Scott McMillan

Efficient dynamic simulation of an underwater vehicle with a robotic manipulator

In this paper, an efficient dynamic simulation algorithm is developed for an underwater robotic vehicle (URV) with a manipulator. It is based on previous work on efficient O(N) algorithms, where N is the number of links in the manipulator, and has been extended to include the effects of a mobile base (the URV body). In addition, the various hydrodynamic forces exerted on these systems in underwater environments are also incorporated into the simulation. The effects modeled in this work are added mass, viscous drag, fluid acceleration, and buoyancy forces. With efficient implementation of the resulting algorithm, the amount of computation with inclusion of the hydrodynamics is almost double that of the original algorithm for a six degree-of-freedom land-based manipulator with a mobile base. Nevertheless, the amount of computation still only grows linearly with the number of degrees of freedom in the manipulator. >

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). >

Forward dynamics of multilegged vehicles using the composite rigid body method

A new method for simulating multilegged vehicles, using the composite rigid body (CRB) method is presented. Previous approaches use hard constraints and result in closed kinematic loops which require the solution of constraint forces. Using the decoupled tree-structure (DTS) approach compliant contact modeling is used when the feet of the vehicle contact the ground. This approach is compared to the articulated body DTS method (AB/DTS), and proves to be the most computationally efficient method for multilegged vehicles when each leg has up to three degrees of freedom.

A computational framework for simulation of Underwater Robotic Vehicle systems

This paper presents a computational framework for efficiently simulating the dynamics and hydrodynamics of Underwater Robotic Vehicle (URV) systems. Through the use of object-oriented mechanisms, a very general yet efficient version of the Articulated-Body (AB) algorithm has been implemented. An efficient solution to branching within chains is developed in the paper so that the algorithm can be used to compute the dynamics for the entire class of open-chain, tree-structured mechanisms. By including compliant contacts with the environment, most closed-chain systems can also be modeled. URV systems with an extended set of topologies can be simulated including proposed underwater walking machines with intra-body powered articulations. Using the encapsulation inherent in C++, the hydrodynamics code has been confined to a single class, thereby explicitly defining this framework and providing an environment for readily implementing desired hydrodynamics algorithms. Resulting simulations are very efficient and can be used in a number of applications both in the development and use of URV systems.

Efficient dynamic simulation of an unmanned underwater vehicle with a manipulator

In this paper, an efficient dynamic simulation algorithm is developed for an unmanned underwater vehicle (UUV) with a robotic manipulator. It is based on an efficient O(N) algorithm where N is the number of links in the manipulator, and has been extended to include the full effects of a mobile base and various hydrodynamic forces that are exerted on these systems in underwater environments. The effects modeled in this paper are added mass, viscous drag, fluid acceleration, and buoyancy forces. With efficient implementation of the resulting algorithm, the amount of computation including hydrodynamics almost doubles over the original algorithm for a six degree-of-freedom land-based manipulator with a mobile base. Nevertheless, the amount of computation still only grows linearly with the number of links in the manipulator.<<ETX>>

Efficient dynamic simulation of multiple manipulator systems with singular configurations

The paper presents an efficient algorithm for the simulation of a system of m manipulators each having N degrees of freedom that are grasping a common object. Algorithms for such a system have been previously developed by others. In Lilly and Orin (1989), an O(mN) algorithm is presented that does not fully consider the case when one or more of the manipulators are in singular configurations. However, it is stated in Rodriguez, Jain, and Kreutz-Delgado (1989) that the algorithm has an O(mN)+O(m/sup 3/) computational complexity when one or more of the chains are singular. This results because the size of the system of equations to be solved grows linearly with the number of chains in the system. The algorithm presented in this paper significantly reduces the size of the system of equations to be solved to one that grows linearly with the number of singular chains, s, and achieves an O(mN)+O(s/sup 3/) complexity. In addition to this result, efficient O(mN) algorithms are also presented for special cases where only one or two chains are in singular configurations. These are particularly useful because it is common to deal with systems consisting of only a few manipulators grasping a common object, and even with more manipulators, it is unlikely that many of them will be singular simultaneously. Finally, by applying the algorithm developed for the case of two singularities to a dual-arm system, an algorithm results that requires fewer computations than that of existing methods, and has the added benefit of being robust in the presence of singular manipulators. >

Object-oriented design of a dynamic simulation for underwater robotic vehicles

An efficient simulation algorithm for an underwater robotic vehicle with a single manipulator was developed by the authors (1994) which included the hydrodynamic effects due to added mass, viscous drag, fluid acceleration, and buoyancy forces. This work has since been extended to the simulation of more general tree-structured mechanisms having star topologies with a number of different joint types while maintaining the O(N) computational complexity (N is the number of links). Using this new algorithm, this paper describes the development of a real-time dynamic simulation system for underwater robotic systems. The primary goal is the efficient implementation of this general algorithm which has been achieved with C++ through the use of object-oriented design techniques of encapsulation, inheritance, and polymorphism. Coupled with realistic 3D graphical models, a powerful tool results for applications ranging from control system development to on-line displays during deployment. The use of this software system has been demonstrated for a number of systems including Aquarobot, an underwater hexapod under development in Japan for seawall construction and surveying.

Toward super-real-time simulation of robotic mechanisms using a parallel integration method

The results of research performed in computational robot dynamics to achieve real-time simulation of a manipulator on a general-purpose vector/parallel computer are presented. After effective vectorization of the complex dynamics equations required in simulation, a coarse-grain parallel block predictor-corrector (BPC) method for performing the motion integration was realized on multiple processors to exploit a form of temporal parallelism. Results on a CRAY Y-MP8/864 show that effective use of vectorization and parallelization yields an order of magnitude speedup resulting in a computational rate 50 times faster than real-time for end-effector position errors on the order of a micron. This translates to real-time performance on a less powerful parallel computing system. >

Parallel dynamic simulation of multiple manipulator systems: temporal versus spatial methods

In this paper, parallel algorithms are developed for real-time dynamic simulation of a multiple manipulator system, cooperating to manipulate a large load. In an effort to achieve real-time computational rates on a general-purpose parallel system, temporal and spatial forms of parallelism are implemented to improve performance. Temporal parallelism is obtained with the use of parallel numerical integration methods. A speedup of 3.78 on four processors of a CRAY Y-MPS was achieved with a parallel four-point block predictor-corrector method for the simulation of a four manipulator system. To overcome a loss of efficiency because of a reduction in accuracy with the block integration methods, spatial parallelism is used in which the dynamics of each chain is computed simultaneously. With the same four manipulator system, this form of parallelism in conjunction with a serial integration method results in a speedup of 3.1 on four processors without the degradation in accuracy. In cases where there are more processors than chains, a new multipoint parallel integration method can still be advantageous despite the reduced accuracy. In this case, it is shown that greater effective speedups are achieved when both forms of parallelism are combined to generate more parallel tasks. >

Efficient dynamic simulation of multiple manipulator systems with singularities

The authors present an efficient algorithm for the simulation of a system of m manipulators each having N degrees of freedom that are grasping a common object. They specifically address the problem when a number, s, of the manipulators are in singular configurations, and the resulting algorithm has a computation complexity of O(mN)+O(s/sup 3/). This is a significant improvement over previous algorithms, which cite an O(mN)+O(m/sup 3/) computation. Efficient O(mN) algorithms are also presented for special cases where only one or two chains are in singular configurations. By applying the algorithm for the latter case to a dual-arm system, an algorithm results that requires fewer computations than that of existing methods, and has the added benefit of being robust in the presence of singular manipulators.<<ETX>>