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Tensegrity-based Robot Leg Design with Variable Stiffness

Erik Mortensen, Jan Petrs, Alexander Dittrich, Dario Floreano

TL;DR

The paper addresses the need for adaptable leg stiffness in robots by integrating a tensegrity-based leg with a cable-driven, continuously tunable stiffness mechanism. It presents a two-joint tensegrity leg architecture with a shared variable stiffness mechanism implemented via a multi-spring system and a lead-screw slider, actuated by a traversing winch. Experimental results demonstrate that increasing joint stiffness enhances load-bearing capacity and reduces impact forces, achieving up to a 34.7% reduction in peak acceleration during a drop and a 10.26 N difference in force under a 10 mm deformation. The work highlights the potential of combining passive tensegrity compliance with active stiffness modulation to improve resilience and adaptability in legged robots, while outlining future work on actuation speed, sensing, and scale-up to full multi-legged systems.

Abstract

Animals can finely modulate their leg stiffness to interact with complex terrains and absorb sudden shocks. In feats like leaping and sprinting, animals demonstrate a sophisticated interplay of opposing muscle pairs that actively modulate joint stiffness, while tendons and ligaments act as biological springs storing and releasing energy. Although legged robots have achieved notable progress in robust locomotion, they still lack the refined adaptability inherent in animal motor control. Integrating mechanisms that allow active control of leg stiffness presents a pathway towards more resilient robotic systems. This paper proposes a novel mechanical design to integrate compliancy into robot legs based on tensegrity - a structural principle that combines flexible cables and rigid elements to balance tension and compression. Tensegrity structures naturally allow for passive compliance, making them well-suited for absorbing impacts and adapting to diverse terrains. Our design features a robot leg with tensegrity joints and a mechanism to control the joint's rotational stiffness by modulating the tension of the cable actuation system. We demonstrate that the robot leg can reduce the impact forces of sudden shocks by at least 34.7 % and achieve a similar leg flexion under a load difference of 10.26 N by adjusting its stiffness configuration. The results indicate that tensegrity-based leg designs harbors potential towards more resilient and adaptable legged robots.

Tensegrity-based Robot Leg Design with Variable Stiffness

TL;DR

The paper addresses the need for adaptable leg stiffness in robots by integrating a tensegrity-based leg with a cable-driven, continuously tunable stiffness mechanism. It presents a two-joint tensegrity leg architecture with a shared variable stiffness mechanism implemented via a multi-spring system and a lead-screw slider, actuated by a traversing winch. Experimental results demonstrate that increasing joint stiffness enhances load-bearing capacity and reduces impact forces, achieving up to a 34.7% reduction in peak acceleration during a drop and a 10.26 N difference in force under a 10 mm deformation. The work highlights the potential of combining passive tensegrity compliance with active stiffness modulation to improve resilience and adaptability in legged robots, while outlining future work on actuation speed, sensing, and scale-up to full multi-legged systems.

Abstract

Animals can finely modulate their leg stiffness to interact with complex terrains and absorb sudden shocks. In feats like leaping and sprinting, animals demonstrate a sophisticated interplay of opposing muscle pairs that actively modulate joint stiffness, while tendons and ligaments act as biological springs storing and releasing energy. Although legged robots have achieved notable progress in robust locomotion, they still lack the refined adaptability inherent in animal motor control. Integrating mechanisms that allow active control of leg stiffness presents a pathway towards more resilient robotic systems. This paper proposes a novel mechanical design to integrate compliancy into robot legs based on tensegrity - a structural principle that combines flexible cables and rigid elements to balance tension and compression. Tensegrity structures naturally allow for passive compliance, making them well-suited for absorbing impacts and adapting to diverse terrains. Our design features a robot leg with tensegrity joints and a mechanism to control the joint's rotational stiffness by modulating the tension of the cable actuation system. We demonstrate that the robot leg can reduce the impact forces of sudden shocks by at least 34.7 % and achieve a similar leg flexion under a load difference of 10.26 N by adjusting its stiffness configuration. The results indicate that tensegrity-based leg designs harbors potential towards more resilient and adaptable legged robots.
Paper Structure (14 sections, 3 equations, 12 figures)

This paper contains 14 sections, 3 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Related Works
  3. Mechanical Design
  4. Tensegrity Joint Design
  5. Joint Actuation
  6. Variable Stiffness Mechanism
  7. Experimental Characterization
  8. Leg deformation under compression
  9. Shock mitigation after drop
  10. Conclusion
  11. Acknowledgements
  12. Joint Characterization
  13. Passive Joint Resistance to Rotation
  14. Passive Joint Resistance to Coaxial Loading

Figures (12)

  • Figure 1: Robot leg design incorporating cable-driven actuation with a variable stiffness mechanism /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A1$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A1$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A1$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A1$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) A1 , /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A2$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A2$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A2$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A2$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) A2 tensegrity-based joints, /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $B$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $B$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $B$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $B$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) B shared variable stiffness mechanism for both joints, /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C1$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C1$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C1$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C1$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) C1 , /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C2$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C2$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C2$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C2$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) C2 winch servos for controlling joint rotation.
  • Figure 2: Proposed mechanical design of robot leg with /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $A$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) A overview of main assembly with core sub-elements, /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $B$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $B$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $B$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $B$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) B explosion graph of tensegrity joint with traversing winch actuation, /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) $C$ /csteps/inner xsep /csteps/inner ysep /csteps/inner ysep (0,) (0,0)*(0,0)(0,) (-.50,0) C explosion graph of variable stiffness mechanism with lead screw and multi-spring system.
  • Figure 3: Rotation of tensegrity joint from minimum (-30°) to maximum displacement (145°).
  • Figure 4: Working principle of the multi-spring system to achieve quadratic stiffness behavior. Tension springs are in series with cables of different lengths, adding backlash in the cables.
  • Figure 5: Fitting of unbiased quadratic function as approximation of the multi-spring system.
  • ...and 7 more figures