Kinematic Solution Research Articles

Design and analysis of a multi-motion self-balancing lower limb exoskeleton based on flat terrain

In this study, a multi-motion self-balancing lower limb exoskeleton is designed to provide crutches-free rehabilitation training for quadriplegic patients on flat terrain without hand support. First, based on the biomechanical characteristics of the human body and the bionic mechanism configuration of the human lower limb, an exoskeleton with a full-drive series-parallel hybrid structure was established. Secondly, the D-H method, geometric method and Newton iteration method were used to establish the forward and reverse kinematic solutions of the exoskeleton. In addition, the static self-balancing principle was used to complete the planning of the multi-motion self-balancing trajectory. Finally, in order to verify the effectiveness of the proposed method, some numerical simulations were performed in this paper. The theoretical trajectories of the waist, ankle joint and foot center were compared with the simulated trajectories. The research results show that the forward and reverse kinematics model of the exoskeleton is feasible. Under the condition of contact force parameters, the exoskeleton has the ability of multi-motion self-balancing walking on flat terrain.

Upper limb exoskeleton rehabilitation robot inverse kinematics modeling and solution method based on multi-objective optimization

The inverse kinematics problem of exoskeleton rehabilitation robots is challenging due to the lack of a standard analytical model, resulting in a complex and varied solution process. This complexity is especially pronounced in redundant upper limb exoskeleton robots, where inefficient solutions hinder the robot’s ability to adapt to the kinematic shape of the upper limb. This paper proposes a modeling and solution method based on multi-objective optimization to address the inverse kinematics of upper limb exoskeleton robots. We analyzed and validated this method using a redundant upper limb exoskeleton rehabilitation robot system developed by ourselves. First, we established a multi-objective inverse kinematics solution model by defining the end-position function, joint motion comfort function, system energy consumption function, motion safety, and human-like constraints. Then, the solution was designed based on the Improved Equilibrium Optimization (IEO) algorithm and validated its computational performance in terms of optimization ability, accuracy, and robustness. Finally, we experimentally tested the inverse kinematics solution model with the IEO algorithm on discrete objectives and continuous training trajectories using a redundant upper limb exoskeleton rehabilitation robot system. The results show that by incorporating the joint comfort function, system energy consumption function, and human-like constraints into the inverse kinematics model, we can not only quickly solve the inverse kinematics of redundant upper limb exoskeleton robots but also significantly improve the robot’s motion shape. Furthermore, it has better solution accuracy and stronger robustness than other algorithms when solving this inverse kinematics model based on the IEO algorithm.

Differential kinematics of a single-point-suspended manipulator with center-of-mass shift compensation

The single cable-suspended manipulator is suitable for special occasions such as aerial operation tasks of unmanned aerial vehicles (UAVs) and deep-well search and rescue. However, due to the lack of complete constraints at the base, the manipulator will have errors in end position due to the center-of-mass offset during the motion. In this paper, the model of CoM shifting is established, and the Jacobian matrix is improved based on this model, to realize the differential kinematics solution for the single cable-suspended manipulator. In addition, by introducing the constraint of CoM shift in the Jacobian matrix, it makes it possible to synchronize the planning of the motion of the end and the center of mass. This can effectively avoid the wobbling of the manipulator in the presence of elasticity or instability at the suspension point. Both simulation and prototype experiments effectively verify the effectiveness of the proposed method. Using the method of this paper, the average error of the trajectories in the z-axis and x-axis can be reduced from 27.0 ± 2.6 mm to 5.6 ± 3.4 mm, and 43.0 ± 64.2 mm to 3.3 ± 4.8 mm, respectively.

