optimization problem is formulated by using the classical Lagrangianfandgcoefficients, which map initial position and velocity vectors to future times, and a universal time variablex. A Newton-Raphson iteration algorithm is introduced for iteratively solving the problem. A generalized problem formulation is introduced for minimizing the TOF as part of the optimization problem. Several examples are presented, and the results are compared with the Hohmann transfer solution approaches. The resulting minimum-energy intercept solution algorithm is expected to be broadly useful as a starting iterative for applications spanning: targeting, rendezvous, interplanetary trajectory design, and so on.

Application of Evolutionary Algorithms for Humanoid Robot Motion Planning

2010 ◽  
Vol 3 (4) ◽  
pp. 21-33
Author(s):  
G. Capi ◽  
K. Mitobe
Keyword(s):  
Motion Planning ◽  
Humanoid Robot ◽  
Optimization Problem ◽  
Walking Speed ◽  
Fitness Function ◽  
Minimum Energy ◽  
Multiple Objectives ◽  
Robot Motion ◽  
Robot Motion Planning ◽  
Minimum Energy Consumption

In this article, the authors present a new method for humanoid robot motion planning, satisfying multiple objectives. In this method, the multiple objectives humanoid robot motion is formulated as a multiobjective optimization problem, considering each objective as a separate fitness function. Three different objectives are considered: (1) minimum energy consumption; (2) stability; and (3) walking speed. The advantage of the proposed method is that, in a single run of multiobjective evolution, generated humanoid robot motions satisfy each objective separately or multiple objectives simultaneously. Therefore, the humanoid robot can switch between different gaits based on environmental conditions. The results show that humanoid robot gaits generated by multiobjective evolution are similar to that of humans. To further verify the performance of optimal motions, they are transferred to the “Bonten-Maru” humanoid robot.

Path constrained time-optimal motion of a cooperative two robot system

Robotica ◽  
1995 ◽  
Vol 13 (4) ◽  
pp. 363-374 ◽  
Author(s):  
Hye-Kyung Cho ◽  
Bum-Hee Lee ◽  
Myoung-Sam Ko
Keyword(s):  
Motion Planning ◽  
Optimal Solution ◽  
Problem Formulation ◽  
Planning Problem ◽  
Optimal Motion ◽  
Robot System ◽  
Admissible Region ◽  
Time Motion ◽  
State Dependent ◽  
Time Optimal

SummaryThis paper presents a systematic approach to the time-optimal motion planning of a cooperative two robot system along a prescribed path. First, the minimum-time motion planning problem is formulated in a concise form by parameterizing the dynamics of the robot system through a single variable describing the path. The constraints imposed on the input actuator torques and the exerted forces on the object are then converted into those on that variable, which result in the so-called admissible region in the phase plane of the variable. Considering the load distribution problem that is also involved in the motion, we present a systematic method to construct the admissible region by employing the orthogonal projection technique and the theory of multiple objective optimization. Especially, the effects of viscous damping and state-dependent actuator bounds are incorporated into the problem formulation so that the case where the admissible region is not simply connected can be investigated in detail. The resultant time-optimal solution specifies not only the velocity profile, but also the force assigned to each robot at each instant. Physical interpretation on the characteristics of the optimal actuator torques is also included with computer simulation results.

Motion Planning of Uncertain Fully-Actuated Dynamical Systems: An Inverse Dynamics Formulation

2011 ◽  
Author(s):  
Joe Hays ◽  
Adrian Sandu ◽  
Corina Sandu ◽  
Dennis Hong
Keyword(s):  
Nonlinear Programming ◽  
Dynamical Systems ◽  
Motion Planning ◽  
Inverse Dynamics ◽  
Initial Conditions ◽  
Practical Importance ◽  
Real Life ◽  
Optimal Motion ◽  
Time Optimal ◽  
New Framework

