Feedback Control—Based Inverse Kinematics Solvers for a Nuclear Decommissioning Robot

In this article we present a technique that enhances an inverse kinematics (IK) solver such that when the results are applied to a computer character, we can generate a level of individualization tailored to both the character and the environment, e.g., a walking motion can become "stiffer" or can be turned into a limping motion. Since the technique is based on an IK solver, we also have the desirable effect of solving retargetting issues when mapping motion data between characters. As the individualization aspect of our technique is very tightly coupled with the inverse kinematics solver, we can achieve both the individualization and retargetting of characters in real time.

The Inverse Kinematics (IK) algorithms implemented in the open-source Orocos Kinematics and Dynamics Library (KDL) are arguably the most widely-used generic IK solvers worldwide. However, KDL's only joint-limit-constrained IK implementation, a pseudoinverse Jacobian IK solver, repeatedly exhibits false-negative failures on various humanoid platforms. In order to find a better IK solver for generic manipulator chains, a variety of open-source, drop-in alternatives have been implemented and evaluated for this paper. This article provides quantitative comparisons, using multiple humanoid platforms, between an improved implementation of the KDL inverse Jacobian algorithm, a set of sequential quadratic programming (SQP) IK algorithms that use a variety of quadratic error metrics, and a combined algorithm that concurrently runs the best performing SQP algorithm and the improved inverse Jacobian implementation. The best alternative IK implementation finds solutions much more often than KDL, is faster on average than KDL for typical manipulation chains, and (when desired) allows tolerances on each Cartesian dimension, further improving speed and convergence when an exact Cartesian pose is not possible and/or necessary.

Robotic manipulation in surgical applications often demands the surgical instrument to pivot around a fixed point, known as remote center of motion (RCM). The RCM constraint ensures that the pivot point of the surgical tool remains stationary at the incision port, preventing tissue damage and bleeding. Precisely and efficiently controlling tool positioning and orientation under this constraint poses a complex Inverse Kinematics (IK) problem that must be solved in real-time to ensure patient safety and minimize complications. To address this problem, we propose PivotIK, an efficient IK solver that combines efficient evolutionary exploration with multi-objective Jacobian-based optimization. PivotIK can track desired tool poses accurately while satisfying the RCM constraint in real-time. We evaluated PivotIK through simulations and real-world experiments using redundant robotic manipulators with multi-degree-of-freedom surgical instruments. We compare PivotIK with other IK solvers in terms of solve rates, computation times, tracking errors, and RCM errors under various scenarios, including unconstrained and RCM-constrained trajectories. Our results show that PivotIK achieves superior performance, solving the IK problem in less than 1 ms with errors below 0.01 and 0.1 mm for tracking and RCM, respectively. Our real-world experiments confirm the effectiveness of PivotIK in ensuring smooth trajectory tracking and RCM compliance. PivotIK offers a promising solution for real-time IK for robotic manipulation under RCM constraints in surgical applications.

The inverse kinematics (IK) problem is a fundamental problem in robotic manipulation. Traditional, Jacobian-based solutions to this problem are known to scale poorly with the number of degrees of freedom (DOF) in the manipulator, necessitating novel IK solutions for high-DOF manipulators. Metaheuristic optimization algorithms such as Particle Swarm Optimization (PSO) are a promising alternative approach to traditional IK techniques due to their strong performance on difficult and high-DOF problems in many diverse domains. Previous applications of PSO to the IK problem have focused on specific classes (e.g., planar) or models of manipulators or specific IK subproblems (e.g., position only IK). Furthermore, the experimental validation of these techniques has considered only manipulators with seven or fewer degrees of freedom and taken place almost exclusively in simulation. In this paper, we (1) generalize previous work to derive a fitness function that can be minimized to solve the full position and orientation IK problem for any serial manipulator while respecting joint limits and avoiding self-collisions, (2) present the first statistical analysis of PSO as a high-DOF IK solver on simulated manipulators with up to 180 DOF using this fitness function, and (3) present an important validation of PSO-based IK using this fitness function on real-world hardware on a difficult precision manipulation task.

In order to grasp an object, we need to solve the inverse kinematics problem, i.e., the coordinate transformation from the visual coordinates to the joint angle vector coordinates of the arm. In human motion control, the learning of the hand position error feedback controller in the inverse kinematics solver is important. Although several models of coordinate transformation learning have been proposed, they suffer from a number of drawbacks. This paper proposes a novel model of the coordinate transformation learning of the human visual feedback controller by using disturbance noise and feedback error signal. The feasibility of the proposed model is illustrated using numerical simulations.

Articulated hand tracking systems have been commonly used in virtual reality applications, including systems with human-computer interaction or interaction with game consoles. However, building an effective real-time hand pose tracker remains challenging. In this paper, we present a simple and efficient methodology for tracking and reconstructing 3d hand poses using a markered optical motion capture system. Markers were positioned at strategic points, and an inverse kinematics solver was incorporated to fit the rest of the joints to the hand model. The model is highly constrained with rotational and orientational constraints, allowing motion only within a feasible set. The method is real-time implementable and the results are promising, even with a low frame rate.

