Customized computational robot dynamics

In 1983 the authors implemented the computer program Algebraic Robot Modeler (ARM) to generate symbolically complete closed-form and recursive dynamic robot models.^1–3 Then, in 1985, we incorporated in ARM heuristic rules for the systematic organization of dynamic robot models to reduce the computational requirements of customized forward and inverse dynamics calculations. We resolve the issue of numerical efficiency of customized closed-form and recursive forward and inverse dynamics algorithms for kinematically and dynamically structured manipulators. We find that ARM-generated customized closed-form algorithms are the most computationally efficient calculators of forward and inverse dynamics of three degree-of-freedom manipulators. For six DOF predominantly rotational manipulators, ARM-generated customized recursive algorithms are the most computationally efficient foward and inverse dynamics algorithms; inverse dynamics can be computed in less than one millisecond on commercially-available processors (in software, without special-purpose hardware). In our companion article,⁴ we compare the symbolic efficiencies of six robot dynamics formulations for generating closed-form and recursive models.     

Symbolically efficient formulations for computational robot dynamics

In 1983, the authors implemented the computer program Algebraic Robot Modeler (ARM) to generate symbolically complete closed-form and recursive dynamic robot models.^1–4 Then, in 1985, we incorporated in ARM heuristic rules for the systematic organization of dynamic robot models to reduce the computational requirements of customized forward and inverse dynamics calculations. We compare the symbolic efficiencies of six robot dynamics formulations for generating closed-form and recursive models. We find that our Lagrange-Christoffel formulation is the most symbolically efficient generator of closed-form dynamic robot models. In our companion paper,³ we resolve the issue of numerical efficiency of customized closed-form and recursive algorithms for computing the forward and inverse dynamics of kinematically and dynamically structured manipulators.     

基于神经网络的机械臂的力控制方法

本文提出一种基于神经网络的力控制方法，由两个串联的神经网络构成机械臂的力控制器，其中一个网络用来学习机械臂本身的逆动力学系统，而另一网络用来学习未知的被接触环境的动力学特征，这种方法避免了困难的接触环境建模问题。一个 双连杆机械臂的力控制的仿真实验描述了种种方法的有效性。     

Recursive modelling in dynamics of Agile Wrist spherical parallel robot

Recursive matrix relations for kinematics and dynamics of the 3-RRR Agile Wrist spherical parallel robot are established in this paper. The prototype of the robot is a three-degrees-of-freedom mechanism with three identical legs. Controlled by concurrent torques, which are generated by some electric motors, the active elements of the robot have three independent rotations. Knowing the rotation motion of the moving platform, we develop first the inverse kinematical problem and determine the velocities and accelerations. Further, the principle of virtual work is used in the inverse dynamic problem. Matrix equations offer iterative expressions and graphs for the power requirement comparison of each of three actuators in two computational complexities: complete dynamic model and simplified dynamic model.     

A survey of efficient computational methods for manipulator inverse dynamics

In this paper, we present an up-to-date survey of various numerically efficient methods for solving the problem of computing manipulator inverse dynamics. The literature on this subject is extensive. However, in this paper, we review only those algorithms which have been derived based on the Euler—Lagrange, Newton—Euler and Kane's formulations of the dynamic equations of motion and are applicable to rigid-link open-chain robot manipulators. In particular, for each of these formulations we present a chronological account of the development of the most important algorithms which compute manipulator inverse dynamics. In this process some classical algorithms are given and a number of issues which make it possible to reduce their computational complexity are emphasized. Also, the most efficient algorithms currently available are compared in terms of their computational complexity.This research was supported by a postdoctoral fellowship funded from NSERC of Canada Grant OGP0001345 and a grant from the Institute of Robotics and Intelligent Systems (IRIS), both awarded to Dr. R. V. Patel.     

