Actuated Tensegrity Structures

To create autonomous movement, a struts-and-cables tensegrity structure can be augmented with actuators, sensors, and a control system. In this distributed compliant environment it is difficult to find actuator control strategies that achieve desired movement of the tensegrity structure. Machine learning was used to find control strategies for the NASA Super Ball Bot and tensegrity spines. Tom characterizes the movement of the Super Ball Bot as a systematic alteration of centripetal forces, and envisions that more energy efficient control can be achieved by actuating controllable linkages in modular tensegrity designs. Using heat-activated artificial muscles to create an actuatable membrane. Actuating a larger model via fractal tensegrity struts that lengthen, shorten, or bend.

Context: Tom Flemons Archive

Distributed, autonomous control

(Feb 22, 2014) Vytas Sunspiral talks about the nature of command and control systems found in the body and the possibility of modelling motor, and sensory neurons and the resultant actions as compliant systems that have distributed not centralized control (which I would define as compliant tensegrity feedback systems). He points out that in lever action models, resultant forces traveling through fulcrums are additive and not dissipative and result in catastrophic failure at the receiving end. This is important in designing robots for service far from any hope of repairs (planetary exploration). Tensegrity models dissipate forces not collect them.

(July 26, 2015) Homeostasis is a cybernetic concept as you are aware. It involves a sensor system, an effector system and a negative feedback loop connected between them. In a tensegrity both systems are embedded in the geometry of the structure. As long as there exists a means for information to be exchanged through a continuous tensional network (tighter looser, more compressed, higher pressure) a homeostatic balance can be maintained.

Two types of control

Internal control alters centripetal forces, as in the NASA Super Ball Bot

(Oct 9, 2015) I make a distinction between forms of control. Internal control means altering the centripetal forces acting upon a discrete tensegrity to affect range of motion and hence movement. This is achieved by altering the lengths of individual tension and/or compression components – this is what has been achieved in the remarkable work on the super ball bot that Vytas and Adrian have been working on. This is akin to causing an inflated ball to move by first deflating a section of the ball in the direction you want it to move and then inflating the section behind. This essentially causes the ball to fall into its own depression or flat spot and then climb out of this topological hole by increasing the internal pressure and “rolling its way up the hill”. This takes energy, some or most of it unrecoverable. How much energy it takes is determined by the overall weight of the structure, which determines how much prestress it needs to maintain its shape, and the kind of terrain it is rolling over.

The Super Ball bot is today the only legitimate form of pure tensegrity movement.  In general, tensegrities are not kinetic structures (not counting oscillations or slight perturbations in the tension net which can cause masts to sway slightly). Tensegrities model envelopes, not articulated structures. A joint or hinge in a tensegrity is caused by a failure of its tensional integrity. It is a ‘disjoint’. Technically, Brian’s segmented worm is not a tensegrity structure.  Just because you tensionally couple rigid bodies using saddle slings does not make it a tensegrity ‘train’. The rigid bodies (stellated or regular tetrahedrons) that form the coaches are not themselves tensegrities and their linkage method is incidental. I understand why he uses rigid bodies – it’s just too much work and probably irrelevant at this stage to make each individual tetrahedron a tensegrity structure on its own. For the same reason, my tensegrity mast made from stellated (rigid bodies) tetrahedrons is also not a tensegrity. To truly take advantage of tensegrity features though, and to get around problems with shear and torque forces, all components in a complex structure eventually have to be modelled as tensegrities.

Videos of NASA Super Ball Bot

Videos of tensegrity spines

The second type of control is based on linkages between tensegrity modules

(Oct 9, 2015, continued) The second type of control employs a means to link individual discrete tensegrity components by means of saddle slings which act as revolute joints. In addition, there is a set of tension control lines between modules that are independent of the tension net that maintains each tensegrity component. In this sense the control lines are external to each tensegrity component but still internal to the overall structure. There is no deux ex machina puppet master controlling the structure from the outside.  Brian’s ‘tensegrity worm’ employed cross-linked tension linkages to effect changes in position between individual rigid bodies (stellated tetrahedrons). These are separate from the saddle slings which couple the components together and act as provisional hinges. I hypothesized that such cross linkages create bistable joints that can be managed with judicious use of control lines or by changing the length of the cross linked lines themselves. I guessed that such a joint would require much less energy to motivate than any internal control system (inflation/deflation) and would be superior to simply pulling on longitudinal control lines because the bistable joint wants to resolve into one of two states – its natural tendency is to flip into one of the two resting states and this can be controlled and constrained to keep the joint in a state of ‘super position’ near the centre of its range of motion. Such a system of control is ideal for a series of revolute joints that form a coupled train of components. Each joint needs only a small range of motion and additively they compound to create a large range of motion across the entire structure. Degrees of freedom can be managed by placing cross-linkages at 90 degrees to each other allowing for complex multi-dimensional movement.

My reasoning for going with this second type of control is that tensegrities are highly compliant structures. To get any sort of rigidity (which equals control and precision of movement) requires a high degree of prestress built into the tension net. If the goal doesn’t require precise movements then the prestress largely is there to provide integrity to the shape, but if movement is the goal then prestress starts to become a problem. Tomohiro Tachi’s work demonstrates form finding from polygonal mesh surfaces but they are asymmetrical envelopes that won’t be easily moveable without either huge energy costs to control or their movement will lack useful precision. To get reasonable rigidity requires high prestress in the tension net which counteracts the requirement to make a tensegrity structure move. Building tensegrity clusters with separate control systems gets around this problem.

