The “Fluid Jacobian”: Modeling force-motion relationships in fluid-driven soft robots

In this paper, we introduce the concept of the Fluid Jacobian, which provides a description of the power transmission that operates between the fluid and mechanical domains in soft robotic systems. It can be understood as a generalization of the traditional kinematic Jacobian that relates the joint space torques and velocities to the task space forces and velocities of a robot. In a similar way, the Fluid Jacobian relates fluid pressure to task space forces and fluid flow to task space velocities. In addition, the Fluid Jacobian can also be regarded as a generalization of the piston cross-sectional area in a fluid-driven cylinder that extends to complex geometries and multiple dimensions. In the following, we present a theoretical derivation of this framework, focus on important special cases, and illustrate the meaning and practical applicability of the Fluid Jacobian in four brief examples.