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Special Events

SHORT COURSE

Course Title: Tensegrity Systems Analysis: Mechanics, Optimization and Control
Sunday, September 9th
10:00am-12:00pm, 1:00pm-4:30pm
Presidio B
Robert Skelton and Manoranjan Majji

Description
This short course investigates fundamental issues between physics and engineering, with specific emphasis on recent advances in tensegrity systems.
We investigate first principles in engineering mechanics to yield minimal mass structures subject to structural and materials response constraints.
Students will be exposed to issues between structure design, structure modeling, and structure control, concluding that accurately modeling structural
dynamics is not just about the physical and constitutive laws. Useful models for simulation or control depend upon the accuracy of the computational
resources, the objectives of the control, as well as the mechanics of the physics. Reduced order models can be produced which are superior to the exact
physics installed in a finite-precision computer. Indeed, we will show that signal processing is the catalyst that allows the integration of modeling
and control.

Tensegrity systems tend to have accurate models because the components of the structure are the most fundamental of elements particles rigid rods,
and tensile members (strings). We will introduce a new approach to Multi-body dynamics, where the mass matrix is constant and invertible, and the
equations are devoid of trigonometric functions. We will derive the nonlinear equations that describe any tensegrity structure, where the overall structure
can bend, but no element of the structure is subjected to bending loads. Examples will include deployable antennas, domes, impact structures, and
shape-controllable structures.

References:
1. Skelton, R. E., and de Oliveira, M., Tensegrity Systems, Springer - Verlag, 2013.
2. Skelton, R. E., Dynamic Systems Control: Linear Systems Analysis and Synthesis, John Wiley and Sons, 1988.
3. Skelton, R. E., Iwasaki, T., Grigoriadis, K. M., A Unified Algebraic Approach to Linear Control Design, Taylor and Francis, 1997.
4. Junkins, J. L., and Kim, Y., Introduction to Dynamics and Control of Flexible Structures, AIAA Education Series, Washington, D.C., 1999.
5. Selected articles from the journals: Journal of Guidance, Control and Dynamics, IEEE Transactions on Automatic Control, and Automatica will be used
5. to supplement the instruction

Topic Number Title References
1 Refs 2-3.
Linear algebra, vector kinematics, dynamics
2 and notation. Systems analysis and dynamic Refs 1-2
3 systems control. Ref 1.
4 Ref 1.
5 Mechanics of flexible structures. Ref 2,5
6 Continuous systems, exact methods, finite Ref 5.
dimensional approximations.

Tensegrity beams, plates and shells

Optimal modeling and simulation

Resource allocation: sensor/actuator
precisions, location and modality selection.

Applications: soft robotics, space
structures, gyroboten

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