Modular tensegrity design uses controllable tension lines to create tensegral linkages between tensegrity modules. Discrete independently integral tensegrities are linked together using secondary saddle slings that maintain a tensegral connection between components and yet act as free moving revolute joints. Tertiary control lines act on these tensegrity linkages to create complex articulations that can do useful work. This design approach allows movement of tensegrity structures to be controlled in an energy efficient way. Think of holarchies rarther than hierarchies.
Context: Tom Flemons Archive
Compliant & controllable connectors between modules
(Aug 7, 2017) The idea behind building modular tensegrities and then hooking them together with a separate set of saddle slings is that the prestress in each tensegrity can be high or low relative to others in the linkage but the connectors (saddle slings) are compliant and free to move in multiple ways. I guess I could imagine a situation where some modules need to be a bit compliant built from more elastic materials and others need to be stiffer and then joined together. For example if you are building a quadruped the foot that strikes the ground needs some compliancy so that it gives a bit when it encounters a rough surface but the leg or torso that connects to the foot can have a higher stress built in so it can support the entire structure. I’ve run into this problem over and over again when I build with elastic cord. It works fine with small structures but when I start to add components (modules) and the weight goes up the larger structure (torso leg etc.) needs to be under higher stress or made of thicker elastic with less compliance to support the weight of the entire structure. In a weightless situation higher prestress in parts corresponds to a great degree of control of the peripheries. The connections between parts (the saddle slings) can be sloppy or compliant but the control lines that keep everything moving in a precise way would have to be very tight.
Criteria for building a quadruped with flexible joints as a series of linked tensegrities
(Aug 7, 2017 continued) This presents problems in that tight control lines cost a lot of energy to move which caused me come up with the criss cross system. Keep in mind that all of this is speculative because I have never had the opportunity to build a working model of an entire system using very stiff materials but as I see it here are the following criteria needed to build a complex system like a quadruped with flexible joints as a series of linked tensegrities.
1– individual modules separately tensioned with a tension network that is under the same tension in all members.
2– saddle slings or equivalents that are tensioned to allow a smooth joint action (this necessitates that two compression member ends rotate around two tension members which are part of the saddle sling, so the tighter the sling the better, providing a way can be found to allow this revolute movement to happen friction free – at some level it is still a standard hinge with issues of friction and wear. Some means will have to found to allow a compression member to rotate around and on a tension member which is never the case in a standard hinge. This is an engineering problem which can be solved – I have some ideas how to do this)
3– criss cross slings which are under high tension which pull two modules towards each other and tend to make the joint flip from one extreme bend to its opposite.
4– vertical control members (actuators) which control the tendency for the criss cross system to flip from one state to the other. These control members will probably allow a limited movement across any one joint but if a number of joints are ganged together then then net result could be a range of motion of over 90 degrees.
All of this is necessary because we can’t emulate how the body modulates and controls its own precision by moving many control lines (muscles/fascia) simultaneously. We don’t have the means or the energy to effect this with the state of material sciences or distributed control systems today. I’m trying to come up with the minimal energy system using the least number of actuators to control multiple joints in a complex system like a quadruped.
But just as the Superball Bot is less jerky and ambulates better the more actuators it has, so too would any articulated model behave better if there were many control lines. For any one joint it needs to have control over its position in 3D space. Normally to constrain any point in space requires 4 vectors to fix its position and 8 more to control rotation along 4 axes (Fuller goes into this in his book Synergy). We can dispense with rotation (torque) for the most part because any joint is going to be compliant to some degree by the nature of tensegrities and so torque is a given but not something we are trying to control for beyond preventing radical twisting of a joint. Certain joints in the body don’t rotate much (knee, finger etc) and have simpler actuator systems. A more complex joint like the pelvis or shoulder has many rotations to control for and has correspondingly many more tension members constraining it. The coordination of such complex joints requires the simultaneous tightening and relaxing of all of these tension members to achieve a specific end (raising the arm, throwing something, stepping forward etc.) I think this is beyond us for now in building analogues so I’m trying to come up with ways to ‘cheat’ with the same effect but with less control members. I think the end result might look a lot like someone with arthritis – an older person moves stiffly and slowly and still manages to accomplish movement albeit with less grace and fluidity.