Design and kinematics of a novel rigid-flexible coupling hybrid robot for aeroengine blades in situ repair

PurposeThis paper aims to present the mechanical design and kinematics of a novel rigid-flexible coupling hybrid robot to develop a promising aeroengine blades in situ repair technology.Design/methodology/approachAccording to requirements analysis, a novel rigid-flexible coupling hybrid robot is proposed by combining a three degrees of freedom (DOF) parallel mechanism with a flexible continuum section. Then the kinematics models of both parallel mechanism and flexible continuum section are derived respectively. Finally, based on equivalent joint method, a two-step numerical iterative inverse kinematics algorithm is proposed for the whole robot: (1) the flexible continuum section is equivalently transformed to a 2-DOF spherical joint, thus the approximate analytical inverse kinematic solution can be obtained; (2) the accurate solution is derived by an iterative derivation of both parallel mechanism and flexible continuum section.FindingsTo verify structure scheme and the proposed kinematics modeling method, numerical simulations and prototype experiments are implemented. The results show that the proposed kinematics algorithm has sufficient accuracy and computational efficiency in the whole available workspace, that is end-effector position error and orientation error are less than 0.2 mm and 0.01° respectively, and computation time is less than 0.22s.Originality/valueA novel rigid-flexible coupling hybrid robot for aeroengine blades in situ repair is designed. A two-step numerical iterative inverse kinematics algorithm is proposed for this unique hybrid robots, which has good accuracy and computational efficiency.

Deep Learning-Driven Analysis of a Six-Bar Mechanism for Personalized Gait Rehabilitation

Abstract Recent advances in robotics and artificial intelligence have highlighted the potential for the integration of computational intelligence in enhancing the functionality and adaptability of robotic systems, particularly in rehabilitation. Designing robotic exoskeletons for the lower limb rehabilitation of post-stroke patients requires frequent adjustments to accommodate individual differences in leg anatomy. This complex engineering challenge necessitates a deep understanding of human physiology, robotics, and optimization to develop adaptive robotic systems and also to swiftly quantify the required adjustments and implement them for each patient. The conventional approaches, which mostly rely on heuristics and manual tuning, often struggle to achieve optimal results. This paper presents a novel method that integrates a genetic algorithm (GA) with a deep learning approach to generate a gait trajectory of the ankle joint from a six-bar linkage mechanism of fixed dimensions. Later, using the same approach, the inverse kinematics solution for this mechanism is also devised whereby, the set of the link dimensions of the six-bar linkage mechanism is obtained for the given gait trajectory of an individual to achieve customization. We simulated the kinematic behavior of the six-bar linkage mechanism within defined mechanical constraints and utilized the generated data for training a feedforward neural network and long short-term memory models. The proposed model, when trained, can produce accurate lengths for the desired gait trajectories in the sagittal plane and vice-versa which further validates our proposed approach for inverse kinematics solution.

Robot inverse kinematics solution for center selection battle royale optimization algorithm

In order to solve the problems of high time complexity and insufficient global exploration ability of the battle royale optimization algorithm, this paper proposes an improved battle royale optimization algorithm based on chaos mapping, center selection and elite adaptive strategy. Through benchmark function testing, compared to particle swarm optimization algorithm, whale optimization algorithm, and the battle royale optimization algorithm, the improved algorithm significantly reduces time complexity and notably enhances convergence precision, speed, and stability. The improved algorithm is applied to the inverse kinematics problem of robots. The accuracy and The stability of the improved algorithm is better than those of the traditional battle royale optimization algorithm, it demonstrates superior solving precision and stability, proving its practicality and potential for development in solving robot inverse kinematics problems.

Lagrangian approach to origami vertex analysis: kinematics.

The use of origami in engineering has significantly expanded in recent years, spanning deployable structures across scales, folding robotics and mechanical metamaterials. However, finding foldable paths can be a formidable task as the kinematics are determined by a nonlinear system of equations, often with several degrees of freedom. In this article, we leverage a Lagrangian approach to derive reduced-order compatibility conditions for rigid-facet origami vertices with reflection and rotational symmetries. Then, using the reduced-order conditions, we derive exact, multi-degree of freedom solutions for degree 6 and degree 8 vertices with prescribed symmetries. The exact kinematic solutions allow us to efficiently investigate the topology of allowable kinematics, including the consideration of a self-contact constraint, and then visually interpret the role of geometric design parameters on these admissible fold paths by monitoring the change in the kinematic topology. We then introduce a procedure to construct lower-symmetry kinematic solutions by breaking symmetry of higher-order kinematic solutions in a systematic way that preserves compatibility. The multi-degree of freedom solutions discovered here should assist with building intuition of the kinematic feasibility of higher-degree origami vertices and also facilitate the development of new algorithmic procedures for origami-engineering design.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Kineto-static analysis of a hybrid manipulator consisting of rigid and flexible limbs with locking function for planar shape morphing

