Leveraging elastic instabilities for amplified performance: Spine-inspired high-speed and high-force soft robots

Abstract

Soft machines typically exhibit slow locomotion speed and low manipulation strength because of intrinsic limitations of soft materials. Here, we present a generic design principle that harnesses mechanical instability for a variety of spine-inspired fast and strong soft machines. Unlike most current soft robots that are designed as inherently and unimodally stable, our design leverages tunable snap-through bistability to fully explore the ability of soft robots to rapidly store and release energy within tens of milliseconds. We demonstrate this generic design principle with three high-performance soft machines: High-speed cheetah-like galloping crawlers with locomotion speeds of 2.68 body length/s, high-speed underwater swimmers (0.78 body length/s), and tunable low-to-high-force soft grippers with over 1 to 10³ stiffness modulation (maximum load capacity is 11.4 kg). Our study establishes a new generic design paradigm of next-generation high-performance soft robots that are applicable for multifunctionality, different actuation methods, and materials at multiscales.

Fig. 1. Spine-inspired bistable soft actuators.

(A) Bioinspired by the active spine mechanism during cheetahs’ high-speed galloping, a bistable spine-based hybrid soft actuator is proposed to realize the similar spine flexion and extension through reversible snap-through bistability for design of high-speed locomotive soft robots. (B) Schematic design of a bistable hybrid soft bending actuator (BH-SBA). It consists of three components: two soft pneumatic two-way bending actuators as skeletal muscle, a three-dimensionally (3D) printed flexible mechanism composed of two rigid hinged links as a spine, and a pretensioned spring that connects two ends of the mechanism for potential mechanical energy storage and release. (C) Schematics of energy landscape of the bistable actuator, showing one peak (unstable state I) and two localized minimum energy states (stable states II and III). It provides two operating regimes: one is the bistable switch in path a, and the other is the monostable state in path b. Insets show the corresponding Ecoflex-based bistable actuator prototypes at each state. (D) Schematic illustration of the bistable working mechanism under both nonactuated (spring pretension release at resting states in i to iii) and actuated states (reversible snapping-through under pneumatic actuation in iii and iv). The inset shows the set of an angular stopper to constrain the maximum bending angle at the preset stopping angle of θ_s.

Fig. 2. Design principle of energy competition and synergy relationship between springs and soft pneumatic actuators.

(A) The total energy of the bistable system (blue curve) as sum of strain energy in the soft bending actuator (red curve) and stretching energy in the spring (yellow curve). The energy difference between the peak and valley defines the energy barrier ΔE. (B) Comparison between theory and experiments on equilibrium bending angle versus spring pretension length at state I (∆x_I). (C) Energy barrier ΔE as a function of Δx_I and k in the spring. (D) Actuator stiffness as a function of spring pretention length and bending angle. (E) The measured actuated bended angle change with the increase of pressure p during the snapping-through bistability switching from state II to state III for the bistable actuators with different pretension. (F) Critical pressure for pneumatically actuating the bistable switch between two stable states as a function of pretention length Δx_I. There exists a threshold value of Δx_I, below which the bistable switch can be activated (yellow and green zone) while beyond which it fails to be activated (purple zone) because of the large energy barrier. The resting position after pretension release is at the equilibrium angle θ_eq with θ_eq < θ_s = 60° in the yellow zone and at the stopping angle of θ_s = 60° in the green zone.

Fig. 3. Bistability for amplified force and fast response.

Comparison of mechanical performances between the bistable hybrid actuator (blue color) and its two bistability-disabled counterparts: a soft actuator without both linkages and springs (yellow color) and a hybrid actuator without springs (red color). (A) Tracking of the bended shapes at two stable states. (B) Dynamic blocking forces at different blocked bending angles. Insets are schematics of front views of the three actuators. (C) Dynamic blocking force as a function of spring pretension. All the actuators in (A) to (C) are pressurized at 20 kPa. (D) The response time of achieving the largest bending angle for three bistable, hybrid, and soft actuators with different spring pretensions under the same actuation. All actuators are pressurized at 30 kPa with the same flow rate of 3 liters/min. For bistable ones, the response time is composed of two parts including before (highlighted by blue color) and after snapping-through (highlighted by pink color). (E) Finite element simulation results on the actuated switch between two stable states of the bistable hybrid actuator through pressurization.