To control for multiple points in space on multiple modules requires a rapid escalation in the number of control lines unless the way they are hooked together does some of the work for you. For example my knee joint links a 4-fold prism to two other 4-fold prisms (one equal to the femur and the other the tib/fib) such that the lines interpenetrate in a way that prevents hyperextension in one plane of rotation (so the knee only bends one way) and controls for lateral rotation by the nature of how the components rotate against each other. This takes care of a lot of control issues.
I hope this answers some of your questions. This is such a new area I don’t think anyone has worked out the implications of how complicated this is going to be. I’m spinning my tires in the sands of possibilities trying to get some traction on the problem
Currently, tensegrity design is more art than science
(Oct 16, 2015) Designing and building tensegrities at this stage is still an art more than a science. The basic construction proceeds from a catalog of modular shapes but rapidly morphs into something unique. For example building my leg, the tensegrity prisms are altered in length and proportion on the fly. How they are hooked up to each other affects their overall proportions. Balancing all of the tension components is really done by feel and observation, a tweak here and a tweak there to get the thing looking right. In other words, an approach that allows one to approximate things quickly may be more helpful than a numerical precise methodology. This is especially true when building an asymmetrical chiral form like the foot. As I build one I don’t know what length the struts should be or what amount of tension I need to apply. What I am aiming for is four struts which contact the ground evenly and their opposite ends forming a perfect rhombus parallel to the ground at some distance from it. (which I can then more easily attach a lower leg prism to). This is not as easy as it may appear. Similarly when I am putting together components to simulate the pelvis I’m faced with a number of connection problems where the angles don’t quite line up and I’m forced to alter the dimensions of the modules that make up the pelvis so that a spinal mast meet it at the right angle. These are complicated geometric spatial problems to solve and a way has to be found to make it possible to make changes quickly and easily. And this is all in aid of making the basic static model even before adding control lines to actuate it. It is still faster for me to build multiple attempts with dowels and elastics that it is for me to simulate in sketch up. I’ll go to SketchUp only after I have a pretty good idea of what I’m looking for.
Semi-compliant joints between modules
(Feb 23, 2014) In my models I design semi compliant joints between modules which are moved by lines exteriorly to the tension network. In other words there is a separate set of tensionable lines that would pull across joints on different parts of the modules.
(Oct 13, 2015) Given the state of material science, battery power and control algorithms, it seems prudent to design for what we have at present which means creating forms that can be motivated using under-actualized systems of control. That is what I’ve tried to keep in mind in designing tensegrity systems that employ linking discrete independently integral tensegrities together using secondary saddle slings that maintain a tensegral connection between components and yet act as free moving revolute joints, and then tertiary control lines that act on these tensegrity linkages to create complex articulations that can do useful work.
(…Oct 13, 2015) If you want to wire together a tension based articulating robotic system then disruptions in the tension system have to be managed to produce the results you want and avoid the ones you don’t.
