# CI-TEAMS CI-Team Objective: A Multi-Disciplinary Engineering Model

We propose to create a comprehensive, multi-disciplinary engineering model of snake robot components, assemblies and subassemblies. Each component, assembly, and sub-system will have associated with it descriptors for component semantics, engineering representations and computational models as shown in Figure 1. We discuss each of these model elements in turn.

**Semantic Models**. The semantics layer associated with the snake robot and its components will enable interpretation of behavioral and performance parameters at several layers. For example, global motion and locomotion constraints can be estimated from shape and parameters on the joints. Mass, mechanical stiffness and strength of components can be used to estimate allowable loads and dynamical properties of the robots.

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Figure 2: An example of the semantics layer: A representation of the semantics of a photo-sensor using description logics and the Ontology Web Language (OWL).

The engineering community has just begun encoding engineering knowledge in XML [26, 127, 128]. To move toward truly shared semantics, students working in emerging engineering areas need to understand how to use the SemanticWeb for markup and annotation to address representation problems [3, 1, 2, 31]. The engineering model developed by this CI-Team will demonstrate how the Ontology Web Language (OWL)) [139] and extensions to it can be used to capture engineering knowledge as well as its association to shape and simulation models representing the artifact. By working with collaborators at NIST and DoE, this CI-Team will increase the usability of SemanticWeb1 tools for engineers and make the results part of new and emerging ISO and W3C standards (e.g., see [45, 116, 115]). Figure 2 show a representative example of a semantic model. In this case, formal methods (description logic) have been used to define the function of a light sensor. Using these semantics, the light sensor object can be stored in an engineering design repository based on its behavior and shape.

**Engineering Models and Representations**. This layer supports various geometry-centric physical representations (combinatorial [102, 93, 20, 131], parametric [121, 49, 48], symmetry reduced [69], lower-dimensional [125, 126]) corresponding to appropriate formulations (both discrete and continuum) of robot models and their components. Figure 3 shows a host of current representations for engineering models and their inter-relationships. The choice of models and representations depends on the designers needs or context. For example, to evaluate whether a particular snake robot is suitable for a pipe inspection task, one would need to analyze the global motion envelope of the robot and see if it can operate within the pipe. This may only require low-fidelity simulation of motion and movement. To evaluate the performance of the robot under conditions of high loads and temperature, a high-fidelity representation is needed that includes a detailed finite element analysis model.

An important requirement of geometric models is that they satisfy the needs for downstream simulation and analysis. Designers of snake robots face challenges that include the complexity of the individual components, the magnitude of component-component interactions, the existence of flexible parts and the complexity of the electro-mechanical elements. For example, surrogate representations may help in achieving computationally tractable analysis, but to do so they must satisfy two conflicting criteria: (1) they must be sufficiently detailed to be useful for analysis and simulation, and (2) must be sufficiently coarse for efficient computational analysis. Surrogate modeling includes removal of non-critical features [29, 122], lumped-modeling [11, 95], exploitation of symmetry [69], dimensional reduction [125, 126], and other methods supporting multi-level and multi-resolution modeling. The CI-Team will integrate various modeling methods and techniques into the shared engineering model for snake-like robots.

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Figure 3: Different classes of geometric models.

**Computational Models**. Finally, the model must include the computational tools and algorithms to perform geometric, dynamic, and spatially-distributed physics computations. For the snake robot, this will include algorithms for collision detection, multi-body dynamics, mechanical simulation. The semantic and geometric models drive the computational analysis of the dynamics, behaviors and capabilities of the prospective snake robot. In this context, “computational models” includes the software systems for simulation and analysis as well as the configuration and parameterization of these systems to answer the query at hand. By archiving this complete sequence in our shared model, the team will create a set of recipes for analyzing not only snake inspired robotic systems but other complex electro-mechanical systems. The computational models in the repository will include software for:

- Adaptive Dynamics. To compute adaptive forward dynamics [37, 13, 19, 34, 50, 84, 35, 36, 106, 88, 14, 42, 9, 144, 33, 44, 96] of complex linkages for snake-like (mini-, micro-, or nano-) robots, designers will need to understand how to use new hybrid-body representations that allow articulated links to be simulated as a combination of articulated and rigid bodies. Parameters to such software will be updated at runtime, based on the bounded “motion error metrics” of simulated motion. The motion error metrics are defined by the error bounds on the acceleration and velocity of joints. Based on the error metrics, software can then determine which joints should be simulated and which should be treated as rigid links. Such algorithms can cull away computations for joints, whose contribution to the overall linkage motion is below a given application-dependent threshold, thus limiting the computation of the joint accelerations and forces to those that contribute most to the overall motion. It also allows a natural trade-off between the precision of the resulting simulation and the time required to compute it.
- Deformable Body Dynamics arises in prototyping wires, cables, flexible nano-systems, as well as tissue and bio-engineering [110, 138, 92, 137, 136, 53, 54, 22, 27, 87, 109, 98, 143]. The behavior of flexible objects is defined by its geometry, physics and internal structures. Software is needed to accurately compute deformable body dynamics in real-time.
- Multi-Level Computation adapts multi-grid methods from computational fluid dynamics to accelerate the computation in multi-scale, physics-based, simulation environments. The basic idea is to define a series of coarse approximations to the initial problem in a hierarchical manner, recursively using solutions of the coarser problem instances to efficiently compute an overall solution. This can enable large-scale simulations with multi-body dynamics and modeling for deformation using finite element methods and mesh-free methods.
- Multi-scale Dynamics Simulation extends the multi-resolution concept to modeling physical behavior, requiring simulation of complex mechanical, physical, or biological systems across a wide range of scales, resulting in varying accuracy, fidelity and runtime performance.
- Inverse Dynamics can be useful for rapid prototyping where the desired end-effect location is given and we need to compute inverse dynamics of a complex linkages adaptively. By appropriately customizing the weight matrices, the motion error metrics makes it possible to perform rigorous adaptive computation of complex linkage inverse dynamics, which would determine the joints that have to be active based on the maximum amount of errors specified by the designer.
- Adaptive control of complex linkages enables simulation to go beyond simulation into developing control systems software and develop adaptive controllers that could be combined with our adaptive dynamics framework. For example, one could imagine that the motion of a snake robot is compensated by a modification of the robot’s tail motion which, in turn, would force the robot to crawl slightly differently.

In the long run, we envision a continuum of adaptive algorithms for the control and simulation of complex chains and linkages, as well as hybrid algorithms using a combination of physically-based simulation, learning techniques, and data-driven modeling.