This work presents a novel nonlinear programming based motion planning framework that treats uncertain fully-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; ignoring uncertainty during design may lead to poor robustness and suboptimal performance. System uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, new design questions related to uncertain dynamical systems can now be answered through the new framework. Specifically, this work presents the new framework through an inverse dynamics formulation where deterministic state trajectories are prescribed and uncertain actuator inputs are quantified. The benefits of the ability to quantify the resulting actuator uncertainty are illustrated in a time optimal motion planning case-study of a serial manipulator pick-and-place application. The resulting design determines a feasible time optimal motion plan—subject to actuator and obstacle avoidance constraints—for all possible systems within the probability space. The forward dynamics formulation (using deterministic actuator inputs and uncertain state trajectories) is presented in a companion paper.

scholarly journals Hypervolume scalarization for shape optimization to improve reliability and cost of ceramic components

2021 ◽  
Author(s):  
Johanna Schultes ◽  
Michael Stiglmayr ◽  
Kathrin Klamroth ◽  
Camilla Hahn
Keyword(s):  
Shape Optimization ◽  
Optimization Problem ◽  
Mechanical Stability ◽  
Adjoint Equation ◽  
Tensile Load ◽  
Problem Formulation ◽  
State Equation ◽  
Efficient Solutions ◽  
Volume Stability ◽  
Shape Optimization Problem

AbstractIn engineering applications one often has to trade-off among several objectives as, for example, the mechanical stability of a component, its efficiency, its weight and its cost. We consider a biobjective shape optimization problem maximizing the mechanical stability of a ceramic component under tensile load while minimizing its volume. Stability is thereby modeled using a Weibull-type formulation of the probability of failure under external loads. The PDE formulation of the mechanical state equation is discretized by a finite element method on a regular grid. To solve the discretized biobjective shape optimization problem we suggest a hypervolume scalarization, with which also unsupported efficient solutions can be determined without adding constraints to the problem formulation. FurthIn this section, general properties of the hypervolumeermore, maximizing the dominated hypervolume supports the decision maker in identifying compromise solutions. We investigate the relation of the hypervolume scalarization to the weighted sum scalarization and to direct multiobjective descent methods. Since gradient information can be efficiently obtained by solving the adjoint equation, the scalarized problem can be solved by a gradient ascent algorithm. We evaluate our approach on a 2 D test case representing a straight joint under tensile load.

scholarly journals Optimization-Based Formulations for Short-Circuit Studies with Inverter-Interfaced Generation in PowerModelsProtection.jl

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2160
Author(s):  
Arthur K. Barnes ◽  
Jose E. Tabarez ◽  
Adam Mate ◽  
Russell W. Bent
Keyword(s):  
Optimization Problem ◽  
Short Circuit ◽  
Problem Formulation ◽  
Power Delivery ◽  
Fault Current ◽  
Protective Device ◽  
Protective Relaying ◽  
Overcurrent Protection ◽  
Short Circuits ◽  
Optimization Problem Formulation

Protecting inverter-interfaced microgrids is challenging as conventional time-overcurrent protection becomes unusable due to the lack of fault current. There is a great need for novel protective relaying methods that enable the application of protection coordination on microgrids, thereby allowing for microgrids with larger areas and numbers of loads while not compromising reliable power delivery. Tools for modeling and analyzing such microgrids under fault conditions are necessary in order to help design such protective relaying and operate microgrids in a configuration that can be protected, though there is currently a lack of tools applicable to inverter-interfaced microgrids. This paper introduces the concept of applying an optimization problem formulation to the topic of inverter-interfaced microgrid fault modeling, and discusses how it can be employed both for simulating short-circuits and as a set of constraints for optimal microgrid operation to ensure protective device coordination.

scholarly journals Near Time-Optimal Path Tracking Method for Waiter Motion Problem

2017 ◽  
Vol 50 (1) ◽  
pp. 4929-4934 ◽  
Author(s):  
Gábor Csorvási ◽  
Ákos Nagy ◽  
István Vajk
Keyword(s):  
Optimal Path ◽  
Path Tracking ◽  
Tracking Method ◽  
Time Optimal ◽  
Motion Problem ◽  
Path Tracking Method
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