I think the control cables can be added to structure post hoc. In other words, if you get the dynamics right which means controlling for unwanted degrees of freedom (hyper-extension in the knee for example) the control lines can be added as a separate system. To stabilize an object (or a tensegrally linked cluster of objects) requires that the rotations be cancelled out along four vectors or axis not three. There’s an old argument that the geodesic list serve hashed out endlessly a few years ago. How many spokes does it take to stabilize the hub of a bicycle wheel around its axle? It centers on the notion how many tension members does it take to stabilize a point in space (one end of the axle for example). Fuller said it took four tension members that are arrayed from that point, ideally tetrahedrally, to fix that point in space with no range of motion. The guys on the listserv and Fuller then added more stabilizing tension members to control the rotation of the point along all 4 vectors. Clockwise and counterclockwise times four vectors equals another eight tension members for a total of 12. Thus for any point in the body there are at minimum 12 vectors which control its position. They all pull in different directions simultaneously but variably. By changing the variance you change the centripetal force and thus the orbital inertia of rigid bodies which allows for controlled dynamic homeostatic movement. By connecting a cluster of tensegrity components in the right way, a lot of this stability is built in already. The control system should be considerably simpler than the prestress tension system. A few days earlier ( Oct 7, 2015) Tom used this text in a different context in The Relationship of Tensegrity to Orbital Mechanics.
How modules relate to each other
(Nov 1, 2015) Rather it seems that instead of talking about structure we should be talking about how these modules relate to each other. In other words there are ways to attach two modules together so that they form a hinge or so that they are self stabilizing by bonding their faces together. Of course Tensegrities don’t really have faces per se – they have polygonal facets which are not exactly planar in all cases. Also edge binding doesn’t work the same way as it does in solid structures. It’s hard to create a hinge when compression struts are rotating along or about a tension member. For one thing the hinge is very compliant and therefore perhaps inefficient; for another unless the tension members are parallel the hinge doesn’t work very well.
Holarchies rather than hierarchies
(May 25, 2015) Maybe it’s best to think of holarchies rather than hierarchies. Holarchies are layered systems composed of holons which are parts at one level and wholes at another. External controls of a group of holons can look like a marionette system from one point of view but from a higher point of view those external controls are embedded in the larger system and are not external. There is no name at present for a group of Tensegrities acting as an articulating meta-system. We may need gravity to propel ourselves but we don’t need gravity to cohere. We are complete unto ourselves.
Highly prestressed components are needed
(Nov 14, 2015) Vytas, when you assign a stiffness to a cable are you giving it some elasticity as a material property? It’s well known that a six bar tensegrity made with invariant length cables and struts will display a degree of elasticity that is a property of the structure and not the materials it is made of. This provides a certain shock absorber quality to tensegrity structures. However I can imagine circumstance where adding a spring inline to the cables would provide additional shock absorbing ability. Conversely, highly prestressed components will be needed to create a reasonably rigid platform to build precision joints off of. This was my original concern regarding how to connect tensegrity modules in an array or linkage such that there is enough internal stability for the structure to support its own weight and yet enough compliance that the joints can move freely. The only way I see to achieve this is to highly prestress the individual module tensegrities and the saddle slings that join them, and invent some frictionless hinge that couples e.g. two modules at a saddle sling. In other words, even tensegrity modules that are hooked together using tension slings will need some way to transfer rotational forces from a cable to a strut.
Need to be able to test compliancy versus rigidity using invariant length materials
(Nov 14, 2015) When I am building a tensegrity using elastic cord and fixed length wooden struts, it is easy to add prestress to the structure by stretching the elastic cord as it is assembled. This works well for rapidly prototyping tensegrities using these materials but does not allow a real world test of compliancy versus rigidity using invariant length materials. With elastics I end up with a structure that is too compliant to be useful as a robot. (unless it is a small robot).
Larger models need high prestress: the right balance between mass and stiffness
(Nov 14, 2015) I assume the NTRT software can model structures that have a significant mass. Scaling up these models to a reasonable size say, a large dog quadruped will require a fair bit of prestress built in to handle the loads. A structure of this size and larger need to have sufficient mass to handle loads (a pack?) or external forces (an impact). This will increase the prestress necessary to hand additional weight… it’s a bit of chasing your tail but eventually the balance is made between mass and stiffness. So the software needs to be able to simulate a range of both.
Additional discussion of modular tensegrity design in Tensegrity Modules, Tensegral Linkages, and New Approaches to Mechanizing Tensegrity Structures. The needed software support is described in Simulation Could Help.