An Inverse Dynamics Optimization Formulation With Recursive B-Spline Derivatives and Partition of Unity Contacts: Demonstration Using Two-Dimensional Musculoskeletal Arm and Gait

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Yujiang Xiang
Keyword(s):  
Muscle Force ◽  
Joint Angle ◽  
Inverse Dynamics ◽  
Partition Of Unity ◽  
High Order ◽  
Control Points ◽  
Two Dimensional ◽  
State Variables ◽  
B Spline ◽  
Optimization Formulation

In this study, an inverse dynamics optimization formulation and solution procedure is developed for musculoskeletal simulations. The proposed method has three main features: high order recursive B-spline interpolation, partition of unity, and inverse dynamics formulation. First, joint angle and muscle force profiles are represented by recursive B-splines. The formula for high order recursive B-spline derivatives is derived for state variables calculation. Second, partition of unity is used to handle the multicontact indeterminacy between human and environment during the motion. The global forces and moments are distributed to each contacting point through the corresponding partition ratio. Third, joint torques are inversely calculated from equations of motion (EOM) based on state variables and contacts to avoid numerical integration of EOM. Therefore, the design variables for the optimization problem are joint angle control points, muscle force control points, knot vector, and partition ratios for contacting points. The sum of muscle stress/activity squared is minimized as the cost function. The constraints are imposed for human physical constraints and task-based constraints. The proposed formulation is demonstrated by simulating a trajectory planning problem of a planar musculoskeletal arm with six muscles. In addition, the gait motion of a two-dimensional musculoskeletal model with sixteen muscles is also optimized by using the approach developed in this paper. The gait optimal solution is obtained in about 1 min central processing unit (CPU) time. The predicted kinematics, kinetics, and muscle forces have general trends that are similar to those reported in the literature.

scholarly journals Trajectory Planning of Manipulator Using Optimization of Uniform B-Spline

1994 ◽  
Vol 6 (6) ◽  
pp. 491-498 ◽  
Author(s):  
Hiroaki Ozaki ◽  
◽  
Hua Chiu ◽  
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Control Points ◽  
State Variables ◽  
B Spline ◽  
Iterative Computation ◽  
Basic Optimization ◽  
Engineering Problems ◽  
Original Objective ◽  
Optimum Solution

A basic optimization algorithm is presented in this paper, in order to obtain the optimum solution of a two-point boundary value variational problem without constraints. The solution is given by a parallel and iterative computation and described as a set of control points of a uniform B-spline. This algorithm can also be applied to solving problems with some constraints, if we introduce an additional component, namely the potential function, corresponding to constraints in the original objective function. The algorithm is very simple and easily applicable to various engineering problems. As an application, trajectory planning of a manipulator with redundant degrees of freedom is considered under the conditions that the end effector path, the smoothness of movement, and the constraints of the control or the state variables are specified. The validity of the algorithm is well confirmed by numerical examples.

Two-Dimensional Team Lifting Prediction With Different Box Weights

2020 ◽  
Author(s):  
Asif Arefeen ◽  
Yujiang Xiang
Keyword(s):  
Joint Angle ◽  
Inverse Dynamics ◽  
Reaction Force ◽  
Optimization Method ◽  
Two Dimensional ◽  
Dynamics Modeling ◽  
Floating Base ◽  
Grasping Forces ◽  
Design Variables ◽  
Grasping Force

Abstract A novel multibody dynamics modeling method is proposed for two-dimensional (2D) team lifting prediction. The box itself is modeled as a floating-base rigid body in Denavit-Hartenberg representation. The interactions between humans and box are modeled as a set of grasping forces which are treated as unknowns (design variables) in the optimization formulation. An inverse-dynamics-based optimization method is used to simulate the team lifting motion where the dynamic effort of two humans is minimized subjected to physical and task-based constraints. The design variables are control points of cubic B-splines of joint angle profiles of two humans and the box, and the grasping forces between humans and the box. Two numerical examples are successfully simulated with different box weights (20 Kg and 30 Kg, respectively). The humans’ joint angle, torque, ground reaction force, and grasping force profiles are reported. The joint angle profiles are validated with the experimental data.

