Articulated-body Algorithm Research Articles

A reduced-order lie group-based race car model for systematic trajectory optimization on 3D tracks

AbstractThis paper derives the dynamic equations of a reduced-order race-car model using Lie-group methods. While these methods are familiar to computational dynamicists and roboticists, their adoption in the vehicle dynamics community is limited. We address this gap by demonstrating how this framework integrates smoothly with the Articulated-Body Algorithm (ABA) and provides a fresh and systematic formulation of vehicle dynamics. For the first time, we model the car body as the end effector of a serial robot with a floating base connected to the track via virtual revolute and prismatic joints. Our formulation also accounts for the effects of 3D track geometry, providing a natural embedding of the car into the 3D track. We rigorously reconcile the ABA steps with key aspects of vehicle dynamics, including road-tire interactions, aerodynamic forces, and load transfers. The resulting model, simple yet accurate, is a powerful tool to efficiently solve Minimum-Lap-Time Planning problems. To demonstrate the effectiveness of our approach, we show numerical results obtained on the Nürburgring circuit. Our optimization problem is formulated via a direct collocation method and solved using the CasADi optimization suite. To validate the results, we test our reduced-order model against a full-fledged multi-body model recently developed by the same authors. The comparison confirms the validity of our reduced-order model, proving both the accuracy of the solution and the computational efficiency achieved.

Analytical differentiation of the articulated-body algorithm: a geometric multilinear approach

This paper presents a new geometric algorithm to efficiently compute the analytical differentiation of the Articulated-body Algorithm (ABA) with respect to the state variables. Despite the fact that ABA solves the forward-dynamics problem in linear time for branched-multibody systems, its explicit differentiation is not straightforward, and computationally demanding tensor products and contractions appear. The proposed algorithm makes use of Lie algebraic and multilinear operations to recursively exploit the underlying sparsity of the linearization problem. As a result, the arithmetic complexity is dramatically reduced without affecting the analytical solution. Since the linealization of forward dynamics is of great importance in robot-trajectory optimization, a differential dynamic programming solver is employed to demonstrate the performance of our algorithm with humanoid robot models such as NAO and HRP-2. In addition, we provide the computational cost with different robots using an optimized C++ implementation that can be found at https://github.com/garechav/geombd_crtp.git .

Minimum-Lap-Time Planning of Multibody Vehicle Models via the Articulated-Body Algorithm

Minimum lap-time planning (MLTP) is a well-established problem in the race car industry to provide guidelines for drivers and optimize the vehicle’s setup. In this paper, we tackle the 3D nature of the problem in its full extension, making no simplifying assumptions on the mechanics of the system. We propose a multibody vehicle model, described by rigorous dynamical equations. To effectively handle the resulting complexity, we devised an efficient direct dynamics computational method based on Featherstone’s articulated-body algorithm (ABA). To solve the MLTP, we employed a direct-collocation technique, discretizing the problem so that all information of the 3D track is pre-processed and directly embedded into the discrete problem. This discretization approach turns out to be perfectly compatible with our vehicle model, leading to a solution in accessible computational time frames. The high level of detail of the model makes the proposed approach most useful for in-depth vehicle dynamics analyses on complex tracks. To substantiate the analysis, we provide a comparison with the results obtained by a double-track model on the Nürburgring Nordschleife circuit. Consistently with the average trend defined by the double track, the proposed model features a more dynamically rich behavior, realistically capturing the higher-order effects elicited by the sharp corners and the highly variable slope of the track.

An o(n) complexity recursive algorithm for multi‐flexible‐body dynamics based on absolute nodal coordinate formulation

SummaryA new algorithm called recursive absolute nodal coordinate formulation algorithm (REC‐ANCF) is presented for dynamic analysis of multi‐flexible‐body system including nonlinear large deformation. This method utilizes the absolute nodal coordinate formulation (ANCF) to describe flexible bodies, and establishes a kinematic and dynamic recursive relationship for the whole system based on the articulated‐body algorithm (ABA). In the ordinary differential equations (ODEs) obtained by the REC‐ANCF, a simple form of the system generalized Jacobian matrix and generalized mass matrix is obtained. Thus, a recursive forward dynamic solution is proposed to solve the ODEs one element by one element through an appropriate matrix manipulation. Utilizing the parent array to describe the topological structure, the REC‐ANCF is suitable for generalized tree multibody systems. Besides, the cutting joint method is used in simple closed‐loop systems to make sure the O(n) algorithm complexity of the REC‐ANCF. Compared with common ANCF algorithms, the REC‐ANCF has several advantages: the optimal algorithm complexity (O(n)) under limited processors, simple derivational process, no location or speed constraint violation problem, higher algorithm accuracy. The validity and efficiency of this method are verified by several numerical tests. Copyright © 2016 John Wiley & Sons, Ltd.

