Implicit Null-space Manifold Generation for Redundant Robotic Systems

Robotic systems with redundant degrees of freedom can achieve the same task outcome using multiple configurations, resulting in solution sets that form manifolds in the configuration space. Existing approaches typically exploit such redundancy locally through Jacobian-based techniques to compute individual solutions or trajectories. While effective for solution computation, these methods do not retain a representation of the geometry of the solution set itself. In this work, we adopt a representation-centric approach to estimate the geometric structure of the solution space. We consider solution manifolds induced by general task-defining maps and construct an implicit scalar field over the configuration space, whose zero-level set corresponds to the solution manifold. To this end, we generate samples in the neighborhood of the solution manifold using a Jacobian-guided exploration strategy, which efficiently captures its local and global structure. The resulting implicit representation is defined over the configuration space and naturally induces a continuous, distance field that encodes proximity to the solution manifold. Experiments on a planar three-link robot and a seven-degree-of-freedom Franka manipulator demonstrate the effectiveness of the proposed representation. Furthermore, the framework enables consistent modeling of solution spaces across families of tasks with continuous variation.

Dynamics Computation of Soft-Rigid Hybrid-Link System and Its Application to Motion Analysis of an Athlete Wearing Sport Prosthesis

This paper presents a motion analysis framework for an athlete wearing sport-specific flexible prosthesis based on the soft-rigid hybrid-link system. Such a motion analysis is a challenging problem because we need to consider the interaction force between the rigid human skeleton system and a flexible prosthesis. However, most of human musculoskeletal models are based on the computation framework of a rigid-body multi-link system. Recently in soft robotics research field, fast and efficient modeling methods were developed for a flexible rod deformation, which allows us to build a hybrid-link system that integrates rigid-link and soft-bodies in a unified formulation. We apply inverse kinematics of the hybrid-link system to motion reconstruction from a motion captured data, and also present the estimation of the joint torques and ground reaction force by inverse dynamics. Through a human subject experiment, we show that the inverse dynamics achieved approximately 12% error on the ground reaction force estimation. Furthermore, we provide the muscle force estimation considering muscle amputation and interaction force with the prosthesis leg deformation.

Viscoelasticity Estimation of Sports Prosthesis by Energy-minimizing Inverse Kinematics and Its Validation by Forward Dynamics

In this study, we present a method for estimating the viscoelasticity of a leaf-spring sports prosthesis using advanced energy minimizing inverse kinematics based on the Piece-wise Constant Strain (PCS) model to reconstruct the three-dimensional dynamic behavior. Dynamic motion analysis of the athlete and prosthesis is important to clarify the effect of prosthesis characteristics on foot function. However, three-dimensional deformation calculations of the prosthesis and viscoelasticity have rarely been investigated. In this letter, we apply the PCS model to a prosthesis deformation, which can calculate flexible deformation with low computational cost and handle kinematics and dynamics. In addition, we propose an inverse kinematics calculation method that is consistent with the material properties of the prosthesis by considering the minimization of elastic energy. Furthermore, we propose a method to estimate the viscoelasticity by solving a quadratic programming based on the measured motion capture data. The calculated strains are more reasonable than the results obtained by conventional inverse kinematics calculation. From the result of the viscoelasticity estimation, we simulate the prosthetic motion by forward dynamics calculation and confirm that this result corresponds to the measured motion. These results indicate that our approach adequately models the dynamic phenomena, including the viscoelasticity of the prosthesis.