scholarly journals OPP approach for multi degree of freedom robotic arm Based on Kinematics and Dynamics of Robot

2015 ◽  
Vol 4 (4) ◽  
pp. 284
Author(s):  
Praneet Dutta ◽  
Rashmi Ranjan Das ◽  
Rupali Mathur ◽  
Deepika Rani Sona
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Minimum Principle ◽  
Equations Of Motion ◽  
Optimal Path ◽  
Minimum Cost ◽  
Simulation Software ◽  
Degree Of Freedom ◽  
The Cost ◽  
Joint Velocity

This paper deals with the trajectory and path generation of the industrial manipulator. The trajectory is obtained using the equations of motion and also the optimal path planning (OPP) approach under kinodynamic constraints. The optimal control problem is defined for the minimum cost function and to obtain the necessary conditions. Here we have used pontrygain’s minimum principle to obtain the limiting value of joint angle and also  the joint velocity and torque. In this paper we have used the “Two degree of freedom (DOF) manipulator” for analysis and designing the optimal control for multi link and multi degree of freedom manipulator. For analysis purposes,  simulation software has been used to formulate the trajectory and minimize the cost function involved.

scholarly journals The reserve of joint torque determines movement coordination

2021 ◽  
Author(s):  
Germain Faity ◽  
Denis Mottet ◽  
Simon Pla ◽  
Jérôme Froger
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Degrees Of Freedom ◽  
Minimum Cost ◽  
Joint Torque ◽  
Movement Coordination ◽  
Trunk Motion ◽  
Additional Load ◽  
The Cost ◽  
Healthy Participants

AbstractHumans coordinate biomechanical degrees of freedom to perform tasks at minimum cost. When reaching a target from a seated position, the trunk-arm-forearm coordination moves the hand to the well-defined spatial goal, while typically minimising hand jerk and trunk motion. However, due to fatigue or stroke, people visibly move the trunk more, and it is unclear what cost can account for this. Here we show that people recruit their trunk when the torque at the shoulder is too close to the maximum. We asked 26 healthy participants to reach a target while seated and we found that the trunk contribution to hand displacement increases from 11% to 27% when an additional load is handled. By flexing and rotating the trunk, participants spontaneously increase the reserve of anti-gravitational torque at the shoulder from 25% to 40% of maximal voluntary torque. Our findings provide hints on how to include the reserve of torque in the cost function of optimal control models of human coordination in healthy fatigued persons or in stroke victims.

scholarly journals The reserve of joint torque determines movement coordination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Germain Faity ◽  
Denis Mottet ◽  
Simon Pla ◽  
Jérôme Froger
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Degrees Of Freedom ◽  
Minimum Cost ◽  
Joint Torque ◽  
Movement Coordination ◽  
Trunk Motion ◽  
Additional Load ◽  
The Cost ◽  
Healthy Participants

AbstractHumans coordinate biomechanical degrees of freedom to perform tasks at minimum cost. When reaching a target from a seated position, the trunk-arm-forearm coordination moves the hand to the well-defined spatial goal, while typically minimising hand jerk and trunk motion. However, due to fatigue or stroke, people visibly move the trunk more, and it is unclear what cost can account for this. Here we show that people recruit their trunk when the torque at the shoulder is too close to the maximum. We asked 26 healthy participants to reach a target while seated and we found that the trunk contribution to hand displacement increases from 11 to 27% when an additional load is handled. By flexing and rotating the trunk, participants spontaneously increase the reserve of anti-gravitational torque at the shoulder from 25 to 40% of maximal voluntary torque. Our findings provide hints on how to include the reserve of torque in the cost function of optimal control models of human coordination in healthy fatigued persons or in stroke victims.

