The specification of the data structures used in EAT, a software system for symbolic computation in algebraic topology, is based on an operation that defines a link among different specification frameworks like hidden algebras and coalgebras. In this paper, this operation is extended using the notion of institution, giving rise to three institution encodings. These morphisms define a commutative diagram which shows three possible views of the same construction, placing it in an equational algebraic institution, in a hidden institution or in a coalgebraic institution. Moreover, these morphisms can be used to obtain a new description of the final objects of the categories of algebras in these frameworks, which are suitable abstract models for the EAT data structures. Thus, our main contribution is a formalization allowing us to encode a family of data structures by means of a single algebra (which can be described as a coproduct on the image of the institution morphisms). With this aim, new particular definitions of hidden and coalgebraic institutions are presented.

We describe the design and implementation of RSTATION, an object-oriented, modular robot simulator with hierarchical analysis capabilities. Modularity is achieved via the features of design encapsulation and enables grouping a set of interconnected components into a single component and dividing the robot system into several sets of subordinate modules recursively. By careful construction of the data types and classes, RSTATION allows for hierarchical simulation of the kinematics, and the dynamics at three levels: considering only main links (high-level), using simplified models including dynamic properties of transmission elements (intermediate level), and taking into account the detailed kinematics and dynamics of transmission elements (low-level). Submodules can be set to different resolution during a single simulation. The data types and classes also exploit a recent set of coordinate invariant robot analysis algorithms based on modern screw theory. Central to the low-level dynamic analysis capability is an algorithm for systematically extracting the constraint equations for general gearing systems. The various features of RSTATION are illustrated with a detailed case study of a commercial industrial robot.