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.

A motion planning strategy for multifingered hands considering sliding and rolling contacts

Robotica ◽  
1995 ◽  
Vol 13 (2) ◽  
pp. 149-158 ◽  
Author(s):  
Nak Young Chong ◽  
Donghoon Choi ◽  
Il Hong Suh
Keyword(s):  
Motion Planning ◽  
Contact Point ◽  
Robotic Hand ◽  
Time Step ◽  
Current Time ◽  
Planning Strategy ◽  
Multifingered Hands ◽  
Rolling Contacts ◽  
Finite Displacements ◽  
Joint Velocity

SummaryAn algorithm for the motion planning of the multifingered hand is proposed to generate finite displacements and changes in orientation of objects by considering sliding contacts as well as rolling contacts between the fingertip and the object at the contact point. Specifically, a nonlinear optimization problem is firstly formulated and solved to find the minimum joint velocity and the minimum contact force to impart a desired motion to the object at each time step. Then, the relative velocity at the contact point is found by calculating the velocity of the fingertip and the object at the contact point. Finally, time derivatives of the surface variables and the contact angle of the fingertip and the object at the current time step is computed using the Montana's contact equation to find the contact parameters of the fingertip and the object at the next time step. To show the validity of the proposed algorithm, a numerical example is illustrated by employing the robotic hand manipulating a sphere with three fingers each of which has four joints

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.

Optimal Throwing Motion Planning for a Biped Human Mechanism

2009 ◽  
Author(s):  
Joo H. Kim ◽  
Yujiang Xiang ◽  
Jingzhou James Yang ◽  
Karim Abdel-Malek ◽  
Jasbir S. Arora
Keyword(s):  
Motion Planning ◽  
Dynamic Models ◽  
Target Location ◽  
Ground Reaction Forces ◽  
Optimal Solutions ◽  
Optimal Motion ◽  
Highly Nonlinear ◽  
Optimal Motion Planning ◽  
Reaction Forces ◽  
Throwing Motion

An optimal motion planning formulation of throwing for a biped human mechanism is proposed as an extension of a previous study. The unique characteristics of the throwing task—highly redundant, highly nonlinear, and highly dynamic—are addressed in this presentation within the framework of multibody dynamics and optimization. To generate physically feasible throwing motions in a fully predictive method without input reference, rigorous dynamic models are associated with the constraints. Given the target location and the object mass, the algorithm outputs the motion, required actuator torques, release parameters, balance criterion, and ground reaction forces. Overarm and sidearm throwing motions are generated as optimal solutions, which demonstrate valid kinematic and kinetic cause-effect relations.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

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.

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