Constrained optimal terrain following/threat avoidance trajectory planning using network flow

2014 ◽  
Vol 118 (1203) ◽  
pp. 523-539 ◽  
Author(s):  
R. Zardashti ◽  
A. A. Nikkhah ◽  
M. J. Yazdanpanah
Keyword(s):  
Cost Function ◽  
Trajectory Planning ◽  
Network Flow ◽  
Equations Of Motion ◽  
Minimum Cost ◽  
Masking Effect ◽  
Search Problem ◽  
Starting Point ◽  
Terrain Following ◽  
Threat Avoidance

AbstractThis paper focuses on the trajectory planning for a UAV on a low altitude terrain following/threat avoidance (TF/TA) mission. Using a grid-based approximated discretisation scheme, the continuous constrained optimisation problem into a search problem is transformed over a finite network. A variant of the Minimum Cost Network Flow (MCNF) to this problem is then applied. Based on using the Digital Terrain Elevation Data (DTED) and discrete dynamic equations of motion, the four-dimensional (4D) trajectory (three spatial and one time dimensions) from a starting point to an end point is obtained by minimising a cost function subject to dynamic and mission constraints of the UAV. For each arc in the grid, a cost function is considered as the combination of the arc length, fuel consumption and flight time. The proposed algorithm which considers dynamic and altitude constraints of the UAV explicitly is then used to obtain the feasible trajectory. The resultant trajectory can increase the survivability of the UAV using the threat region avoidance and the terrain masking effect. After obtaining the feasible trajectory, an improved algorithm is proposed to smooth the trajectory. The numeric results are presented to verify the capability of the proposed approach to generate admissible trajectory in minimum possible time in comparison to the previous works.

PREDICTION OF MUSCLE FORCES USING STATIC OPTIMIZATION FOR DIFFERENT CONTRACTILE CONDITIONS

2013 ◽  
Vol 13 (03) ◽  
pp. 1350022 ◽  
Author(s):  
YUNUS ZIYA ARSLAN ◽  
AZIM JINHA ◽  
MOTOSHI KAYA ◽  
WALTER HERZOG
Keyword(s):  
Cost Function ◽  
Fiber Type ◽  
Degree Of Freedom ◽  
Muscle Forces ◽  
Cross Sectional ◽  
Satisfactory Description ◽  
New Approach ◽  
Force Sharing ◽  
Synergistic Muscles ◽  
The Cost

In this study, we introduced a novel cost function for the prediction of individual muscle forces for a one degree-of-freedom musculoskeletal system. Unlike previous models, the new approach incorporates the instantaneous contractile conditions represented by the force-length and force-velocity relationships and accounts for physiological properties such as fiber type distribution and physiological cross-sectional area (PCSA) in the cost function. Using this cost function, it is possible to predict experimentally observed features of force-sharing among synergistic muscles that cannot be predicted using the classical approaches. Specifically, the new approach allows for predictions of force-sharing loops of agonistic muscles in one degree-of-freedom systems and for simultaneous increases in force in one muscle and decreases in a corresponding agonist. We concluded that the incorporation of the contractile conditions in the weighting of cost functions provides a natural way to incorporate observed force-sharing features in synergistic muscles that have eluded satisfactory description.

scholarly journals Optimal Control of Virus Spread under Different Conditions of Resources Limitations

Information ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 214
Author(s):  
Paolo Di Giamberardino ◽  
Daniela Iacoviello
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Virus Spread ◽  
Human Virus ◽  
Positive Diagnosis ◽  
Control Actions ◽  
The People ◽  
Different Types ◽  
The Cost ◽  
Instantaneous Control

The paper addresses the problem of human virus spread reduction when the resources for the control actions are somehow limited. This kind of problem can be successfully solved in the framework of the optimal control theory, where the best solution, which minimizes a cost function while satisfying input constraints, can be provided. The problem is formulated in this contest for the case of the HIV/AIDS virus, making use of a model that considers two classes of susceptible subjects, the wise people and the people with incautious behaviours, and three classes of infected, the ones still not aware of their status, the pre-AIDS patients and the AIDS ones; the control actions are represented by an information campaign, to reduce the category of subjects with unwise behaviour, a test campaign, to reduce the number of subjects not aware of having the virus, and the medication on patients with a positive diagnosis. The cost function considered aims at reducing patients with positive diagnosis using as less resources as possible. Four different types of resources bounds are considered, divided into two classes: limitations on the instantaneous control and fixed total budgets. The optimal solutions are numerically computed, and the results of simulations performed are illustrated and compared to put in evidence the different behaviours of the control actions.

