Y. Futakata’s research while affiliated with The University of Tokyo and other places

Mechanical systems can often be controlled efficiently by exploiting a resonance. An optimal trajectory minimizing an energy cost function is found at (or near) a natural mode of oscillation. Motivated by this fact, we consider the natural entrainment problem: the design of nonlinear feedback controllers for linear mechanical systems to achieve a prescribed mode of natural oscillation for the closed-loop system. We adopt a set of distributed central pattern generators (CPGs) as the basic control architecture, inspired by biological observations. The method of multivariable harmonic balance (MHB) is employed to characterize the condition, approximately, for the closed-loop system to have a natural oscillation as its trajectory. Necessary and sufficient conditions for satisfaction of the MHB equation are derived in the forms useful for control design. It is shown that the essential design freedom can be captured by two parameters, and the design parameter plane can be partitioned into regions, in each of which approximate entrainment to one of the natural modes, with an error bound, is predicted by the MHB analysis. Control mechanisms underlying natural entrainment, as well as limitations and extensions of our results, are discussed.

This paper considers the design of feedback controllers for a class of collocated mechanical systems, aiming to achieve a natural mode of oscillation as a stable limit cycle of the closed-loop system. Motivated by recent results on central pattern generators, the controller is formed as a collection of multiple identical agents without direct communications to each other. Each agent is described as a transfer function followed by a static nonlinearity, and is placed between a sensor/actuator pair. Several simple linear dynamics are considered for the agents. The method of multivariable harmonic balance (MHB) is used to obtain approximate conditions for achieving entrainment to a natural oscillation, and numerical examples suggest that the proposed design conditions are fairly reliable in spite of sinusoidal approximations adopted in the MHB method. It is found that a band-pass filtering property is essential for the linear dynamics of each agent to achieve entrainment to an arbitrarily specified mode of natural oscillation.

Tensegrity structures, which consist of struts and cables, have high strength to mass ratio and high energetic efficiency in deforming its shapes. This structure is sometimes observed in biological systems, which consists of muscles and skeletons, and this structure is adopted to a simplified model of animal body dynamics. From the aspect of engineering, applications of this structure to robotics are an interesting topic of research. On the other hand, for moving a mechanical system with the minimum input energy, to exploit a natural mode of the system is important because of a resonance effect. To exploit a natural mode of a system, a controller consisting of biological oscillators called a central pattern generator (CPG) was studied. In this paper, we use the CPG controller to exploit natural entrainment of tensegrity systems, and evaluate its applicability through numerical experiments. To design the CPG controller, we use the multivariable harmonic balance method, and the tensegrity system is linearized at an equilibrium point.

Rhythmic movements during animal locomotion are controlled by the neuronal circuits called central pattern generators (CPGs). The intrinsic frequency of a CPG in isolation is often different from that of observed movements, but appears to entrain to a natural mode of body oscillation through sensory feedback to achieve efficient locomotion. The objective of this paper is to reveal the feedback control mechanism underlying the entrainment of CPGs. Motivated by musculo-skeletal biomechanics, we consider the class of mechanical systems for which actuators, sensors, springs and dampers, are all collocated. Our main result provides a condition under which a CPG-based controller approximately achieves a selected mode of natural oscillation with a bound on the entrainment error.

The neuronal circuit controlling the rhythmic movements in animal locomotion is called the central pattern generator (CPG). The biological control mechanism appears to exploit mechanical resonance to achieve efficient locomotion. The objective of this paper is to reveal the fundamental mechanism underlying entrainment of CPGs to resonance through sensory feedback. To uncover the essential principle, we consider the simplest setting where a pendulum is driven by the reciprocal inhibition oscillator. Existence and properties of stable oscillations are examined by the harmonic balance method, which enables approximate but insightful analysis. In particular, analytical conditions are obtained under which harmonic balance predicts existence of an oscillation at a frequency near the resonance frequency. Our result reveals that the resonance entrainment can be maintained robustly against parameter perturbations through two distinct mechanisms: negative integral feedback and positive rate feedback.

The neuronal circuit controlling the rhythmic movements in animal locomotion is called the central pattern generator (CPG). The biological control mechanism appears to exploit mechanical resonance to achieve efficient locomotion. The objective of this paper is to reveal the fundamental mechanism underlying entrainment of CPGs to resonance through sensory feedback. To uncover the essential principle, we choose to consider the simplest setting where a pendulum is driven by the reciprocal inhibition oscillator. Existence and properties of stable oscillations are examined by the harmonic balance method, which enables approximate but insightful analysis. The method predicts, and simulations confirm, that the resonance entrainment can be maintained robustly against parameter perturbations through two distinct mechanisms: negative rate feedback and positive integral feedback.