Timed trajectory generation using dynamical systems: Application to a Puma arm

We present an attractor based dynamics that autonomously generates trajectories with stable timing (limit cycle solutions), stably adapted to changing online sensory information. Autonomous differential equations are used to formulate a dynamical layer with either stable fixed points or a stable limit cycle. A neural competitive dynamics switches between these two regimes according to sensorial context and logical conditions. The corresponding movement states are then converted by simple coordinate transformations and an inverse kinematics controller into spatial positions of a robot arm. Movement initiation and termination is entirely sensor driven. In this article, the dynamic architecture was changed in order to cope with unreliable sensor information by including this information in the vector field.We apply this architecture to generate timed trajectories for a Puma arm which must catch a moving ball before it falls over a table, and return to a reference position thereafter. Sensory information is provided by a camera mounted on the ceiling over the robot. A flexible behavior is achieved. Flexibility means that if the sensorial context changes such that the previously generated sequence is no longer adequate, a new sequence of behaviors, depending on the point at which the changed occurred and adequate to the current situation emerges.The evaluation results illustrate the stability and flexibility properties of the dynamical architecture as well as the robustness of the decision-making mechanism implemented.     

An efficient method for inverse dynamics of manipulators based on the virtual work principle

The computational efficiency of inverse dynamics of a manipulator is important to the real-time control of the system. For serial manipulators, the recursive Newton-Euler method has been proven to be the most efficient. However, for more general manipulators, such as serial manipulators with closed kinematic loops or parallel manipulators, it must be modified accordingly and the resultant computational efficiency is degraded. This article presents a computationally efficient scheme based on the virtual work principle for inverse dynamics of general manipulators. The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion. This method is equally effective for serial and parallel manipulators. For serial manipulators, its computational efficiency is comparable to the recursive Newton-Euler method. For parallel manipulators or serial manipulators with closed kinematic loops, it is more efficient than the existing methods. As an example, the computations of inverse dynamics (including inverse kinematics) of a general Stewart platform require only 842 multiplications, 511 additions, and 12 square roots.     

Task-space neuro-sliding mode control of robot manipulators under Jacobian uncertainties

Cartesian robot control is an appealing scheme because it avoids the computation of inverse kinematics, in contrast to joint robot control approach. For tracking, high computational load is typically required to obtain Cartesian robot dynamics. In this paper, an alternative approach for Cartesian tracking is proposed under assumption that robot dynamics is unknown and the Jacobian are uncertain. A neuro-sliding second order mode controller delivers a low dimensional neural network, which roughly estimates inverse robot dynamics, and an inner smooth control loop guarantees exponential tracking. Experimental results are presented to confirm the performance in a real time environment.     

机械臂惯性矩阵的并行计算

本文在给出一种非递推形式的逆动力学计算公式的基础上，针对机械臂惯性矩阵的计算提出了一种面向Ｏ（ｎ）个处理器的并行算法，并以ＰＵＭＡ５６０机器人的前３个臂为例进行了计算效率分析。     

A genetic algorithm for multiprocessor scheduling

The problem of multiprocessor scheduling can be stated as finding a schedule for a general task graph to be executed on a multiprocessor system so that the schedule length can be minimized. This scheduling problem is known to be NP-hard, and methods based on heuristic search have been proposed to obtain optimal and suboptimal solutions. Genetic algorithms have recently received much attention as a class of robust stochastic search algorithms for various optimization problems. In this paper, an efficient method based on genetic algorithms is developed to solve the multiprocessor scheduling problem. The representation of the search node is based on the order of the tasks being executed in each individual processor. The genetic operator proposed is based on the precedence relations between the tasks in the task graph. Simulation results comparing the proposed genetic algorithm, the list scheduling algorithm, and the optimal schedule using random task graphs, and a robot inverse dynamics computational task graph are presented     

Adaptive tracking control of manipulators: Theory and experiments

This paper considers the trajectory tracking problem for uncertain robot manipulators and proposes two adaptive controllers as solutions to this problem. The first controller is derived under the assumption that the manipulator state is measurable, while the second strategy is developed for those applications in which only position measurements are available. The adaptive schemes are very general and computationally efficient since they do not require knowledge of either the mathematical model or the parameter values of the manipulator dynamics, and are implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategies ensure uniform boundedness of all signals in the presence of bounded disturbances, and that the ultimate size of the tracking errors can be made arbitrarily small. Experimental results are presented for a PUMA 560 manipulator and demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed controllers.     

