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Improved recursive algorithms compute dynamics of robotic manipulator driven through gears by motors located away from joints. Rotation of each link of manipulator arm about joint at inboard end driven by motor and gears mounted on adjacent inboard link. Inertias of motors and gears taken into account.
In this paper a new algorithm for fast serial and parallel dynamics simulation of space robots as characterized by serial chain systems with a floating base is presented.
Two efficient mapping algorithms for scheduling the robot inverse dynamics computation consisting of m computational modules with precedence relationship to be executed on a multiprocessor system consisting of p identical homogeneous processors with processor and communication costs to achieve minimum computation time are presented. An objective function is defined in terms of the sum of the processor finishing time and the interprocessor communication time. The minimax optimization is performed on the objective function to obtain the best mapping. This mapping problem can be formulated as a combination of the graph partitioning and the scheduling problems; both have been known to be NP-complete. Thus, to speed up the searching for a solution, two heuristic algorithms were proposed to obtain fast but suboptimal mapping solutions. The first algorithm utilizes the level and the communication intensity of the task modules to construct an ordered priority list of ready modules and the module assignment is performed by a weighted bipartite matching algorithm. For a near-optimal mapping solution, the problem can be solved by the heuristic algorithm with simulated annealing. These proposed optimization algorithms can solve various large-scale problems within a reasonable time. Computer simulations were performed to evaluate and verify the performance and the validity of the proposed mapping algorithms. Finally, experiments for computing the inverse dynamics of a six-jointed PUMA-like manipulator based on the Newton-Euler dynamic equations were implemented on an NCUBE/ten hypercube computer to verify the proposed mapping algorithms. Computer simulation and experimental results are compared and discussed.
The formulation of an Order (n) algorithm for DISCOS (Dynamics Interaction Simulation of Controls and Structures), which is an industry-standard software package for simulation and analysis of flexible multibody systems is presented. For systems involving many bodies, the new Order (n) version of DISCOS is much faster than the current version. Results of the experimental validation of the dynamics software are also presented. The experiment is carried out on a seven-joint robot arm at NASA's Goddard Space Flight Center. The algorithm used in the current version of DISCOS requires the inverse of a matrix whose dimension is equal to the number of constraints in the system. Generally, the number of constraints in a system is roughly proportional to the number of bodies in the system, and matrix inversion requires O(p exp 3) operations, where p is the dimension of the matrix. The current version of DISCOS is therefore considered an Order (n exp 3) algorithm. In contrast, the Order (n) algorithm requires inversion of matrices which are small, and the number of matrices to be inverted increases only linearly with the number of bodies. The newly-developed Order (n) DISCOS is currently capable of handling chain and tree topologies as well as multiple closed loops. Continuing development will extend the capability of the software to deal with typical robotics applications such as put-and-place, multi-arm hand-off and surface sliding.
In this paper parallel 0(log N) algorithms for dynamic simulation of single closed-chain rigid multibody system as specialized to the case of a robot manipulatoar in contact with the environment are developed.
This paper tells the story of spatial operators in robot dynamics, emphasizing their physical interpretation, while avoiding lengthly matematical derivations.
An efficient O(mN) algorithm for dynamic simulation of simple closed-chain robotic mechanisms is presented, where m is the number of chains, and N is the number of degrees of freedom for each chain. It is based on computation of the operational space inertia matrix (6 x 6) for each chain as seen by the body, load, or object. Also, computation of the chain dynamics, when opened at one end, is required, and the most efficient algorithm is used for this purpose. Parallel implementation of the dynamics for each chain results in an O(N) + O(log sub 2 m+1) algorithm.
General methods are described by which the mathematical complexities of explicit and exact state equations of robot arms can be reduced to a simplified and compact state equation representation without introducing significant errors into the robot arm dynamic model. The model reduction methods are based on homogeneous coordinates and on the Langrangian algorithm for robot arm dynamics, and utilize matrix, vector and numeric analysis techniques. The derivation of differential vector representation of centripetal and Coriolis forces which has not yet been established in the literature is presented.
Spatially random models provide an alternative to the more traditional deterministic models used to describe robot arm dynamics. These alternative models can be used to establish a relationship between the methodologies of estimation theory and robot dynamics. A new class of algorithms for many of the fundamental robotics problems of inverse and forward dynamics, inverse kinematics, etc. can be developed that use computations typical in estimation theory. The algorithms make extensive use of the difference equations of Kalman filtering and Bryson-Frazier smoothing to conduct spatial recursions. The spatially random models are very easy to describe and are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. The models can also be used to generate numerically the composite multibody system inertia matrix. This is done without resorting to the more common methods of deterministic modeling involving Lagrangian dynamics, Newton-Euler equations, etc. These methods make substantial use of human knowledge in derivation and minipulation of equations of motion for complex mechanical systems.
Explicit state equations provide detailed analytic insight into the dynamic behavior of a robot arm and facilitate the understanding of the control problem. The analytic strength of explicit state equations is exemplified for a given robot arm. In fact, for the quoted example, the explicit and exact state equations involve considerably less computation than the use of the known most efficient general-purpose computational algorithm for robot arm dynamics.
