Robots fabricated with soft materials can provide higher flexibility and, thus, better safety while interacting in unpredictable situations. However, the usage of soft material makes it challenging to predict the deformation of a continuum body under actuation and, therefore, brings difficulty to the kinematic control of its movement. In this article, we present a geometry-based framework for computing the deformation of soft robots within the range of linear material elasticity. After formulating both manipulators and actuators as geometry elements, deformation can be efficiently computed by solving a constrained optimization problem. Because of its efficiency, forward and inverse kinematics for soft manipulators can be solved by an iterative algorithm with a low computational cost. Meanwhile, components with multiple materials can also be geometrically modeled in our framework with the help of a simple calibration. Numerical and physical experimental tests are conducted on soft manipulators driven by different actuators with large deformation to demonstrate the performance of our approach.

Rigid registration is a fundamental process in many applications that require alignment of different datasets. Iterative closest point (ICP) is a widely used algorithm that iteratively finds point correspondences and updates the rigid transformation. One of the key variants of ICP to its success is the selection of points, which is directly related to the convergence and robustness of the ICP algorithm. Besides uniform sampling, there are a number of normal-based and feature-based approaches that consider normal, curvature, and/or other signals in the point selection. Among them, normal-space sampling (NSS) is one of the most popular techniques due to its simplicity and low computational cost. The rationale of NSS is to sample enough constraints to determine all the components of transformation, but this paper finds that NSS actually can constrain the translational normal space only. This paper extends the fundamental idea of NSS and proposes Dual NSS (DNSS) to sample points in both translational and rotational normal spaces. Compared with NSS, this approach has similar simplicity and efficiency without any need of additional information, but has a much better effectiveness. Experimental results show that DNSS can outperform the normal-based and feature-based methods in terms of convergence and robustness. For example, DNSS can achieve convergence from an orthogonal initial position while no other methods can achieve. Note to Practitioners-ICP is commonly used to align different data to a same coordination system. While NSS is often used to speed up the alignment process by down-sampling the data uniformly in the normal space. The implementation of NSS only has three steps: 1) construct a set of buckets in the normal-space; 2) put all points of the data into buckets based on their normal direction; and 3) uniformly pick points from all the buckets until the desired number of points is selected. The algorithm is simple and fast, so that it is still the common practice. However, the weakness of NSS comes from the reason that it cannot handle rotational uncertainties. In this paper, a new algorithm called DNSS is developed to constrain both translation and rotation at the same time by introducing a dual-normal space. With a new definition of the normal space, the algorithm complexity of DNSS is the same as that of NSS, and it can be readily implemented in all types of application that are currently using ICP. The experimental results show that DNSS has better efficiency, quality, and reliability than both normal-based and feature-based methods have.

Robots fabricated by soft materials can provide higher flexibility and thus better safety while interacting with natural objects with low stiffness such as food and human beings. However, as many more degrees of freedom are introduced, the motion simulation of a soft robot becomes cumbersome, especially when large deformations are presented. Moreover, when the actuation is defined by geometry variation, it is not easy to obtain the exact loads and material properties to be used in the conventional methods of deformation simulation. In this paper, we present a direct approach to take the geometric actuation as input and compute the deformed shape of soft robots by numerical optimization using a geometry-based algorithm. By a simple calibration, the properties of multiple materials can be modeled geometrically in the framework. Numerical and experimental tests have been conducted to demonstrate the performance of our approach on both cable-driven and pneumatic actuators in soft robotics.

We present a novel method for caging grasps in this paper by stretching ropes on the surface of a 3D object. Both topology and shape of a model to be grasped has been considered in our approach. Our algorithm can guarantee generating local minimal rings on every topological branches of a given model with the help of a Reeb graph. Cages and grasps can then be computed from these rings, and physical experimental tests have been conducted to verify the robustness of our approach.

We present an evolution method for designing the styling curves of garments. The procedure of evolution is driven by aesthetics-inspired scores to evaluate the quality of styling designs, where the aesthetic considerations are represented in the form of streamlines on human bodies. A dual representation is introduced in our platform to process the styling curves of designs, based on which robust methods for realizing the operations of evolution are developed. Starting from a given set of styling designs on human bodies, we demonstrate the effectiveness of set evolution inspired by aesthetic factors. The evolution is adaptive to the change of aesthetic inspirations. By this adaptation, our platform can automatically generate new designs fulfilling the demands of variations in different human bodies and poses.

Given a set of corresponding user-specified anchor points on a pair of models having similar features and topologies, the cross parameterization technique can establish a bijective mapping constrained by the anchor points. In this paper, we present an efficient algorithm to optimize the complexes and the shape of common base domains in cross parameterization for reducing the distortion of the bijective mapping. The optimization is also constrained by the anchor points. We investigate a new signature, Length-Preserved Base Domain (LPBD), for measuring the level of stretch between surface patches in cross parameterization. This new signature well balances the accuracy of measurement and the computational speed. Based on LPBD, a set of metrics are studied and compared. The best ones are employed in our domain optimization algorithm that consists of two major operators, boundary swapping and patch merging. Experimental results show that our optimization algorithm can reduce the distortion in cross parameterization efficiently.

In this paper, we present a fast algorithm for filling unknown regions in an image using the strategy of exemplar-matching. Unlike the original exemplar-based method using exhaustive search, we decompose exemplars into the frequency coefficients and select fewer coefficients which are the most significant to evaluate the matching score. We have also developed a local gradient-based algorithm to fill the unknown pixels in a query image block. These two techniques bring the ability of input with varied dimensions to the fast query of similar image exemplars. The fast query is based upon a search-array data structure, and can be conducted very efficiently. Moreover, the evaluation of search-arrays runs in parallel maps well on the modern graphics hardware with graphics processing units (GPU). The functionality of the approach has been demonstrated by experimental results on real photographs.