Dynamics analysis of the Star parallel manipulator

Matrix relations in kinematics and dynamics of the Star parallel manipulator are established in this paper. The prototype of the manipulator is a three-degree-of-freedom mechanism, which consists of a system of parallel kinematical chains connecting to a moving platform. Knowing the translation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each robot’s link. Further, the inverse dynamics problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with their multipliers. Recursive formulae offer expressions and graphs for the power requirement comparison of each of three actuators in two computational complexities: complete dynamic model and simplified dynamic model.     

A New Geometric Subproblem to Extend Solvability of Inverse Kinematics Based on Screw Theory for 6R Robot Manipulators

Geometric inverse kinematics procedures that divide the whole problem into several subproblems with known solutions, and make use of screw motion operators have been developed in the past for 6R robot manipulators. These geometric procedures are widely used because the solutions of the subproblems are geometrically meaningful and numerically stable. Nonetheless, the existing subproblems limit the types of 6R robot structural configurations for which the inverse kinematics can be solved. This work presents the solution of a novel geometric subproblem that solves the joint angles of a general anthropomorphic arm. Using this new subproblem, an inverse kinematics procedure is derived which is applicable to a wider range of 6R robot manipulators. The inverse kinematics of a closed curve were carried out, in both simulations and experiments, to validate computational cost and realizability of the proposed approach. Multiple 6R robot manipulators with different structural configurations were used to validate the generality of the method. The results are compared with those of other methods in the screw theory framework. The obtained results show that our approach is the most general and the most efficient.

     

General-purpose inverse kinematics transformations for robotic manipulators

Real-time robot control requires efficient inverse kinematics transformations to compute the temporal evolution of the joint coordinates from the motion of the end-effector. The development of a coherent, general-purpose framework, incorporating position, velocity and acceleration transformations, is the theme of this paper. In this framework, the computational requirements of a new inverse kinematic algorithm are delineated. The algorithm is applicable to serial (open-chain) manipulators with arbitrary axes of motion. Comparative evaluations of the computational cost of the algorithm demonstrate its efficacy and feasibility for real-time applications.     

A Kane’s based algorithm for closed-form dynamic analysis of a new design of a 3RSS-S spherical parallel manipulator

This paper proposes a systematic methodology to obtain a closed-form formulation for dynamics analysis of a new design of a fully spherical robot that is called a 3(RSS)-S parallel manipulator with real co-axial actuated shafts. The proposed robot can completely rotate about a vertical axis and can be used in celestial orientation and rehabilitation applications. After describing the robot and its inverse position, velocity and acceleration analysis is performed. Next, based on Kane’s method, a methodology for deriving the dynamical equations of motion is developed. The elaborated approach shows that the inverse dynamics of the manipulator can be reduced to solving a system of three linear equations in three unknowns. Finally, a computational algorithm to solve the inverse dynamics of the manipulator is advised and several trajectories of the moving platform are simulated.

     

Parallel computation of manipulator inverse dynamics

In this article, parallel computation of manipulator inverse dynamics is investigated. A hierarchical graph-based mapping approach is devised to analyze the inherent parallelism in the Newton-Euler formulation at several computational levels, and to derive the features of an abstract architecture for exploitation of parallelism. At each level, a parallel algorithm represents the application of a parallel model of computation that transforms the computation into a graph whose structure defines the features of an abstract architecture, i.e., number of processors, communication structure, etc. Data flow analysis is employed to derive the time lower bound in the computation as well as the sequencing of the abstract architecture. The features of the target architecture are defined by optimization of the abstract architecture to exploit maximum parallelism while minimizing various overheads and architectural complexity. An algorithmically specialized, highly parallel, MIMD-SIMD architecture is designed and implemented that is capable of efficient exploitation of parallelism at several computational levels. The computation time of the Newton-Euler formulation for a 6-degree-of-freedom (dof) general manipulator is measured as 187 μs. The increase in computation time for each additional dof is 23 μs, which leads to a computation time of less than 500 μs, even for a 12-dof redundant arm.     