The incorporation of lockable passive backbones into active compliant morphing systems efficiently results in lightweight, high-load, and large deformation systems. However, there exist challenges in kineto-static analysis due to the interaction between rigid reconfigurable kinematic constraints and the nonlinear deformation of actuated flexible limbs. This paper addresses these issues by developing a kineto-static method to analyze the motion in a novel planar 3-DOF shape-morphing manipulator. The manipulator features two actuated flexible limbs with a lockable variable geometry truss (LVGT). In this study, two isostatic topologies are selected for reconfigurable motion control under external tip loads. A multi-step sequential control strategy is proposed to maneuver the manipulator's platform for desired poses. Then, a constrained-trajectory-based kinematic model is proposed for an inverse kinematic solution considering motion planning. Subsequently, a kineto-static model is introduced, considering constraints from rigid and flexible limbs, aiming to distribute distributing redundant actuation forces. Finally, nonlinear finite element analysis (FEA) and experiments are carried out to validate the effectiveness of the proposed method.

Direct and inverse kinematics solutions of a particular type of 3-PSP parallel manipulator

Abstract In this paper, the direct and inverse kinematics problems for a particular type of 3-DOF, 3-PSP parallel manipulator are considered. The proposed direct kinematics solution is based on an existing one in the literature, but with an alternative, simplified second stage in the solution’s formulation. An explicit analytical solution of the inverse kinematics problem is also proposed for one of the manipulator’s operational modes, requiring one pass through the direct kinematics solution. The proposed solutions can be seamlessly extended to the inverted parallel structure.

Kinematics-guided data-driven energy surrogate model for robotic additive manufacturing

With the increase in the usage of industrial robots for manufacturing applications, there will be a corresponding rise in energy consumption. Especially, robotic additive manufacturing (AM) has demonstrated significant potential for working autonomously in hazardous or extraterrestrial settings, as well as for producing large-scale structures. Recent advancements have made it possible for teams of robots to collaborate for printing structures even larger than their sizes together. Utilizing robots efficiently for AM is essential for achieving energy sustainability goals. The literature on energy models for robots and AM processes lacks a comprehensive energy model for robotic AM. To address this gap, a multi-point trajectory-based energy model is proposed for robotic AM. The model is created to help users manufacture parts in an energy-efficient way. These simulations require a significant amount of computation time, which limits their usage to offline purposes only. Hence, we propose two energy surrogate models for real-time predictions: a pure data-driven model and a kinematics-guided data-driven model. The kinematics-guided approach is an enhanced version of pure data-driven model which learns from inverse kinematics solutions along the trajectory to understand the robot’s dynamics and kinematics. There were two test cases conducted. The first test case consisted of paths that were feasible, printable, and within the robot’s reach, while the second test case consisted of a mixture of paths that were both feasible and infeasible. In comparison to the pure data-driven approach, the kinematics-guided approach stood out in both testing cases. Two real-world case studies have been used to demonstrate that the proposed approach can be used in lieu of simulations for real-time applications. Especially in the second case, where the part was placed very close to the robot making a portion of the part infeasible to print, the proposed approach correctly identified that it was not possible to print the geometry due to the robot’s kinematics. The proposed kinematics-guided approach is 195 and 700 times faster than the simulation results, respectively, in two case studies, and thus supporting the use of the proposed approach for real-time applications.