Recursive forward dynamics algorithms are developed for an arbitrary number of robot arms moving a commonly held object. The multiarm forward dynamics problem is to find the angular accelerations at the joints and the contact forces that the arms impart to the task object. The problem also involves finding the acceleration of this object. The multiarm forward dynamics solutions provide a thorough physical and mathematical understanding of the way several arms behave in response to a set of applied joint moments. Such an understanding simplifies and guides the subsequent control design and experimentation process. The forward dynamics algorithms also provide the necessary analytical foundation for conducting analysis and simulation studies. The multiarm algorithms are based on the filtering and smoothing approach recently advanced for single-arm dynamics, and they can be built up modularly from the single-arm algorithms. The algorithms compute recursively the joint-angle accelerations, the contact forces, and the task-object accelerations. Algorithms are also developed to evaluate in closed form the linear transformations from the active joint moments to the joint-angle accelerations, to the task-object accelerations., and to the task-object contact forces. A possible computing architecture is presented as a precursor to a more complete investigation of the computational performance of the dynamics algorithms.
Recursive forward dynamics algorithms are developed and presented for an arbitrary number of robot arms moving a commonly held object. The multiarm forward dynamics problem is to find the angular accelerations at the joints and the contact forces that the arms impart to the task object. The problem also involves finding the acceleration of this object. The multiarm forward dynamics solutions provide a thorough physical and mathematical understanding of the way several arms behave in response to a set of applied joint moments. Such an understanding simplifies and guides the subsequent control design and experimentation process. The forward dynamics algorithms also provide the necessary analytical foundation for conducting analysis and simulation studies. The multiarm algorithms are based on the filtering and smoothing approach recently advanced for single-arm dynamics, and they can be built up modularly from the single-arm algorithms. The algorithms compute recursively the joint angle accelerations, the contact forces, and the task-object accelerations. Algorithms are also developed to evaluate in closed form the linear transformations from the active joint moments to the joint angle accelerations, to the task object accelerations, and to the task-object contact forces. A possible computing architecture is presented as a precursor to a more complete investigation of the computational performance of the dynamics algorithms.
Report discusses use of random-field mathematical models as alternatives to deterministic models of classical mechanics to describe dynamics of robot arms. These alternative models used to establish relationship between methods of estimation theory and robot dynamics. Approach yields new class of algorithms performing computations typical of estimation theory to solve such fundamental problems in robotics as forward and inverse dynamics and inverse kinematics.
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Ndarts software provides algorithms for computing quantities associated with the dynamics of articulated, rigid-link, multibody systems. It is designed as a general-purpose dynamics library that can be used for the modeling of robotic platforms, space vehicles, molecular dynamics, and other such applications. The architecture and algorithms in Ndarts are based on the Spatial Operator Algebra (SOA) theory for computational multibody and robot dynamics developed at JPL. It uses minimal, internal coordinate models. The algorithms are low-order, recursive scatter/ gather algorithms. In comparison with the earlier Darts++ software, this version has a more general and cleaner design needed to support a larger class of computational dynamics needs. It includes a frames infrastructure, allows algorithms to operate on subgraphs of the system, and implements lazy and deferred computation for better efficiency. Dynamics modeling modules such as Ndarts are core building blocks of control and simulation software for space, robotic, mechanism, bio-molecular, and material systems modeling.
The kinematics, dynamics, Jacobian, and their corresponding inverse computations are six essential problems in the control of robot manipulators. Efficient parallel algorithms for these computations are discussed and analyzed. Their characteristics are identified and a scheme on the mapping of these algorithms to a reconfigurable parallel architecture is presented. Based on the characteristics including type of parallelism, degree of parallelism, uniformity of the operations, fundamental operations, data dependencies, and communication requirement, it is shown that most of the algorithms for robotic computations possess highly regular properties and some common structures, especially the linear recursive structure. Moreover, they are well-suited to be implemented on a single-instruction-stream multiple-data-stream (SIMD) computer with reconfigurable interconnection network. The model of a reconfigurable dual network SIMD machine with internal direct feedback is introduced. A systematic procedure internal direct feedback is introduced. A systematic procedure to map these computations to the proposed machine is presented. A new scheduling problem for SIMD machines is investigated and a heuristic algorithm, called neighborhood scheduling, that reorders the processing sequence of subtasks to reduce the communication time is described. Mapping results of a benchmark algorithm are illustrated and discussed.
Report discusses applicability of conjugate-gradient algorithms to computation of forward dynamics of robotic manipulators. Rapid computation of forward dynamics essential to teleoperation and other advanced robotic applications. Part of continuing effort to find algorithms meeting requirements for increased computational efficiency and speed. Method used for iterative solution of systems of linear equations.
A variational-vector calculus approach is employed to derive a recursive formulation for dynamic analysis of flexible multibody systems. Kinematic relationships for adjacent flexible bodies are derived in a companion paper, using a state vector notation that represents translational and rotational components simultaneously. Cartesian generalized coordinates are assigned for all body and joint reference frames, to explicitly formulate deformation kinematics under small deformation kinematics and an efficient flexible dynamics recursive algorithm is developed. Dynamic analysis of a closed loop robot is performed to illustrate efficiency of the algorithm.