A fast and scalable architecture to run convolutional neural networks in low density FPGAs

Deep learning and, in particular, convolutional neural networks (CNN) achieve very good results on several computer vision applications like security and surveillance, where image and video analysis are required. These networks are quite demanding in terms of computation and memory and therefore are usually implemented in high-performance computing platforms or devices. Running CNNs in embedded platforms or devices with low computational and memory resources requires a careful optimization of system architectures and algorithms to obtain very efficient designs. In this context, Field Programmable Gate Arrays (FPGA) can achieve this efficiency since the programmable hardware fabric can be tailored for each specific network. In this paper, a very efficient configurable architecture for CNN inference targeting any density FPGAs is described. The architecture considers fixed-point arithmetic and image batch to reduce computational, memory and memory bandwidth requirements without compromising network accuracy. The developed architecture supports the execution of large CNNs in any FPGA devices including those with small on-chip memory size and logic resources. With the proposed architecture, it is possible to infer an image in AlexNet in 4.3 ms in a ZYNQ7020 and 1.2 ms in a ZYNQ7045.     

Computational robot dynamics: Foundations and applications

In 1984, the authors unveiled the computer program Algebraic Robot Modeler (ARM) for the symbolic generation of complete closed-form dynamic robot models. In this paper, we introduce computational robot dynamics as the synthesis of classical mechanics and computer software for the symbolic and numeric modeling of robotic mechanisms, and branch-out in three directions. First, we outline the foundations of computational robot dynamics. From its inception (in 1973), we review chronologically the contributions of prominent roboticists, tracing the parallel development of robot dynamics formulations and computational robot dynamics. We then highlight our research activities, the current capabilities of ARM, and our plans for the continuing development and application of ARM and computational robot dynamics. Finally, we focus on practical applications of computational robot dynamics. We apply ARM to produce examples illustrating the comparative computational requirements of robot dynamics formulations for symbolic processing and customized algorithms for numeric processing.     

面向全方位双足步行跟随的路径规划

双足步行机器人的足迹规划方法难以满足快速步行条件下的计算效率要求, 并存在步幅变化时运动失稳的风险, 2D环境下点机器人栅格规划则难于生成针对双足步行的高效路径.本文提出针对各向异性特征全方位步行机器人的一种路径规划策略, 将状态网格图方法拓展到全方位移动机器人领域, 基于三项基本假设及基元类型划分给出了系统的运动基元枚举及选择方法, 借助实时修正的增量式AD*搜索算法实现仿人机器人在动态环境下的快速路径规划, 通过合理选择启发函数及状态转移代价, 生成了平滑高效的路径, 为后续足迹生成的动力学优化提供了基础.计算机仿真证实了方法对各类环境的适应性, Robocup避障竞速挑战赛的成功表现证明了方法对于机器人样机部署的可行性及其提高步行效率的潜力.     

翻滚目标逼近的虚拟域逆动力学轨迹规划

针对追踪星自主逼近和跟踪翻滚目标特定部位的最优规划问题,提出了一种基于虚拟域逆动力学的多约束最优逼近轨迹规划方法.首先,在翻滚目标本体系下建立追踪星相对于翻滚目标特定部位的相对轨道动力学方程,并建立追踪星本体系相对于翻滚目标期望固连坐标系的相对姿态动力学方程;其次,考虑目标星外形、敏感器视场和执行机构控制能力等约束条件,建立时间/能量最优规划模型;然后,采用序列二次规划(sequential quadratic programming,SQP)方法求解时间/能量最优规划问题;最后,数值仿真验证了该方法在满足多约束条件下,可实现对翻滚目标自主逼近与跟踪的最优轨迹规划,同时与高斯伪谱法进行了对比,验证了本方法在计算效率方面的优势.