This paper develops on the process of inverse kinematics (IK) for manipulator robots based on a recent technique from the computer graphics area that has been highlighted by its simplicity and low computational cost. This IK solver is known as Forward And Backward Reaching Inverse Kinematics (FABRIK) suffers from singularities when applied in kinematic chains composed of one degree of freedom (1-DOF) joints. Some extensions of this method have been proposed to incorporate the constraints in some of the most common joints, however, their application over kinematic chains with only 1-DOF joints is still not possible. Since several manipulators have kinematic chains composed of 1-DOF joints, this work presents a new method, named FABRIK-R, to extend the original method for applications in the robotics manipulators field.

We present a novel, hybrid neuro-genetic visuomotor architecture for object grasping on a humanoid robot. The approach combines the state-of-the-art object detector RetinaNet, a neural network-based coordinate transformation and a genetic-algorithm-based inverse kinematics solver. We claim that a hybrid neural architecture can utilise the advantages of neural and genetic approaches: while the neural components accurately locate objects in the robot’s three-dimensional reference frame, the genetic algorithm allows reliable motor control for the humanoid, despite its complex kinematics. The modular design enables independent training and evaluation of the components. We show that the additive error of the coordinate transformation and inverse kinematics solver is appropriate for a robotic grasping task. We additionally contribute a novel spatial-oversampling approach for training the neural coordinate transformation that overcomes the known issue of neural networks with extrapolation beyond training data and the extension of the genetic inverse kinematics solver with numerical fine-tuning. The grasping approach was realised and evaluated on the humanoid robot platform NICO in a simulation environment.

This paper presents a technique for adapting existing motion of a human-like character to have the desired features that are specified by a set of constraints. This problem can be typically formulated as a spacetime constraint problem. Our approach combines a hierarchical curve fitting technique with a new inverse kinematics solver. Using the kinematics solver, we can adjust the configuration of an articulated figure to meet the constraints in each frame. Through the fitting technique, the motion displacement of every joint at each constrained frame is interpolated and thus smoothly propagated to frames. We are able to adaptively add motion details to satisfy the constraints within a specified tolerance by adopting a multilevel Bspline representation which also provides a speedup for the interpolation. The performance of our system is further enhanced by the new inverse kinematics solver. We present a closed-form solution to compute the joint angles of a limb linkage. This analytical method greatly reduces the burden of a numerical optimization to find the solutions for full degrees of freedom of a human-like articulated figure. We demonstrate that the technique can be used for retargetting a motion to compensate for geometric variations caused by both characters and environments. Furthermore, we can also use this technique for directly manipulating a motion clip through a graphical interface. CR Categories: I.3.7 [Computer Graphics]: Threedimensional Graphics—Animation; G.1.2 [Numerical Analysis]: Approximation—Spline and piecewise polynomial approximation

We propose a geometric method to solve inverse kinematics (IK) problems of 7-DoF manipulators with joint offsets at shoulder, elbow, and wrist. Traditionally, inverse position kinematics for redundant manipulators are solved by using an iterative method based on the pseudo-inverse of the manipulator Jacobian. This provides a single solution among the infinitely many possible solutions for the IK problem of redundant manipulators. There are no closed-form IK solutions for redundant manipulators with multiple joint offsets. Using our method we can compute multiple IK solutions using two-parameter search by exploiting geometry of the structure of a redundant manipulator. Our proposed IK algorithm can handle multiple joint offsets and is mathematically simple to implement in a few lines of code. We apply our algorithm to compute IK solutions for 7-DoF redundant Baxter robot (that has joint offsets at shoulder, wrist, and elbow joints) for end-effector configurations where existing geometry-based IK solvers fail to find solutions. We also demonstrate the use of our algorithm in an application where we want to compute an IK solution (among the infinitely many possible solutions) that has minimum error bound in end-effector position, in the presence of random joint actuation and sensing uncertainties.

In this work, a novel design of a portable leg rehabilitation system (PLRS) is presented. The main purpose of this paper is to provide a portable system, which allows patients with lower-limb disabilities to perform leg and foot rehabilitation exercises anywhere without any embarrassment compared to other devices that lack the portability feature. The model of the system is identified by inverse kinematics and dynamics analysis. In kinematics analysis, the pattern of motion of both leg and foot holders for different modes of operation has been investigated. The system is modeled by applying Lagrangian dynamics approach. The mathematical model derived considers calf and foot masses and moment of inertias as important parameters. Therefore, a gait analysis study is conducted to calculate the required parameters to simulate the model. Proportional derivative (PD) controller and proportional-integral-derivative (PID) controller are applied to the model and compared. The PID controller optimized by hybrid spiral-dynamics bacteria-chemotaxis (HSDBC) algorithm provides the best response with a reasonable settling time and minimum overshot. The robustness of the HSDBC–PID controller is tested by applying disturbance force with various amplitudes. A setup is built for the system experimental validation where the system mathematical model is compare with the estimated model using system identification (SI) toolbox. A significant difference is observed between both models when applying the obtained HSDBC–PID controller for the mathematical model. The results of this experiment are used to update the controller parameters of the HSDBC-optimized PID.