Fig. 4. Bistability for high-speed crawler.

(A) Locomotion gaits of the proposed bio-inspired crawler by the spine actuation in the fastest galloping cheetahs. The spine bends upward to store energy when touching ground and bends downward to release energy and extend its stride length with legs lifting off the ground during the high-speed locomotion. (B) Left: Mechanism of directional locomotion. The Ecoflex elastomer pads attached to the claws provide tunable friction force (i, high friction; ii, low friction) and transit the symmetric bending of the bistable actuator into directional locomotion. Right: Static friction forces of claws with and without Ecoflex pad–substrate contact. The claw shows ~280% increase in the friction force (1.82 N) when the attached Ecoflex pad contacts the substrate. The inset shows the schematic of friction force measurement. (C) Demonstration of locomotion in the high-speed bistable crawler and its two counterparts with disabled bistability at different actuation time: soft crawler based on the soft actuator and hybrid soft crawler based on the hybrid one. All actuators are pressurized at the same pressure of 20 kPa and the same frequency of 3.2 Hz. The bistable hybrid soft crawler shows the fastest speed (~2.49 BL/s). (D) Demonstration of locomotion in the high-speed bistable crawler with different values of spring’s stored energy in the bistable actuator. All actuators are pressurized at the same pressure of 30 kPa and the same frequency of 2.63 Hz. The one with largest spring pretension shows the fastest speed (~2.68 BL/s). (E) Demonstration of the proposed bistable hybrid soft crawler’s capability in climbing slightly titled surfaces (tilting angle of 17°). The other two counterparts fail to climb. Scale bars, 25 mm. (F) Comparison of locomotion velocity measured in BL/s between our proposed bistable hybrid soft crawler (denoted as star-shaped symbol) and reported locomotive soft robots in literatures. LEAP, Leveraging Elastic instabilities for Amplified Performance. Photo credit: Yichao Tang, Temple University.

Fig. 5. Bistability for high-speed underwater fish-like soft robot.

(A) Schematic of the proposed fish-like robot, which is composed of the bistable actuator attached with a polymeric fin. The schematic head is for decoration purpose only. (B) Comparison between the bistable actuator and its two counterparts of hybrid and soft actuators in dynamic blocking force versus blocked bending angle. All actuators are pressurized at 160 kPa and an average frequency of 1.3 Hz. (C) Demonstration of underwater locomotion in bistable hybrid soft swimmer and its two counterparts at different actuation time: soft swimmer based on encapsulated soft actuator and hybrid soft swimmer based on encapsulated hybrid actuator. The bistable hybrid soft swimmer shows the fastest speed. Scale bars, 50 mm. (D) Comparison of swimming velocity between the proposed bistable hybrid soft fish-like robot (denoted as star-shaped symbol) and various reported underwater soft swimmers (denoted as round symbols). Photo credit: Yichao Tang, Temple University.

Fig. 6. Bistable hybrid soft grippers with wide-range variable stiffness modulation.

(A) Schematic of the encapsulated bistable hybrid actuator driven by tendon. (B) Stiffness test of the encapsulated actuator (bent at 75°; insets). We characterize the force as a function of spring extension. The solid line is the mean of three experiments (with shaded error bar), and the dashed line presents the theoretical model result. The stiffness is calculated as the slope of the force versus indentation depth. (C) Schematic illustration of the proposed gripper by assembling two actuators. The manipulation can be controlled by both motors, through pulling the spring, and pneumatic signals. (D) Demonstrations of its capability in grasping various objects in different shapes and weight. (E) Demonstration of high-load manipulation. Scale bars, 50 mm. Photo credit: Yichao Tang, Temple University.