This paper concerns optimization of prestress of a tensegrity
structure to achieve the optimal mixed dynamic and control
performance. A linearized dynamic model of the structure is
derived. The force density variables that parameterize prestress
of the structure appear linearly in the model. The feasible region
of these parameters is defined in terms of the extreme directions
of the prestress cone. Several properties of the problem are
established inside the feasible region of the parameters. The
problem is solved using a gradient method that provides a
monotonic decrease of the objective function inside the feasible
region. A numerical example of a cantilevered planar tensegrity
beam is shown.
This paper concerns open-loop control laws for reconfiguration of
tensegrity towers. By postulating the control strategy as an
equilibrium tracking control, very little control energy is
required. Several different reconfiguration scenarios are possible
for different string connectivity schemes. This includes unit
radius control, twist angle control and truncation parameter
control. All these control laws allow a nonuniform distribution of
the control parameters among units. By defining a wave--like
reference signal and injecting it in the open--loop control law,
we demonstrate the concept of self--propelled tensegrity structure
that are capable of locomotion.
KEYWORDS: Chemical elements, Optimization (mathematics), Matrices, Electroluminescence, Metals, Inspection, Aerospace engineering, Control systems design, Control systems, Lanthanum
This paper concerns the optimal mass-to-stiffness ratio design
of class-2 tensegrity towers. For different loading scenarios,
the procedure seeks the topology and geometry of the structure
that yields an optimal design satisfying common constraints. The
domain of feasible tensegrity geometries is defined by imposing
tensegrity equilibrium conditions on both unloaded and loaded
structure. Remaining constraints include strength constraints for
all elements of the structure and buckling constraints for bars.
The symmetry of the design is imposed by restricting the domain of
geometric variables and element parameters. The static response of
the structure is computed by using a nonlinear large displacement
model. The problem is cast in the form of a nonlinear program. The
influence of material parameters on the optimal shape of the
structure is investigated.
Tensegrity structures consist of tendons (in tension) and bars (in
compression). Tendons are strong, light, and foldable, so
tensegrity structures have the potential to be light but strong
and deployable. Pulleys, NiTi wire, or other actuators to
selectively tighten some strings on a tensegrity structure can be
used to control its shape. This article describes the problem of
asymmetric reconfiguration of tensegrity structures and poses one
method of finding the open loop control law for tendon lengths to
accomplish the desired geometric reconfiguration. In addition, a
practical hardware experiment displays the readiness and
feasibility of the method to accomplish shape control of the
structure.
One of the main properties of tensegrity structures, that sets them apart from most of structures, is that they are vary suitable for shape control. This can be accomplished by controlling lengths of string members. Tensegrity deployment is considered herein as a tracking control problem. Therefore, the required trajectories should be feasible for a given structure. For tensegrity structures, this means that in every desired configuration, the structure has to satisfy tensegrity conditions, which require strings to be in tension, and the structure to be stable. To define an open-loop deployment control law, geometry parameterization of those configurations and corresponding rest lengths of string elements guaranteeing equilibrium are defined first. By slowly varying desired geometry, an open-loop string rest length control is defined. This makes the structure track trajectories defined by the time dependent geometry parameters. Two examples are illustrated: 1. Deployment of planar tensegrity beams made of symmetric stable tensegrity units, $2)$ Deployment of plates made of stable symmetric shell class tensegrity units.
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