Multibody simulation of the musculoskeletal system of the human hand

This paper presents a numerical model of the forward multibody dynamics of the human hand. This model forms the basic foundation in the development of a five-fingered anthropomorphic hand prosthesis. The model is composed of two parts: a model for the rigid-body dynamics of the bone and joint structure of the human hand using the modified articulated-body algorithm for tree structures, and a model to represent the action the muscles tendons present in the hand. The resulting nonlinear model takes as input the actuation of each muscle and outputs the movements of the joints of the hand. This model will be used in the development of a nonlinear controller for the prosthesis and in its testing before being applied into the prosthesis prototype.

An efficient parallel dynamics algorithm for simulation of large articulated robotic systems

This paper presents a new parallel computer algorithm for the simulation of large articulated robotic systems. The method employs the Divide and Conquer Algorithm (DCA) multibody methodology and achieves significant increases in speed by using a variation of the Articulated Body Algorithm (ABA) to efficiently construct the DCA subsystems. The method outperforms contemporary parallel dynamics algorithms for a serial topology and degenerates to the ABA in the absence of parallel resources. The implementation and comparison with the ABA demonstrate useful speed increases with as few as two parallel processors and speed ups by a factor of 2.25 in the presence of four processors for serial manipulators. The paper also addresses the practical limitations on obtainable speedups due to the interprocessor communication costs and its consequences on choosing optimal DCA subsystems.

Simulation of rigid-body impact using the articulated-body algorithm

SUMMARYThis paper presents a numerical algorithm to model the impact between articulated structures, or between an articulated structure and an object. The proposed algorithm, called impulse articulated-body algorithm (IABA), is based on the ABA but uses impulses and velocities rather than forces and accelerations. The algorithm also inherits the advantages of the ABA: versatility and low computational cost. The IABA provides a method to determine the impact impulse, without increasing the order of the algorithm.

Comparative Study on Serial and Parallel Forward Dynamics Algorithms for Kinematic Chains*

The main focus of this paper is to investigate the essential differences among four forward dynamics algorithms: the Articulated-Body Algorithm (ABA) and Divide-and-Conquer Algorithm (DCA) by Featherstone; the Constraint Force Algorithm (CFA) by Fijany et al.; and the Assembly—Disassembly Algorithm (ADA) by the present authors. All of the algorithms have O(N) asymptotic complexity for serial computation where N is the number of rigid bodies, and three of them can also be processed in parallel which results in O (log N ) complexity on O (N) processors. We start by summarizing two essential backgrounds of the forward dynamics algorithms, i.e. articulated-body inertias and joint constraint representation. We then present a new formulation of ADA as well as the outlines of the other three algorithms using the same notation. Finally, we perform qualitative as well as quantitative comparisons of the algorithms using our implementations of ABA, CFA, and ADA.

USING ARTICULATED BODY ALGORITHM WITHIN SLIDING-MODE CONTROL TO COMPENSATE DYNAMIC COUPLING IN UNDERWATER-MANIPULATOR SYSTEMS

A control scheme is presented for compensating dynamic coupling between an underwater robotic vehicle (URV) and a manipulator. During task execution the torques commanded at the manipulator joints lead to reactions at the junction point of the manipulator and vehicle. These reactions disturb the vehicle position and orientation and are the source of the vehicle-manipulator coupling. In many underwater robotic vehicle-manipulator (URVM) applications, the URV serves as a base while the manipulator performs a required task. Therefore, it is necessary to hold the URV as stationary as possible. In the current work, Slotine’s sliding mode control approach is used to compensate the dynamic effect of the underwater manipulator on the URV. The articulated body (AB) algorithm is used both for the time-domain simulation of the system and for the dynamic equations within the model-based sliding-mode controller. The AB algorithm is preferred for the time-domain system simulation, as it provides a computationally efficient simulation scheme. Finally, a three DOF manipulator mounted on a URV is considered, and results of time-domain numerical simulations of the proposed control scheme are presented.

Efficient computation of articulated-body inertias using successive axial screws

The articulated-body (AB) algorithm for dynamic simulation of chains of rigid bodies was developed by Featherstone (1983). The mast costly step in this algorithm is the computation of the AB inertias at each link which involves a spatial (6/spl times/6) congruence transformation. The amount of computation required is closely coupled to the kinematic modeling technique used. This paper examines this computation in detail and presents an efficient step-by-step procedure for its evaluation in a serial chain with revolute and prismatic joints using modified Denavit-Hartenberg parameters for modeling the kinematics. The result is a very efficient procedure using successive axial screws that reduces the computational requirements of the AB algorithm by about 15% from results obtained by Brandl, Johanni, and Otter (1986). The procedure developed defines a general approach and can be used to improve the efficiency of spatial congruence transformations of other types of matrices, such as spatial rigid-body inertias (used in the composite rigid-body simulation algorithm). >