A QP-Based Approach to Kinematic Motion Planning of Multibody Systems

2015 ◽  
Author(s):  
Junggon Kim ◽  
Rudranarayan Mukherjee
Keyword(s):  
Motion Planning ◽  
Multibody Systems ◽  
Linear Constraints ◽  
Software Implementation ◽  
Robotic Systems ◽  
Time Step ◽  
Kinematic Constraints ◽  
Cartesian Space ◽  
Kinematic Motion ◽  
Dual Arm

This article presents a quadratic programming (QP) based approach to local kinematic motion planning of general multibody robotic systems. Given kinematic constraints and targets such as desired positions and orientations in Cartesian space, we find locally optimal joint velocities toward the targets at every time step by formulating the problem into a constrained optimization with a quadratic objective function and linear constraints in terms of the joint velocities. The solution is integrated to obtain the joint displacements at the next time step, and this process is repeated until reaching the targets or converging to a certain configuration. Our formulation based on relative Jacobian is particularly useful in handling constraints on relative motions, which arises in many practical problems such as dual-arm manipulation and self-collision avoidance, in a concise manner. A brief overview of our software implementation and its applications to manipulation and mobility planning of a simulated multi-limbed robot are also presented.

scholarly journals Dynamical System-Based Motion Planning for Multi-Arm Systems: Reaching for Moving Objects

2017 ◽  
Author(s):  
Seyed Sina Mirrazavi Salehian ◽  
Nadia Figueroa ◽  
Aude Billard
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Motion Planning ◽  
Moving Objects ◽  
Robotic Systems ◽  
Virtual Object ◽  
Control Law ◽  
Robot System ◽  
Object Based ◽  
Dual Arm

The use of coordinated multi-arm robotic systems allows to preform manipulations of heavy or bulky objects that would otherwise be infeasible for a single-arm robot. This paper concisely introduces our work on coordinated multi-arm control [Salehian et al., 2016a], where we proposed a virtual object based dynamical systems (DS) control law to generate autonomous and synchronized motions for a multi-arm robot system. We show theoretically and empirically that the multi-arm + virtual object system converges asymptotically to a moving object. The proposed framework is validated on a dual-arm robotic system. We demonstrate that it can re-synchronize and adapt the motion of each arm in a fraction of a second, even when the object’s motion is fast and not accurately predictable.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

1997 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Stiff Systems ◽  
Step Size ◽  
Step Method ◽  
Integral Of Motion ◽  
Time Step ◽  
Time Step Size ◽  
Variable Time ◽  
Numerical Integrator

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

Dimensional Synthesis and Constrained Motion Interpolation for Planar and Spherical 6R Closed Chains

2008 ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Qiaode Jeffrey Ge
Keyword(s):  
Rational Curve ◽  
Dimensional Synthesis ◽  
Constrained Motion ◽  
Initial Attempt ◽  
Kinematic Constraints ◽  
Constraint Manifold ◽  
Cartesian Space ◽  
Closed Chain ◽  
Kinematic Mapping ◽  
The Given

In the recent past, we have studied the problem of synthesizing rational interpolating motions under the kinematic constraints of any given planar and spherical 6R closed chain. This work presents some preliminary results on our initial attempt to solve the inverse problem, that is to determine the link lengths of planar and spherical 6R closed chains that follow a given smooth piecewise rational motion under the kinematic constraints. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of planar and spherical closed chains in the Cartesian space. By using kinematic mapping and a quaternions based approach to represent displacements of the coupler of the closed chains, the given smooth piecewise rational motion is mapped to a smooth piecewise rational curve in the space of quaternions. In this space, the aforementioned workspace constraints on the coupler of the closed chains define a constraint manifold representing all the positions available to the coupler. Thus the problem of dimensional synthesis may be solved by modifying the size, shape and location of the constraint manifolds such that the mapped rational curve is contained entirely inside the constraint manifolds. In this paper, two simple examples with preselected moving pivots on the coupler as well as fixed pivots are presented to illustrate the feasibility of this approach.

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

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