Six-degree-of-freedom (6-DOF) haptic rendering for fine manipulation in narrow space is a challenging topic because of frequent constraint changes caused by small tool movement and the requirement to preserve the feel of fine-features of objects. In this paper, we introduce a configuration-based constrained optimization method for solving this rendering problem. We represent an object using a hierarchy of spheres, i.e., a sphere tree, which allows faster detection of multiple contacts/collisions among objects than polygonal mesh and facilitates contact constraint formulation. Given a moving graphic tool as the avatar of the haptic tool in the virtual environment, we compute its quasi-static motion by solving a configuration-based optimization. The constraints in the 6D configuration space of the graphic tool is obtained and updated through online mapping of the nonpenetration constraint between the spheres of the graphic tool and those of the other objects in the three-dimensional physical space, based on the result of collision detection. This problem is further modeled as a quadratic programming optimization and solved by the classic active-set methods. Our algorithm has been implemented and interfaced with a 6-DOF Phantom Premium 3.0. We demonstrate its performance in several benchmarks involving complex, multiregion contacts. The experimental results show both the high efficiency and stability of haptic rendering by our method for complex scenarios. Nonpenetration between the graphic tool and the object is maintained under frequent contact switches. Update rate of the simulation loop including optimization and constraint identification is maintained at about 1 kHz.

Objective. Despite converging neuroimaging studies investigating how neural activity is modulated by various motor related factors, such as movement velocity and force magnitude, little has been devoted to identifying the effect of force accuracy. This study thus aimed to investigate the effect of task difficulty on cortical neural responses when participants performed a visuomotor task with varying demands on force accuracy. Approach. Fourteen healthy adults performed a set of force generation operations with six levels of force accuracy. The participants held a pen-shaped tool and moved the tool along a planar ring path, meanwhile producing a constant force against the plane under visual guidance. The required force accuracy was modulated by allowable tolerance of the force during the task execution. We employed functional near-infrared spectroscopy to record signals from bilateral prefrontal, sensorimotor and occipital areas, used the hemoglobin concentration as indicators of cortical activation, then calculated the effective connectivity across these regions by Granger causality. Main results. We observed overall stronger activation (oxy-hemoglobin concentration, p = 0.015) and connectivity (p < 0.05) associated with the initial increase in force accuracy, and the diminished trend in activation and connectivity when participants were exposed to excessive demands on accurate force generation. These findings suggested that the increasing task difficulty would be only beneficial for the mental investment up to a certain point, and above that point neural responses would show patterns of lower activation and connections, revealing mental overload at excessive task demands. Significance. Our results provide the first evidence for the inverted U-shaped effect of force accuracy on hemodynamic responses during fine visuomotor tasks. The insights obtained through this study also highlight the essential role of inter-region connectivity alterations for coping with task difficulty, enhance our understanding of the underlying motor neural processes, and provide the groundwork for developing adaptive neurorehabilitation strategies.

Six degree-of-freedom (DoF) haptic rendering of multi-region contacts between a moving hand avatar and varied-shaped components of a music instrument is fundamental to realizing interactive simulation of music playing. There are two aspects of computational challenges: first, some components have significantly small sizes in some dimensions, such as the strings on a seven-string plucked instrument (e.g., Guqin), which makes it challenging to avoid pop-through during multi-region contact scenarios. Second, deformable strings may produce high-frequency vibration, which requires simulating diversified and subtle force sensations when a hand interacts with strings in different ways. In this paper, we propose a constraint-based approach to haptic interaction and simulation between a moving hand avatar and various parts of a string instrument, using a cylinder model for the string that has a large length-radius ratio and a sphere-tree model for the other parts that have complex shapes. Collision response algorithms based on configuration-based optimization is adapted to solve for the contact configuration of the hand avatar interacting with thin strings without penetration. To simulate the deformation and vibration of a string, a cylindrical volume with variable diameters is defined with response to the interaction force applied by the operator. Experimental results have validated the stability and efficiency of the proposed approach. Subtle force feelings can be simulated to reflect varied interaction patterns, to differentiate collisions between the hand avatar with a static or vibrating string and the effects of various colliding forces and touch locations on the strings.

Interacting with virtual objects via haptic feedback using the user's hand directly (virtual hand haptic interaction) provides a natural and immersive way to explore the virtual world. It remains a challenging topic to achieve 1 kHz stable virtual hand haptic simulation with no penetration amid hundreds of hand-object contacts. In this paper, we advocate decoupling the high-dimensional optimization problem of computing the graphichand configuration, and progressively optimizing the configuration of the graphic palm and fingers, yielding a decoupled-andprogressive optimization framework. We also introduce a method for accurate and efficient hand-object contact simulation, which constructs a virtual hand consisting of a sphere-tree model and five articulated cone frustums, and adopts a configuration-based optimization algorithm to compute the graphic-hand configuration under non-penetration contact constraints. Experimental results show both high update rate and stability for a variety of manipulation behaviors. Non-penetration between the graphic hand and complex-shaped objects can be maintained under diverse contact distributions, and even for frequent contact switches. The update rate of the haptic simulation loop exceeds 1 kHz for the whole-hand interaction with about 250 contacts.

Quantifiable differences among fingers in force control capability have both important practical and theoretical values in characterizing force control of accurate finger-tapping tasks. Following the classical Fitts' law paradigm, we quantified the differences among ten fingers in term of speed-accuracy trade-off (SAT) in performing repetitive discrete force control tasks. Visual cues displaying targeted force magnitudes and tolerances were provided. Users were required to apply the targeted force within the given tolerance quickly and accurately by pressing a force sensor using the specified finger. We found that ten fingers obeyed the Meyer model in the SAT performance and they differed in reaction time, the index of performance (IP), and the goodness of fit for the Meyer model. A modified Meyer model was proposed to quantify the difference between ten fingers in the SAT performance using only one parameter, making the quantification easier than using the original Meyer model. Pairwise comparisons showed that the differences between symmetrical fingers on both hands were insignificant except for the pair of index fingers. These findings provided us with multiple perspectives on the differentiation among ten fingers in the force control capabilities. Our study helps lay the foundation for engineering systems that rely on finger force control ability.