Fig. 4: Steerable crawling and rotation in water and non-polar solvents.

a Schematic illustration of the photodriven crawling of hydrogel sheet in water. During the scanning, the contraction forces (Fc₁ and Fc₂) or expansion forces (Fe₁ and Fe₂) competing with frictional forces (f₁ and f₂) enabled the gel to move opposite to the light. Schematic on the right showed open and low-tortuosity cell network as fast mass transfer channels to accelerate the release (i) and absorption (ii) of water. b Schematics of orientation angle (α) defined as the angle between the lamellae and long axis of the gel. c Motion trajectory and force analysis showing the controllable crawling dictated by regulating the α. The contraction force Fc acting on the tail was decomposed into a component force F_// to drive horizontal movement ∆x and a vertical component force F_⊥ to drive the motion angle θ. A torque τ was generated at the tail. d Optical images of the gel (α = 90°) and time-variant displacements of the head and tail under cyclic scanning from right to left. e Optical images, time-variant displacements and motion angles of the gel (α = 45°) under cyclic scanning. f Motion angle (black sphere) and displacement (red sphere) were summarized as a function of α (negative signs indicated clockwise movements). g Schematics, optical images and rotated angle of the gel (α = 90°) under cyclic scanning along the diagonal direction. The component force F_R⊥ of contraction force F_R perpendicular to the diagonal generated a torque τ_R to actuate rotational dynamics. The red dashed arrows and red solid arrows indicated the scanning and rotation direction, respectively. h Rotation angle was summarized as a function of α. i, Summary of linear crawling, steered crawling and rotation of hydrogel with different α in non-polar solvents, such as n-hexene, toluene and paraffin. Striped and solid columns represented crawling velocity and rotation velocity, respectively. Data in (f), (h), and (i) are presented as mean values  ±  SD (n = 3).