Improved rheometry is provided using an autonomous swimming robot that can be driven at least in an angular velocity mode and in a torque mode. The resulting improved capability can enable measurement of multiple rheological parameters, such as both normal stress components ψ₁ and ψ₂, by observing motion of the robot in the fluid. The robot is preferably rotationally symmetric, but with a fore-aft head-tail asymmetry that enables propulsion in complex fluids when the head and tail are driven to rotate opposite each other about the rotational axis of symmetry.