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The output layer of a feedforward neural network approximates nonlinear functions as a linear combination of a fixed set of basis functions, or "features". These features are learned by the hidden-layer units, often by a supervised algorithm such as a back-propagation algorithm. This paper investigates features which are optimal for computing desired output functions from a given distribution of input data, and which must therefore be learned using a mixed supervised and unsupervised algorithm. A definition is proposed for optimal nonlinear features, and a constructive method, which has an iterative implementation, is derived for finding them. The learning algorithm always converges to a global optimum and the resulting network uses two layers to compute the hidden units. The general form of the features is derived for the case of continuous signal input, and this result is related to transmission of information through a bandlimited channel. The results of other algorithms can he compared to the optimal features, which in some cases have easily computed closed-form solutions. The application of this technique to the inverse kinematics problem for a simulated planar two-joint robot arm is demonstrated here.

In this paper, we present a motion editing algorithm for the human biped locomotion captured by a motion capturing device. Our algorithm adopts footprints to describe the space-time constraints which should be satisfied during biped locomotion. The footprints are also used as an interface to enable the user to control the space-time constraints directly. A real-time Inverse Kinematics (IK) solver is adapted to compute the configuration of the human body and motion displacement mapping is then constructed using hierarchical B-spline. In order to facilitate the IK solver, we propose a sampling-based scheme to generate root trajectory. Hermit interpolation is then employed to generate the whole root trajectory. This scheme provides a speedup to root trajectory generation. The performance of our algorithm is further enhanced by the real-time IK solver, which directly computes the displacement angles as solution.

In this paper, we present a method for controlling a motorized, string-driven marionette using motion capture data from human actors and from a traditional marionette operated by a professional puppeteer. We are interested in using motion capture data of a human actor to control the motorized marionette as a way of easily creating new performances. We use data from the hand-operated marionette both as a way of assessing the performance of the motorized marionette and to explore whether this technology could be used to preserve marionette performances. The human motion data must be extensively adapted for the marionette because its kinematic and dynamic properties differ from those of the human actor in degrees of freedom, limb length, workspace, mass distribution, sensors, and actuators. The motion from the hand-operated marionette requires less adaptation because the controls and dynamics are a closer match. Both data sets are adapted using an inverse kinematics algorithm that takes into account marker positions, joint motion ranges, string constraints, and potential energy. We also apply a feedforward controller to prevent extraneous swings of the hands. Experimental results show that our approach enables the marionette to perform motions that are qualitatively similar to the original human motion capture data.

A method of computing humanoid robot joint angles from human motion data is presented in this paper. The proposed method groups the motors of an upper-body humanoid robot into pan-tilt and spherical modules, solves the inverse kinematics (IK) problem for each module, and finally resolves the coordinate transformations among the modules to yield the full solution. Scaling of the obtained joint angles and velocities is performed to ensure that their limits are satisfied and their smoothness preserved. To address robustness-accuracy tradeoff when handling kinematic singularity, we design an adaptive regularization parameter that is active only when the robot is operating near any singular configuration. This adaptive algorithm is provably robust and is simple and fast to compute. Simulation on a seven degree-of-freedom (DOF) robot arm shows that tracking accuracy is slightly reduced in a neighborhood of a singularity to gain robustness, but high accuracy is recovered outside this neighborhood. Experimentation on a 17-DOF upper-body humanoid robot confirms that user-demonstrated gestures are closely imitated by the robot. The proposed method outperforms state-of-the-art Jacobian-based IK in terms of overall imitation accuracy, while guaranteeing robust and smoothly scaled trajectories. It is ideally suited for applications such as humanoid robot teleoperation or programming by demonstration.

This paper focuses on developing a consistent methodology for deriving a closed-form inverse kinematic joint solution of a humanoid robot with decision equations to select a proper solution from multiple solutions. Most researchers resort to iterative methods for inverse kinematics using the Jacobian matrix to avoid the difficulty of finding a closed-form joint solution. Since a closed-form joint solution, if available, has many advantages over iterative methods, we have developed a novel reverse-decoupling method by viewing the kinematic chain of a limb of a humanoid robot in reverse order and then decoupling it into the positioning and orientation mechanisms, and finally utilizing the inverse-transform technique to derive a consistent joint solution for the humanoid robot. The proposed method presents a simple and efficient procedure for finding the joint solution for most of the existing humanoid robots. Extensive computer simulations of the proposed approach on a Hubo KHR-4 humanoid robot show that it can be applied easily to most humanoid robots such as HOAP-2, HRP-2 and ASIMO humanoid robots with slight modifications.