Flight controllers for micro-air UAVs are generally designed using proportional-integral-derivative (PID) methods, where the tuning of gains is difficult and time-consuming, and performance is not guaranteed. In this paper, we develop a rigorous method based on the sliding mode analysis and nonlinear backstepping to design a PID controller with guaranteed performance. This technique provides the structure and gains for the PID controller, such that a robust and fast response of the UAV (unmanned aerial vehicle) for trajectory tracking is achieved. First, the second-order sliding variable errors are used in a rigorous nonlinear backstepping design to obtain guaranteed performance for the nonlinear UAV dynamics. Then, using a small angle approximation and rigorous geometric manipulations, this nonlinear design is converted into a PID controller whose structure is naturally determined through the backstepping procedure. PID gains that guarantee robust UAV performance are finally computed from the sliding mode gains and from stabilizing gains for tracking error dynamics. We prove that the desired Euler angles of the inner attitude controller loop are related to the dynamics of the outer backstepping tracker loop by inverse kinematics, which provides a seamless connection with existing built-in UAV attitude controllers. We implement the proposed method on actual UAV, and experimental flight tests prove the validity of these algorithms. It is seen that our PID design procedure yields tighter UAV performance than an existing popular PID control technique.

The problem of computing a human arm posture that will take the hand to a desired hand position given by vision is called an inverse kinematics problem. To solve this problem, the human nervous system has a system for solving the inverse kinematics problem computing the proper joint angles from the desired hand position.Although the direct inverse modeling method is popular for the acquisition of an inverse kinematics model, a sufficient inverse model cannot be obtained for such systems with many‐to‐one input‐output correspondence as a human arm system.This paper, proposes a new model of a human inverse kinematics solver which uses the learned inverse model of the linearized model of the human arm. This inverse model transforms the hand position error to the update vector of the joint angles. The solver inverse kinematics problems by using the hand position error feedback. The performance of the solver is shown using numerical simulations.

PurposeThis paper aims to develop a new real‐time effective method for solving the inverse kinematics (IK) problem, especially for those manipulators with high‐dimensional nonlinear kinematic equations.Design/methodology/approachThe paper transforms the IKs problem into a minimization problem. Then, a novel meta‐heuristic algorithm, called the electromagnetism‐like method (EM), is used to solve this equivalent problem. Moreover, in order to further improve the computational efficiency and accuracy of EM, a hybrid method which combines EM with the Davidon‐Fletcher‐Powell (DFP) method is proposed.FindingsThe results showed that EM is a powerful yet easy algorithm for solving the IKs problem of robot manipulators. Its complexity is independent on the characteristics of the kinematic equations involving dimensionality and the degree of nonlinearity. Moreover, EM can be used as an accompanying algorithm for DFP method to get better precision at a lower iteration number.Originality/valueThe method developed in this paper is a generalized approach that is efficient enough to obtain IK solutions independent of robot geometry and the number of degrees of freedom.

This paper presents a comparative study of analytical and deep learning (DL) approaches for solving the inverse kinematics (IK) problem in high-degree-of-freedom (DOF) robotic manipulators, focusing on the Lunar Exploration Rover System (LERS). The IK problem, central to robotic motion control, is traditionally solved using analytical methods, but recent advances in deep learning provide new opportunities to enhance precision and efficiency. The study evaluates the performance of DL Neural Networks, in addressing the complexities of high-DOF manipulators. A detailed comparison is conducted between traditional geometric solutions and DL-based models, with an emphasis on robustness and computational efficiency under noisy conditions. The results demonstrate the potential of DL methods to outperform traditional techniques in high-DOF environments, paving the way for future advancements in autonomous robotic systems. In addition to the IK study, the paper discusses the design and integration of the LERS robotic system, which plays a critical role in advancing autonomous lunar exploration under the ARTEMIS program. As part of this international collaboration involving NASA, the Canadian Space Agency (CSA), the European Space Agency (ESA), and the Japan Aerospace Exploration Agency (JAXA), LERS is tasked with supporting both crewed and unmanned missions on the Moon. LERS is designed to perform precise robotic manipulation tasks such as deploying infrastructure, gathering scientific data, and managing lunar resources, all of which are vital for future missions to Mars. The implementation of advanced IK solutions is key to enabling the precise control of LERS’s robotic arms, allowing for the successful execution of complex tasks such as assembling habitats, handling materials, and conducting scientific analyses on the lunar surface. This work highlights the importance of IK in ensuring that robotic systems like LERS can operate with the precision needed for the next generation of lunar missions.