Locomotion Without a Brain: Physical Reservoir Computing in Tensegrity Structures

Abstract

Embodiment has led to a revolution in robotics by not thinking of the robot body and its controller as two separate units, but taking into account the interaction of the body with its environment. By investigating the effect of the body on the overall control computation, it has been suggested that the body is effectively performing computations, leading to the term morphological computation. Recent work has linked this to the field of reservoir computing, allowing one to endow morphologies with a theory of universal computation. In this work, we study a family of highly dynamic body structures, called tensegrity structures, controlled by one of the simplest kinds of "brains." These structures can be used to model biomechanical systems at different scales. By analyzing this extreme instantiation of compliant structures, we demonstrate the existence of a spectrum of choices of how to implement control in the body-brain composite. We show that tensegrity structures can maintain complex gaits with linear feedback control and that external feedback can intrinsically be integrated in the control loop. The various linear learning rules we consider differ in biological plausibility, and no specific assumptions are made on how to implement the feedback in a physical system.

Developing an embodied gait on a compliant quadrupedal robot

“…For the controller to learn to deal with its own errors, we add a second training phase, with RLS still active. In this stage, the output signals sent to the motors are mixtures of the target signals and the signals generated by the linear transformation [17]. The fraction of the target signals is reduced over time until it becomes zero.…”

“…In earlier work [9], [17], it was shown that for a tensegrity robot, a linear transformation from the sensor signals to the motor signals was enough to generate stable locomotion. The idea behind this is that the body of the robot itself has computing power, and that this power is being harvested by using it as a reservoir.…”

“…While physical implementations exist ranging from a water bucket [15] to integrated photonics devices [16], robotic implementations are rare. Nevertheless, recent work [9], [17] illustrated that locomotion control can be outsourced to the body of a tensegrity robot: a structure composed of compression elements held together by a compliant tensile network. Stable gait generation was achieved by using only optimized linear feedback from the robot's stretch sensors to its actuator control signals.…”

Advances in photonic reservoir computing

“…Typical reservoirs comprise several hundred nodes, a complexity readily present in physical systems. Full analog physical implementations such as water ripples [12], mechanical oscillators [26], tensegrity structures [27,28], soft bodies [29], and the optical devices and circuits which are the subject of this review have all been implemented. RC has indeed grown to include systems which are not necessarily based on a network topology of discrete components.…”

Simple or Complex Bodies? Trade-offs in Exploiting Body Morphology for Control

“…The spirit of the morphological computation literature that follows the "offloading" or "trade-off" perspective, is that complex (highly dimensional, dynamic, nonlinear, compliant, deformable, "soft" ) bodies are advantageous for control because they can take over the "computation" that a controller would otherwise have to perform (e.g., [15,16,39] or [9] explicitly in Fig. 1).…”