There is a lot more to say about these issues – I’m only scratching the surface here, but if the goal is to utilize the enormous advantages of tensegrity structures to build real articulating robots that are akin to bipeds or quadrupeds then something like what I am proposing will have to be entertained. I’ll leave it to your capable hands to figure out how to control them – my goal is to design something worth controlling.

Simulate bipedal or quadrupedal motion via tensegrity models wrapped in a woven mast sleeve

(March 9, 2016) If you want to simulate bipedal or quadrupedal motion on a computer then it should be possible to combine simple tensegrity models such as my spine/pelvis/leg/foot linkage, wrap it in a woven mast sleeve and it may emulate biological motion reasonably well. My assumption is if you want to build a functional model of the body using tensegrity either as a simulation or eventually in the real world the limits to computation or control must be acknowledged. Over 600 myofascial relationships wrapping over 200 bones all adjusting rigidity and compliance on the fly in real time is too much information and beyond the capacity or need of a modelling system.

I’ve assumed with my models that we can’t really utilize the technique used on the superball bot in such a case. i.e. actuating all of the tension members to effect motion. Thus I felt a simpler solution was to connect discrete tensegrities in a series of linkages using tension slings and actuate them with a separate limited set of actuated lines. As it turns out doing things this way creates movement that is plausibly similar to the biomechanics of vertebrates but only because I’m fudging a lot of variables. For example using elastic cord allows them to flex and move in a smooth manner because the elasticity allows forces to be transferred smoothly and dampens any abrupt changes in alignment.

Tom’s experimentation with manually-manipulated actuators

If nuanced output is desired, more actuators are needed

(Feb 23, 2014) I think it worthwhile to investigate if and how an actuator can have multiple outputs. For example, in all of my mast models [e.g. youtube video of a tensegrity mast] the actuators each had a single fixed end point (near the top). So I was able to cause the mast to bend but not make an ‘s’ curve. For that I needed to add another set of three actuators attached at the midpoint. The gripper arm was very simplistic but worked because I split it in three near the top so that each claw pulled evenly along with the other two. The more nuanced the output, the more actuators needed.

Create actuators that can tighten and rotate tetrahedrons and octahedrons in the tensegrity structure

(Feb 23, 2014, continued) The way I would proceed is to note that different geometries have different degrees of freedom and ranges of motion. For example if the torso/pelvis is modelled as an expanded octahedron it’s useful to realize that octahedrons have three pairs of axes of rotation corresponding the Cartesian graph. Shortening the distance between two parallel struts causes the whole system to tighten and become smaller down ultimately to a simpler stellated octahedron. Or if the shoulders are torqued counterclockwise and the pelvis torqued clockwise the two ‘X’ axes (top and bottom parallel struts of the tensegrity) describe a tetrahedral relationship. (see images attached) The body becomes smaller and denser in a rotation pose. Thus actuators that can effect these types of tightenings and rotations are required. Similarly the spine needs a series of actuators that effect local rotation between adjacent vertebrae but also ones that have a more global range and effect. Perhaps the metaphor Tom Myers uses to distinguish between local trains and express trains in describing muscle lines in the body (Anatomy Trains) is the appropriate model here.

Using heat-activated artificial muscles to create an actuatable membrane

(Oct 24, 2014, repeated from Fractal and Membrane Structures) There is some fascinating research being done, which you probably are aware of using monofilament line coiled tightly to create heat activated artificial muscles 100X stronger than human ones. I’ve built some of them in my shop and hope to employ them in some of my future models. Imagine a fabric composed of such coiled ‘muscles’ stretched across the base of a tensegrity module to form a heat actuatable membrane! They make mention of incorporating electrical resistance filaments into the fabric which generated the requisite heat when a current is applied, to cause the muscles to contract or expand. The possibilities are intriguing…

Actuating a larger model via fractal tensegrity struts that lengthen, shorten, or bend


(April 4, 2016 repeated from Fractal and Membrane Structures) If a fractal tensegrity strut could be actuated it would allow for the possibility of changing the shape of the strut. Because the strut is now a tensegrity it can lengthen, shorten or even bend – which would be another unique way to actuate a larger model. In the examples [the two images above], I’ve taken the 6 bar X-octa and face bonded a number of them to form a tensegrity strut. I then made a larger X-octa tensegrity using six tensegrity struts [the two images below]. If the lines were given a compliant (passive elasticity) quality then actuating the interior strut lines would change the strut dimensions and thus the larger tensegrity. Just another way of thinking about how to actuate a tensegrity linkage.



Vibrating motors can move a tensegrity structure

(Jan 28, 2018 in response to Rieffel and Mouret (2017) Soft tensegrity robots, with video) Good to see someone is finally using this idea to move a small Tensegrity around.  About 12 years ago I strapped a solar panel on top of a Tensegrity horse that powered an eccentric motor attached to its chassis. It would vibrate and walk across the room. But no controller. Yes very cool but maybe not able to vibrate out of a hole…