In this work we show how precomputed reachability information can be used to efficiently solve complex inverse kinematics (IK) problems such as bimanual grasping or re-grasping for humanoid robots. We present an integrated approach which generates collision-free IK solutions in cluttered environments while handling multiple potential grasping configurations for an object. Therefore, the spatial reachability of the robot's workspace is efficiently encoded by discretized data structures and sampling-based techniques are used to handle arbitrary kinematic chains. The algorithms are employed for single-handed and bimanual grasping tasks with fixed robot base position and methods are developed that allow to efficiently incorporate the search for suitable robot locations. The approach is evaluated in different scenarios with the humanoid robot ARMAR-III.

Inverse-kinematics is an emphasis and difficulty in the design and application of the humanoid robot hand with coupled joints because of nonlinearity induced by trigonometric transcendental function. In this paper, a power series based inverse-kinematics algorithm is presented, by which the transcendental equation including trigonometric function can be converted into an algebraic equation. An approximate solution is derived first by means of power series expansions; with 1D linear interpolation for errors compensating, the final solution with small error can then be achieved. For robot with linearly coupled joints, the algorithms based on power series expanded to quadratic and quartic terms are used to calculate the accurate joint angles. For robot with nonlinearly coupled joints, the specific procedures are proposed to select appropriate transmission ratio. Simulation and experimental results demonstrate effectiveness of the proposed inverse kinematics method.

In this paper, we propose a computationally fast method of sampling-based global path planning for humanoids under Manifold Constraints such as closed kinematic chains and Volume-Reducing Constraints such as collision avoidance. In multi-contact and whole-body manipulation of humanoids, narrow collision-free space causes path planning to take a long computation time (narrow corridor problem). In previous research of constrained planning, Manifold Constraints are locally approximated by tangent plane, and steering motions along Manifold Constraints are found efficiently by projection or continuation methods. In this paper, we applied constrained planning algorithms to collision avoidance. Since tangent plane cannot approximate Volume-Reducing Constraints, we adopted convex polytope instead of tangent plane. Both Manifold Constraints and Volume-Reducing Constraints are locally approximated by convex polytope with linear equality and inequality constraints, and steering motions inside the convex polytope are found efficiently by the SQP-based prioritized inverse kinematics. We developed CP-KPIECE (Convex Polytope approximation-based KPIECE) with this approach. Benchmarks using the humanoid JAXON proved the effectiveness of our approach for fast path planning in narrow collision-free space of humanoids.

An autonomous surface manipulator system (ASMS) is a novel intelligent system consisting of a robotic manipulator and an unmanned surface vehicle (USV). Due to the waves and the motions of the manipulators, ASMSs experience rolling while performing tasks, reducing their stability and working accuracy. Hence, two methods are proposed for improving the anti-rolling abilities of ASMSs based on their mathematical models. The first method is to solve the inverse kinematics issues of the manipulator with the objective of minimizing the moment between the manipulator and its base, and to design angle-time curves for each joint using seven-order polynomials. Experiment results demonstrate that the motion optimization of manipulators can reduce the maximum and stable roll angles of the USV by over 40%. The second method involves assembling a moving-mass system into the ASMS and controlling the motion of the moving mass using a dual-loop PID controller. The moving-mass system can significantly reduce the roll angle of USV caused by waves and the operations of manipulators, as validated by simulation on a proposed accurate dynamic model. The research work can greatly enhance the operation stability of ASMSs.

With the rise in remote work culture and increased computing capabilities of head-mounted displays (HMDs), more immersive, collaborative experiences are desired in remote–local mixed/augmented reality (MR/AR). Photorealistic full-body avatar representations of users in remote workspace interactions have shown to have increased social presence, nonverbal behavior, and engagement. However, a direct mapping of the body pose angles from local to the remote workspace will, in most cases, result in positional errors during human–object interaction, caused by the dissimilarity between remote and local workspaces. Hence, the interaction must be retargeted, but it should be retargeted in such a way that the original intent of the body pose should be preserved. However, these two objectives sometimes contradict each other. As a result, a multi-objective optimization (MO) problem can be formulated where the primary objective is to minimize positional errors and the secondary objective is to preserve the original interaction body pose. The current state-of-the-art solution uses an evolutionary computation-based inverse kinematic (IK) approach to solve the MO problem where the weights between the objectives must be set by the user based on trial and error, leading to a suboptimal solution. In this paper, we present a new dynamic weight allocation approach to this problem, where a user has the flexibility to set a chosen minimum error tolerance, and the weights will be distributed between the objectives based on a dynamic allocation algorithm. We have used a two-pronged approach to test the adaptability and robustness of this mechanism: (i) on motion-captured human animations of varying levels of speeds, error tolerances, redirections and (ii) we conducted an experiment involving 12 human participants and recorded, redirected their actions performed during a book-shelving task in AR. Compared to the static weighting, the dynamic weighted mechanism showed a net ($\mathrm{\text{primary}}+\mathrm{\text{secondary}}$ objective) decrease in error ranging from 20.5% to 34.42% across varying animation speeds and a decrease in error ranging from 11.44% to 36.2% for the recorded human actions during the AR task, demonstrating its robustness and better pose preservation across interactions.

