Negative stiffness honeycombs (NSHs) have multiple advantages compared to traditional honeycomb structures. These advantages include recoverable elastic buckling, shock absorption, and vibration isolation. As a result, NSHs have great potential in applications such as acoustic wave guiding, shape morphing, design of impact-protection devices and robotic grippers. In this paper, we present a design methodology for metamaterial consisting of negative stiffness beams assembled in a honeycomb structure. Based on analytical results, our methodology allows designing NSH mesostructures with predetermined buckling sequence. An NSH prototype was designed based on our algorithm and fabricated using a 3D printer with a nylon filament. The validity of our approach was experimentally verified by performing displacement controlled compression force measurements. Our methodology gives the ability to design NSH mesostructures with desired force–displacement characteristics.

Variable stiffness actuation has recently attracted great interest in robotics, especially in areas involving a high degree of human-robot interaction. After investigating various design approaches for variable stiffness actuated (VSA) robots, currently the focus is shifting to the control of these systems. Control of VSA robots is challenging due to the intrinsic nonlinearity of their dynamicsdynamics and the need to satisfy constraints on input and state variables. Contrary to the partially open-loop state-of-the-art approaches, in this paper, we present a close-loop control framework for VSA robots leveraging recent increases in computational resources and advances in optimization algorithms. In particular, we generate reference trajectories by means of open-loop optimal control, and track these trajectories via nonlinear model predictive control in a closed-loop manner. In order to show the advantages of our proposed scheme with respect to the previous (partially open-loop) ones, extensive simulation and real-world experiments were conducted using a two link planar manipulator for a ball throwing task. The results of these experiments indicate that the closed-loop scheme outperforms the partially open loop one due to its ability to compensate for model uncertainties and external disturbances, while satisfying the imposed constraints.

Tensegrity structures, emerged initially as an art form, have recently gained substantial interest among engineering researchers. The distinctive attribute of these structures is using pretensioned tensile elements connected to rigid bars to establish equilibrium of the whole structure. Thanks to these elements, tensegrity structures are lightweight and yet robust. The main challenge impeding their widespread use is the intricate constrained nonlinear dynamics caused by the tensegrity topology. In this paper, we extend the dynamics of tensegrities by adding damping forces and incorporating forces along the connected strings passing through several nodes. As an experimental platform, a two-stage stacked tensegrity manipulator was constructed. The system was actuated using six actuators and the kinematic information of the system was acquired by measuring the node coordinates using an optical motion capture. Afterward, we compared the structure behavior to the simulated one using our dynamics formulation. The results of these experiments show that our dynamics formulation is capable of representing the rich nonlinear dynamics of stacked tensegrity manipulators effectively.

Variable stiffness actuation is a new design paradigm for high performance and energy efficient robots with inherent safety features. Nonlinear model predictive control (NMPC) was employed to control these robots due to its ability to cope with constrained and nonlinear systems. Even though the results for NMPC are promising, one major weakness is the computational cost of this algorithm. It restricts the use of NMPC to low degree of freedom robots with relatively slow dynamics. This problem can be alleviated by finding an approximate linear representation of the system and using less computation hungry traditional model predictive control (MPC). In this work, we present our successive linearization based MPC (SLMPC) framework for variable stiffness actuated (VSA) robots. The system is linearized and discretized at every sampling instant and a quadratic problem is formulated using this discrete-time linear model. Solution of this quadratic problem provides the control inputs for the control horizon. In order to compare our scheme to NMPC, we conducted experiments with a reaction wheel augmented VSA system. For a 16 s trajectory tracking experiment, the root-mean-square errors were 0.54 and 0.64 degrees for NMPC and SLMPC methods, respectively, whereas the average computation time of the control rule was 2.17 ms for NMPC and 1.25 ms for SLMPC. Halving the computation time without compromising tracking performance shows the potential of our approach as a viable control alternative for VSA robots.

Variable-stiffness actuation exhibits promising features for obtaining human-like behavior and safer human robot physical interaction. Task planning and closed-loop control of these systems pose many challenges due to their complicated structure and the need of satisfying many constraints during task execution. This paper introduces a framework for the design and numerical solution of time-optimal control problems for variable-stiffness-actuated (VSA) systems. Two different time-optimal control problems, namely, minimum time for target performance and minimum time for maximum performance, are formally defined, and methods for solving them are presented based on existing numerical software tools for nonlinear optimization. Two experimental case studies, focusing on ball-throwing tasks with antagonistically actuated VSA systems, are used to test the presented methods and show their validity.

This paper presents an augmented reality-based method to increase human cognitive awareness of the danger/safety in the workspace of a variable impedance actuated (VIA) robot. Specifically, the "safety aura" around the robot was created using a safety/index defined for each point of the workspace. The safety-index is a composite metric incorporating the measurements of the distance from a point in the workspace to the VIA robot and the corresponding velocity during its motion. The safety aura is task-specific and is able to represent the safety levels in the workspace of the robot as it follows different trajectories. We developed a robot simulator which allows the visualization of the robot's motion and assessment of the corresponding safety aura in 3D space. The generated safety aura was overlaid into mixed reality using Unity 3D platform together with Vuforia and web camera. Simulation results demonstrated the ability of the safety metric based on distance and velocity measurements to qualitatively assess the amount of danger. Our method has the potential to make the physical human robot interaction safer.