Jaden Zhang

Robotics/Tensegrity Research

Summer Undergraduate Research at CLIMB Lab

The CLIMB lab, formerly the RIS lab from Hong Kong, has recently moved to the University of Toronto, and so, I took the chance to emmerse myself in a research-focused environment for the summer of 2026. With the lab's focus on multimodel (terrestrial/aerial mainly), the hopcopter platform was the main building blocks of most of our projects. Going into the summer, the goal was to investigate the possibility of implementing tensegrity principles and structures to increase the efficiency/robustness of the base hopcopter.

The Hopcopter is a hybrid robotic platform designed to overcome the strict endurance limits of standard fully aerial drone by utilizing passive terrestrial hopping to minimize energy-intensive thruster usage. To optimize its landing and rebound mechanics, this project integrated tensegrity—a lightweight structural system stabilized entirely by a continuous network of members purely in axial compression or tension. This unique layout diffuses loads to prevent localized weak points and offers an exceptionally high strength-to-weight ratio, amd making it ideal for safely absorbing high-G landing impacts from any orientation.

Through the summer, my main focus was the development of a Matlab physics engine to simulate the movements and efficiency of Class-1 tensegrity structures, as well as a brief building of a final conceptual design validated through the simulation. Worked under Prof. Pakpong Chirarattananon

May 2026 - August 2026

Key Skills: Theoretical design, physics simulator building, Matlab, vector based kinematics/dynamics.

Matlab Tensegrity Physics Engine

To quantitatively evaluate tensegrity structures for a hybrid aerial-terrestrial robot, a custom physics engine was developed in MATLAB to simulate complex internal forces, structural stiffness, and rebound efficiency. Evaluating these metrics was critical because tensegrity impact dynamics are stiff, non-linear, and mathematically chaotic, making standard rigid-body simulations inadequate.

The engine was designed to handle form finding by discovering equilibrium layouts from initial strut coordinates, as well as simulating dynamic drop tests and vectorized ground collisions. This allowed for the virtual prototyping of structural responses before committing to time-intensive physical builds.

  • Developed a 4th-Order Runge-Kutta (RK4) numerical integration scheme in MATLAB, utilizing a microsecond time step to successfully stabilize high-stiffness spring calculations without high explicit Euler integration error accumulation
  • Modeled viscoelastic material hysteresis in elastomers (as tendons) using Hooke's Law combined with a viscous damper to accurately simulate energy lost to heat during rapid load-cycles
  • Implemented a mass-scaled spring-damper penalty model for ground collisions, ensuring stability and continuous contact constraints without causing high-frequency integration blow-ups when landing is detected.
  • Developed a "Ghost Leg" abstraction to benchmark 1-DOF telescoping leg dynamics against the 3D multi-body tensegrity framework, isolating tangential velocity to model linear bearing binding under lateral shear
  • Logged kinetic and potential energy states to isolate translational kinetic energy from parasitic rotational spin, producing a pure performance metric of structural hopping efficiency

Final Conceptual Design Build

The physical and conceptual design phase addressed the critical vulnerabilities of the initial 1-DOF telescoping leg, which suffered from bearing binding and required aggressive, energy-intensive airframe tilting to achieve desired landing attitudes. To resolve this, the design transitioned to a 3D Class-1 Tensegrity Wheel.

The final conceptual design enclosed the drone payload inside an 8+1 strut protective rolling cage designed to absorb multi-axis impact forces from any direction without collapsing. This completely decoupled the leg attitude from the main body, allowing the robot to survive and rebound from high-G landings on uneven terrain.

  • Designed an 8+1 strut Class-1 tensegrity wheel configuration, isolating a central payload axle strut using elastic spokes within an 8-strut octagonal outer rim
  • Balanced the strut count to maintain polygonal rolling efficiency while maximizing the internal cavity stroke length to prevent hard mechanical collisions between the central drone body and the outer rim struts
  • Optimized the face-to-face twist angle of the octagonal prism to dramatically increase radial stiffness, ensuring lateral squeezing forces were converted into pure axial compression along the rigid carbon fiber struts
  • Implemented a fully triangulated structural network by routing a 4th cross-shear diagonal Kevlar tendon across open facets
  • Facilitated physical assembly of the notoriously complex tensegrity geometry by designing and utilizing a 3D printed PLA jig to hold struts in proper spatial alignment while the tendon network was strung

Final Presentation (UnERD Podium)

As with any somewhat long lasting project, documentation of design choices and any issues that arise is incredibly important. Troubleshooting has taken up the majority of my time throughout this project, and being able to track why decision were made and how to solve common issues is an integral part of staying efficiently progressing.

Presentation (UnERD 2026) was on August 25th.

  • Podium presentation of 10 minutes + 5 minutes questioning period