Collision-Free Trajectory Planning for a Two-Dimensional Mobile Robot by Optimizing Continuous Curves

1998 ◽  
Vol 10 (4) ◽  
pp. 364-369 ◽  
Author(s):  
Hiroaki Ozaki ◽  
◽  
Chang-jun Lin
Keyword(s):  
Mobile Robot ◽  
Trajectory Planning ◽  
Performance Index ◽  
Nonlinear Problems ◽  
Complex Method ◽  
Control Points ◽  
Two Dimensional ◽  
B Spline ◽  
Spline Curves ◽  
Continuous Curves

We propose a new algorithm for planning collision-free trajectories for a mobile robot. The trajectories of the mobile robot are described by uniform B-spline curves and these control points are optimized using the complex method. The complex method is very effective for this type of optimization of nonlinear problems because it does not require any computation of the gradient of performance index. B-spline curves have advantages for trajectory generation in that they guarantee the continuity of trajectories and the order of trajectories can be changed easily. Effectiveness is also confirmed by trajectory planning simulation of a two-dimensional mobile robot.

Explicit Kutta condition for unsteady two-dimensional high-order potential boundary element method

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1080-1081
Author(s):  
Giuseppe Davi ◽  
Rosario M. A. Maretta ◽  
Alberto Milazzo
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
High Order ◽  
Two Dimensional ◽  
Kutta Condition ◽  
Element Method

scholarly journals Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1054
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
Isfarita Ismail ◽  
Mohammad Izat Emir Zulkifly
Keyword(s):  
Complex Surface ◽  
Complex Data ◽  
Fuzzy Data ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Surface Data ◽  
Model Complex

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

scholarly journals On the BIC for determining the number of control points in B-spline surface approximation in case of correlated observations

2020 ◽  
Vol 10 (1) ◽  
pp. 110-123
Author(s):  
Gaël Kermarrec ◽  
Hamza Alkhatib
Keyword(s):  
Shape Control ◽  
Simple Procedure ◽  
Spline Approximation ◽  
Autoregressive Process ◽  
Optimal Number ◽  
Information Criteria ◽  
General Effect ◽  
Control Points ◽  
B Spline ◽  
Correlated Observations

Abstract B-spline curves are a linear combination of control points (CP) and B-spline basis functions. They satisfy the strong convex hull property and have a fine and local shape control as changing one CP affects the curve locally, whereas the total number of CP has a more general effect on the control polygon of the spline. Information criteria (IC), such as Akaike IC (AIC) and Bayesian IC (BIC), provide a way to determine an optimal number of CP so that the B-spline approximation fits optimally in a least-squares (LS) sense with scattered and noisy observations. These criteria are based on the log-likelihood of the models and assume often that the error term is independent and identically distributed. This assumption is strong and accounts neither for heteroscedasticity nor for correlations. Thus, such effects have to be considered to avoid under-or overfitting of the observations in the LS adjustment, i.e. bad approximation or noise approximation, respectively. In this contribution, we introduce generalized versions of the BIC derived using the concept of quasi- likelihood estimator (QLE). Our own extensions of the generalized BIC criteria account (i) explicitly for model misspecifications and complexity (ii) and additionally for the correlations of the residuals. To that aim, the correlation model of the residuals is assumed to correspond to a first order autoregressive process AR(1). We apply our general derivations to the specific case of B-spline approximations of curves and surfaces, and couple the information given by the different IC together. Consecutively, a didactical yet simple procedure to interpret the results given by the IC is provided in order to identify an optimal number of parameters to estimate in case of correlated observations. A concrete case study using observations from a bridge scanned with a Terrestrial Laser Scanner (TLS) highlights the proposed procedure.

Decentralized adaptive tracking control for high-order interconnected stochastic nonlinear time-varying delay systems with stochastic input-to-state stable inverse dynamics by neural networks

2019 ◽  
Vol 41 (13) ◽  
pp. 3612-3625 ◽  
Author(s):  
Wang Qian ◽  
Wang Qiangde ◽  
Wei Chunling ◽  
Zhang Zhengqiang
Keyword(s):  
Neural Networks ◽  
Tracking Control ◽  
Large Scale ◽  
Inverse Dynamics ◽  
Small Neighborhood ◽  
High Order ◽  
Interconnected Systems ◽  
Delay Systems ◽  
Rbf Neural Networks ◽  
Stochastic Input

The paper solves the problem of a decentralized adaptive state-feedback neural tracking control for a class of stochastic nonlinear high-order interconnected systems. Under the assumptions that the inverse dynamics of the subsystems are stochastic input-to-state stable (SISS) and for the controller design, Radial basis function (RBF) neural networks (NN) are used to cope with the packaged unknown system dynamics and stochastic uncertainties. Besides, the appropriate Lyapunov-Krosovskii functions and parameters are constructed for a class of large-scale high-order stochastic nonlinear strong interconnected systems with inverse dynamics. It has been proved that the actual controller can be designed so as to guarantee that all the signals in the closed-loop systems remain semi-globally uniformly ultimately bounded, and the tracking errors eventually converge in the small neighborhood of origin. Simulation example has been proposed to show the effectiveness of our results.

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

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