This work presents a five-segment biomechanical model of the human body for paraplegics of spinal cord injury (SCI) with thoracic nerve injury. When the functional electrical stimulation (FES) system is used to restore sit-to-stand function, the biomechanical model can be used to analyze the position, force, and moment of the human body at every joint through inverse dynamics. A series of data taking from SCI patient under FES of restoring sit-to-stand function are implemented on the model. The results help realize the role of each joint and muscle in the sit-to-stand process so as to improve the rehabilitation in the future plan.

Recurrent neural networks are discussed for real-time inverse kinematic control of redundant manipulators. Three recurrent neural network models, the Lagrangian neural network, the primal-dual neural network, and the dual neural network. We begin with the Lagrangian neural network for the inverse kinematics computation based on the Euclidean norm of the joint velocities to show the feasibility. Next, we present the primal-dual neural network for minimum infinity norm kinematic control of redundant manipulators. To reduce the model complexity and increase the computational efficiency, the dual neural network is developed with the advantages of simple architecture and exponential convergence. Simulation results based on the PA10 robot manipulator substantiate the effectiveness of the present recurrent neural network approach.

The output layer of a feedforward neural network approximates nonlinear functions as a linear combination of a fixed set of basis functions, or "features". These features are learned by the hidden-layer units, often by a supervised algorithm such as a back-propagation algorithm. This paper investigates features which are optimal for computing desired output functions from a given distribution of input data, and which must therefore be learned using a mixed supervised and unsupervised algorithm. A definition is proposed for optimal nonlinear features, and a constructive method, which has an iterative implementation, is derived for finding them. The learning algorithm always converges to a global optimum and the resulting network uses two layers to compute the hidden units. The general form of the features is derived for the case of continuous signal input, and this result is related to transmission of information through a bandlimited channel. The results of other algorithms can be compared to the optimal features, which in some cases have easily computed closed-form solutions. The application of this technique to the inverse kinematics problem for a simulated planar two-joint robot arm is demonstrated here.

To obtain the inverse kinematics solution for 8 DOF onboard craning manipulator in the process of lifting and traversing, the equations of the forward kinematics model is constructed on the basis of assignment description, based on the homogeneous transformation matrix method. This paper analyzes the model according to the machinery's characteristics, and then a novel algorithm—extension multi-particle swarm optimization algorithm (EMPSO) — is proposed. Besides being simple to implement, the new algorithm is also easily used for global optimization and has a high computational precision, thereby gaining only a set of solutions. Simulations show that the present method is effective.

This paper demonstrates the usefulness of a six-legged robot dynamic model in the gait generation mechanism. Particularly, contact forces between the legs and the ground are computed through a general visco-elastic model, and shows the necessity of enhancing the simple fixed gait, pattern in order to avoid an-tagonist contact forces with the soil.

The lifetimes and the relative g factors of the first excited states in ^104,106,108Pd are reported here. The first state in these Pd isotopes were excited by inverse kinematics Coulomb excitation on a ²⁴Mg target and the lifetime was measured by the Recoil Distance Doppler Shift with the New Yale Plunger Device combined with the SPEEDY array of Clover detectors. The results show the feasibility of the new method, which should be applicable to experiments with radioactive ion beams.

The E1 strength of exotic Ni isotopes has been measured at the R³B-LAND setup at GSI in Darmstadt. The experimental method relied on Coulomb excitation in inverse kinematics, for beam energies around 500 MeV/u. The excitation energy was reconstructed using the invariant mass, enabling the observation of the GDR and of additional low-lying E1 strength. The analysis of the neutron kinetic energies also allowed the extraction of the branching ratio for the direct neutron decay of ⁶⁸Ni, amounting to 25(2)%.