This paper introduces a novel method for controlling multirotor aerial robots connected by passive flexible elements. Despite the growing popularity of multirotor aerial robots, their real-world applications remain limited due to difficulties adapting to complex environments. Soft robotics, due to its inherent flexibility, offers a potential solution, although research on integrating flexible elements into aerial robots is still in the early stages. In this study, we propose control methods for a system where multiple aerial robots are interconnected with passive flexible elements. These robotic systems enhance adaptability, enabling tasks like object manipulation. We model the flexible parts using the piecewise constant strain (PCS) model, which allows for model-based closed-loop control and stabilizes various configurations of the system. Through simulations and experiments, we validated that the proposed method achieves both stable flight and flexible deformation. Notably, we succeeded in maintaining stable flight, which traditional methods could not achieve, and demonstrated both positional controllability and the ability of the flexible parts to bend dynamically during flight.

Flexibility and softness play a significant role in dynamic human motions. This includes the flexibility owing to ligaments in the human body and the softness of external structures such as a leaf-spring-type prosthesis. Thus, robotic systems need to utilize such flexibility to achieve dynamic and energy-efficient motion. In this study, we proposed a compliance optimization-based control framework for a rigid-soft hybrid robot system where the continuous deformation of a flexible structure is represented using the piece-wise constant strain (PCS) model. We divided the hybrid system into two states: single support and double support. We validated the proposed method in these states using forward dynamics simulations, assuming a hybrid link system that consists of a humanoid robot with a flexible prosthesis.

In this study, we present a framework to en-sure seamless transition in humanoid push recovery involving hopping strategy. We propose a method to adaptively change the time constant that integrated the ankle strategy and variable height strategy. This framework excites a hopping motion against a large disturbance, which provides a seamless transition from the variable height to the hopping strategies. We analyze the applicable region of each strategy based on the simplified model. Moreover, we show that the hopping strategy prevents falling through whole-body dynamic simulations.

In this study, we present an application of the Piece-wise Constant Strain (PCS) model to a flexible deformation analysis of a sports prosthesis leg. Dynamic motion analysis of an athlete wearing a sports prosthesis is important to clarify a relationship between the prosthesis characteristics and the performance of an athlete, which contributes to training of an athlete or design of the prosthesis. However, there are few studies on modeling of the three-dimensional deformation of the sports prosthesis. In soft robotics, the PCS model was proposed for calculating a flexible deformation of a beam or rod structure with a low computational cost. We employ the PCS model to calculate the flexible deformation of the prosthesis, assuming that its structure can be discretized into a finite number of segments. Moreover, we propose an estimation method of the prosthesis stiffness using optical motion capture data and calculating the semi-definite programming.

This article discusses a compliance optimization approach that satisfies positive definiteness. Physical human–robot interactions are an important topic in robotics, for which force or compliance control is a key technology. Operational space control (OSC) is one of the most common approaches for robot force control with redundant degrees of freedom. By linearizing OSC, we can derive joint stiffness and viscosity matrices equivalent to the OSC. For an appropriate control, it is important that these matrices are positive definite. However, the stiffness matrix equivalent to the OSC is not always positive definite. In this case, a high kinetic energy is required, which is a problem in terms of the control performance. Therefore, the control performance can be improved by explicitly considering the positive definiteness of the stiffness or compliance. In this article, the authors derive a dynamically consistent compliance formulation and propose a compliance optimization that satisfies positive definiteness. The space of the symmetric positive definite matrix is a Riemannian manifold. We show that minimizing the Riemaniann geodesic distance results in a better performance compared with using OSC. The proposed method is validated via forward dynamics simulations and experiments using a hydrostatically driven humanoid Hydra.

This study presents dynamics computation and control of a hybrid multi-link system that integrates rigid- and soft-bodies. It is a challenging problem to install a softness in a robot system, which is an important factor in human body. Softness achieved by human muscles and ligaments contributes to dynamic motion. Flexibility of a sports prosthetic leg allows a handicapped person to run. However, traditional algorithms of dynamics computation for a robot system or human skeletal model only consider a rigid-body multi-link system. Recent progress in soft robotics such as piecewise constant strain (PCS) model provides the way to compute dynamics of soft deformation with a low computational cost. We construct a hybrid multi-link system integrating rigid-body and the PCS model. For controlling a humanoid robot with soft links, we implement a dynamics computation with a floating-base and derive the center-of-gravity Jacobian matrix of the hybrid link system. Moreover, we demonstrate a forward dynamics simulation of a humanoid robot with prosthetic legs.