LEARNING AND RECOGNITION OF HUMAN ACTIONS USING OPTIMAL CONTROL PRIMITIVES

2009 ◽  
Vol 06 (03) ◽  
pp. 459-479
Author(s):  
SUMITRA GANESH ◽  
RUZENA BAJCSY
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Estimation Method ◽  
Nonlinear Least Squares ◽  
Performance Criterion ◽  
Human Motion ◽  
Human Actions ◽  
Mode Estimation ◽  
Nonlinear Least Squares Problem ◽  
The Cost

We propose a unified approach for recognition and learning of human actions, based on an optimal control model of human motion. In this model, the goals and preferences of the agent engaged in a particular action are encapsulated as a cost function or performance criterion, that is optimized to yield the details of the movement. The cost function is a compact, intuitive and flexible representation of the action. A parameterized form of the cost function is considered, wherein the structure reflects the goals of the actions, and the parameters determine the relative weighting of different terms. We show how the cost function parameters can be estimated from data by solving a nonlinear least squares problem. The parameter estimation method is tested on motion capture data for two different reaching actions and six different subjects. We show that the problem of action recognition in the context of this representation is similar to that of mode estimation in a hybrid system and can be solved using a particle filter if a receding horizon formulation of the optimal controller is adopted. We use the proposed approach to recognize different reaching actions from the 3D hand trajectory of subjects.

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.

Time-optimal control of multiple unmanned aerial vehicles with human control input

2019 ◽  
Vol 12 (1) ◽  
pp. 138-152 ◽  
Author(s):  
Tao Han ◽  
Bo Xiao ◽  
Xi-Sheng Zhan ◽  
Jie Wu ◽  
Hongling Gao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Minimum Principle ◽  
Time Optimal Control ◽  
Control Problems ◽  
Control Input ◽  
Content Type ◽  
Human Control ◽  
Time Optimal ◽  
The Cost

Purpose The purpose of this paper is to investigate time-optimal control problems for multiple unmanned aerial vehicle (UAV) systems to achieve predefined flying shape. Design/methodology/approach Two time-optimal protocols are proposed for the situations with or without human control input, respectively. Then, Pontryagin’s minimum principle approach is applied to deal with the time-optimal control problems for UAV systems, where the cost function, the initial and terminal conditions are given in advance. Moreover, necessary conditions are derived to ensure that the given performance index is optimal. Findings The effectiveness of the obtained time-optimal control protocols is verified by two contrastive numerical simulation examples. Consequently, the proposed protocols can successfully achieve the prescribed flying shape. Originality/value This paper proposes a solution to solve the time-optimal control problems for multiple UAV systems to achieve predefined flying shape.

A qualitative study of the optimal control model for an electric power generating system

2012 ◽  
Vol 23 (2) ◽  
pp. 65-72
Author(s):  
Yidiat O. Aderinto ◽  
Mathias O. Bamigbola
Keyword(s):  
Optimal Control ◽  
Electric Power ◽  
Real Life ◽  
Minimum Cost ◽  
Fuel Cost ◽  
Transmission Losses ◽  
Factors Affecting ◽  
Real Life Data ◽  
The Cost ◽  
Generating System

The economic independence of any nation depends largely on the supply of abundant and reliable electric power and the extension of electricity services to all towns and villages in the country. In this work, the mathematical study of an electric power generating system model was presented via optimal control theory, in an attempt to maximize the power generating output and minimize the cost of generation. The factors affecting power generation at minimum cost are operating efficiencies of generators, fuel cost and transmission losses, but the most efficient generator in the system may not guarantee minimum cost as it may be located in an area where fuel cost is high. We choose the generator capacity as our control ui(t), since we cannot neglect the operation limitation on the equipment because of its lifespan, the upper bound for ui(t) is choosing to be 1 to represent the total capability of the machine and 0 to be the lower bound. The model is analyzed, generation loss free equilibrium and stability is established, and finally applications using real life data is presented using one generator and three generator systems respectively.

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