Stochastic Optimal Motion Planning for the Attitude Kinematics of a Rigid Body With Non-Gaussian Uncertainties

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Taeyoung Lee
Keyword(s):  
Rigid Body ◽  
Motion Planning ◽  
Uncertainty Propagation ◽  
Planck Equation ◽  
Uncertain Environments ◽  
Stochastic Motion ◽  
Stochastic Optimal Control Problem ◽  
Optimal Motion Planning ◽  
Non Gaussian ◽  
Global Uncertainty

This paper investigates global uncertainty propagation and stochastic motion planning for the attitude kinematics of a rigid body. The Fokker–Planck equation on the special orthogonal group is numerically solved via noncommutative harmonic analysis to propagate a probability density function along flows of the attitude kinematics. Based on this, a stochastic optimal control problem is formulated to rotate a rigid body while avoiding obstacles within uncertain environments in an optimal fashion. The proposed intrinsic, geometric formulation does not require the common assumption that uncertainties are Gaussian or localized. It can be also applied to complex rotational maneuvers of a rigid body without singularities in a unified way. The desirable properties are illustrated by numerical examples.

Motion Planning Under External Constraints for Redundant Dynamic Systems

2010 ◽  
Author(s):  
Joo H. Kim ◽  
Karim Abdel-Malek ◽  
Yujiang Xiang ◽  
Jingzhou James Yang ◽  
Jasbir S. Arora
Keyword(s):  
Rigid Body ◽  
Motion Planning ◽  
Dynamic Equilibrium ◽  
Contact Point ◽  
Whole Body ◽  
Time Step ◽  
Motion Trajectories ◽  
External Objects ◽  
Optimal Motion Planning ◽  
Reaction Forces

Dynamics of mechanical systems during motion usually involves reaction forces and moments due to the interaction with external objects or constraints from the environment. The problem of predicting the external reaction loads under rigid-body assumption has not been addressed extensively in the literature in terms of optimal motion planning and simulation. We propose a formulation of determining the external reaction loads for redundant systems motion planning. For dynamic equilibrium, the resultant reaction loads that include the effects of inertia, gravity, and general applied loads, are distributed to each contact point. Unknown reactions are determined along with the system configuration at each time step using iterative nonlinear optimization algorithm. The required actuator torques as well as the motion trajectories are obtained while satisfying given constraints. The formulation is applied to several example motions of multi-rigid-body systems such as a simple welding manipulator and a highly articulated whole-body human mechanism. The example results are compared with the cases where the reactions are pre-assigned.

Dynamic Motion Generation for Redundant Systems Under External Constraints

2010 ◽  
Author(s):  
Joo H. Kim ◽  
Karim Abdel-Malek ◽  
Yujiang Xiang ◽  
Jingzhou James Yang ◽  
Jasbir S. Arora
Keyword(s):  
Rigid Body ◽  
Motion Planning ◽  
Dynamic Equilibrium ◽  
Whole Body ◽  
Motion Generation ◽  
Time Step ◽  
Motion Trajectories ◽  
Contact Points ◽  
Optimal Motion Planning ◽  
Redundant Systems

Dynamics of mechanical systems during motion usually involves reaction forces and moments due to the interaction with external objects or constraints from the environment. The problem of predicting the external reaction loads under rigid-body assumption has not been addressed extensively in the literature in terms of optimal motion planning and simulation. In this presentation, we propose a formulation of determining the external reaction loads for redundant systems motion planning. For dynamic equilibrium, the resultant reaction loads that include the effects of inertia, gravity, and general applied loads, are distributed to each contact points. Unknown reactions are determined along with the system configuration at each time step using iterative nonlinear optimization algorithm. The required actuator torques as well as the motion trajectories are obtained while satisfying given constraints. The formulation is applied to several example motions of multi-rigid-body systems such as a simple 3-degree-of-freedom welding manipulator and a highly articulated whole-body human mechanism. The example results are compared with the cases where the reactions are pre-assigned. The proposed formulation demonstrates realistic distribution of external reaction loads and the associated goal-oriented motions that are dynamically consistent.

Optimal motion planning for localization of avalanche victims by multiple UAVs

2021 ◽  
pp. 1-1
Author(s):  
Camilla Tabasso ◽  
Nicola Mimmo ◽  
Venanzio Cichella ◽  
Lorenzo Marconi
Keyword(s):  
Motion Planning ◽  
Optimal Motion ◽  
Multiple Uavs ◽  
Optimal Motion Planning

On the Optimal Robot Manipulator Motion Planning for Solid Freeform Fabrication by Thermal Spraying

1995 ◽  
Author(s):  
J. Rastegar ◽  
Y. Qin ◽  
Q. Tu
Keyword(s):  
Motion Planning ◽  
Robot Manipulator ◽  
Solid Freeform Fabrication ◽  
Thermal Spraying ◽  
Freeform Fabrication ◽  
Novel Approach ◽  
Solid Objects ◽  
Optimal Motion Planning ◽  
Spatial Geometry ◽  
Probabilistic Nature

Abstract A novel approach to optimal robot manipulator motion planning for Solid Freeform Fabrication (SFF) by thermal spraying is presented. In this approach, given the desired spatial geometry of the object, the motion of the spray gun relative to a forming platform is synthesized for minimal masking requirements considering the probabilistic nature of the thermal spraying process. The material build-up rate can be planned to achieve the desired distribution of the physical/material properties within the object volume. Examples of optimal motion planning for the generation of some basic solid objects and computer simulation of the effectiveness of the developed methodology are presented.

Governing equations for probability densities of Marcus stochastic differential equations with Lévy noise

2016 ◽  
Vol 17 (05) ◽  
pp. 1750033 ◽  
Author(s):  
Xu Sun ◽  
Xiaofan Li ◽  
Yayun Zheng
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Probability Density ◽  
Lévy Processes ◽  
Planck Equation ◽  
Levy Processes ◽  
Stochastic Dynamical Systems ◽  
Non Gaussian ◽  
Fokker Planck Equations ◽  
Fokker Planck

Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Lévy processes and have wide applications in engineering and physical sciences. The probability density of the solution to an SDE offers complete statistical information on the underlying stochastic process. Explicit formula for the Fokker–Planck equation, the governing equation for the probability density, is well-known when the SDE is driven by a Brownian motion. In this paper, we address the open question of finding the Fokker–Planck equations for Marcus SDEs in arbitrary dimensions driven by non-Gaussian Lévy processes. The equations are given in a simple form that facilitates theoretical analysis and numerical computation. Several examples are presented to illustrate how the theoretical results can be applied to obtain Fokker–Planck equations for Marcus SDEs driven by Lévy processes.

Optimal motion planning and stopping test for 3-D object reconstruction

2018 ◽  
Vol 12 (1) ◽  
pp. 103-123 ◽  
Author(s):  
Heikel Yervilla-Herrera ◽  
J. Irving Vasquez-Gomez ◽  
Rafael Murrieta-Cid ◽  
Israel Becerra ◽  
L. Enrique Sucar
Keyword(s):  
Motion Planning ◽  
Object Reconstruction ◽  
Optimal Motion ◽  
Optimal Motion Planning
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