Chunhai Jiao

Chunhai Jiao, Jin Guo, Haoyan Zhang et al.

We study the problem of detecting the onset of path splitting in stochastic interpolation between probability distributions. This question is especially subtle when the target distribution is nonconvex or supported on disconnected components, where interpolating trajectories may separate into distinct branches. Motivated by the stochastic control and Schrödinger bridge viewpoint, we propose a Jacobi field based indicator for identifying candidate splitting times and locations. Our approach is based on the Jacobi field associated with the linearization of an induced interpolating flow. Starting from a stochastic interpolation ansatz, we construct an Eulerian velocity field by conditional averaging and derive its spatial Jacobian in terms of the local posterior geometry of the target sample cloud. This allows us to interpret the symmetric part of the Jacobian as a local strain tensor and to use its spectral structure to quantify the amplification of infinitesimal perturbations along reference trajectories. Numerical experiments on non-convex and disconnected target distributions show that the proposed indicator consistently localizes the emergence of branching regions and captures the temporal development of splitting. These results suggest that Jacobi field analysis provides a natural mathematical framework for studying local instability and splitting phenomena in stochastic interpolation.

Sainan Zhang, Tzu-Hao Huang, Chunhai Jiao et al.

Pediatric exoskeletons offer great promise to increase mobility for children with crouch gait caused by cerebral palsy. A lightweight, compliant and user-specific actuator is critical for maximizing the benefits of an exoskeleton to users. To date, pediatric exoskeletons generally use the same actuators as adult exoskeletons, which are heavy and resistive to natural movement. There is yet no easy way for robotic exoskeletons to accommodate the changes in design requirements that occur as a child ages. We developed a lightweight (1.65 kg unilateral mass) and compliant pediatric knee exoskeleton with a bandwidth of 22.6 Hz that can provide torque assistance to children with crouch gait using high torque density motor. Experimental results demonstrated that the robot exhibited low mechanical impedance (1.79 Nm average backdrive torque) under the unpowered condition and 0.32 Nm with zero-torque tracking control. Root mean square (RMS) error of torque tracking result is less than 0.73 Nm (5.7% with respect to 12 Nm torque). To achieve optimal age-specific performance, we proposed the first optimization framework that considered both motor and transmission of the actuator system that can produce optimal settings for children between 3 and 18 years old. The optimization generated an optimal motor air gap radius that monotonically increases with age from 0.011 to 0.033 meters, and optimal gear ratio varies from 2.6 to 11.6 (3-13 years old) and 11.6 to 10.2 (13-18 years old), leading to actuators of minimal mass.

Shuangyue Yu, Tzu-Hao Huang, Xiaolong Yang et al.

High-performance actuators are crucial to enable mechanical versatility of lower-limb wearable robots, which are required to be lightweight, highly backdrivable, and with high bandwidth. State-of-the-art actuators, e.g., series elastic actuators (SEAs), have to compromise bandwidth to improve compliance (i.e., backdrivability). In this paper, we describe the design and human-robot interaction modeling of a portable hip exoskeleton based on our custom quasi-direct drive (QDD) actuation (i.e., a high torque density motor with low ratio gear). We also present a model-based performance benchmark comparison of representative actuators in terms of torque capability, control bandwidth, backdrivability, and force tracking accuracy. This paper aims to corroborate the underlying philosophy of "design for control", namely meticulous robot design can simplify control algorithms while ensuring high performance. Following this idea, we create a lightweight bilateral hip exoskeleton (overall mass is 3.4 kg) to reduce joint loadings during normal activities, including walking and squatting. Experimental results indicate that the exoskeleton is able to produce high nominal torque (17.5 Nm), high backdrivability (0.4 Nm backdrive torque), high bandwidth (62.4 Hz), and high control accuracy (1.09 Nm root mean square tracking error, i.e., 5.4% of the desired peak torque). Its controller is versatile to assist walking at different speeds (0.8-1.4 m/s) and squatting at 2 s cadence. This work demonstrates significant improvement in backdrivability and control bandwidth compared with state-of-the-art exoskeletons powered by the conventional actuation or SEA.