Study on behavior rules of the licorice-soil-licorice oscillating harvester coupled system using numerical method

Licorice oscillating harvester is a new type of energy-saving and resistance-reducing licorice harvester, and the interaction of licorice-soil-harvester is the critical factor affecting the working performance. Based on the licorice distribution in the harvested field and soil characteristics, a licorice-soil-licorice oscillating harvester coupled model was developed using the discrete element method. An efficient simulation method of a complex mechanism combined with a kinematic solution was proposed to study the behavior rules of the coupled system. The results indicate that licorice on the working surface was transported and separated by the topsoil’s holding effect and the front soil’s pushing effect; more than 70 % of the soil fell to the surface through the dispersion area, and the soil separation velocity in the dispersion area was lower than 0.3 m/s. When the harvester’s amplitude and forward speed increased, the licorice’s horizontal displacement was reduced, and the translational kinetic energy increased to obtain a strong transport ability. When the harvester’s amplitude and vibration frequency increased, the licorice’s separation velocity, the licorice force, and the rotational kinetic energy increased, and the relative motion between the licorice and shovel-rod working surface was violent, reducing the licorice’s buried mass. The forward speed has the greatest influence on the driving force of harvester. With an amplitude of 10 mm, a vibration frequency of 9 Hz, and a forward speed of 0.2 m/s, the shovel-rod working surface has a strong transporting ability for licorice, a strong relative motion, and a simulated licorice harvesting rate of 98.04 %. The field test results showed that the harvester worked smoothly, and the licorice harvesting rate was 97.26 %. The simulation model can predict the behavior rules of the coupled system. This study provides technical support for researching new principles and methods for deep-rooted crop harvesting.

Accuracy and reliability improved GNSS partial ambiguity resolution assisted by a MEMS inertial measurement unit

Traditional partial ambiguity resolution (PAR) methods based on integer least-squares (ILS-PAR) assume that the ambiguity terms are unbiased integers, which is seldomly true in challenging environments of the Global Navigation Satellite System (GNSS). The bias will lead to unreliable positioning solutions. This study proposes a reliable PAR method based on the tightly coupling of GNSS and inertial navigation system (INS) and the solution separation with external solution (SSE) statistical testing algorithm. First, the inertial measurement unit (IMU) mechanization results are compensated using the latest fixed real-time kinematic (RTK) solutions, thus high-accuracy INS predictions are obtainable at the current GNSS epoch. Second, the SSE method based on double-differenced (DD) carrier-phase measurements are applied to select and validate the ambiguity subset and perform the GNSS/INS integration. A dynamic vehicular experiment with a low-cost microelectromechanical systems (MEMS) device has been conducted and the results indicate that the proposed method can ensure good performance of both accuracy and reliability.

Inverse kinematic solution and singularity avoidance using a deep deterministic policy gradient approach

<p>The robotic arm emerges as a subject of paramount significance within the industrial landscape, particularly in addressing the complexities of its kinematics. A significant research challenge lies in resolving the inverse kinematics of multiple degree of freedom (M-DOF) robotic arms. The inverse kinematics of M-DOF robotic arms pose a challenging problem to resolve, thus it involves consideration of singularities which affect the arm robot movement. This study aims a novel approach utilizing deep reinforcement learning (DRL) to tackle the inverse kinematic problem of the 6-DOF PUMA manipulator as a representative case within the M-DOF manipulator. The research employs Jacobian matrix for the kinematics system that can solve the singularity, and deep deterministic policy gradient (DDPG) as the kinematics solver. This chosen technique offers enhancing speed and ensuring stability. The results of inverse kinematic solution using DDPG were experimentally validated on a 6-DOF PUMA arm robot. The DDPG successfully solves inverse kinematic solution and avoids the singularity with 1,000 episodes and yielding a commendable total reward of 1,018.</p>

Flexible control and trajectory planning of medical two-arm surgical robot.

This paper introduces the flexible control and trajectory planning medical two-arm surgical robots, and employs effective collision detection methods to ensure the safety and precision during tasks. Firstly, the DH method is employed to establish relative rotation matrices between coordinate systems, determining the relative relationships of each joint link. A neural network based on a multilayer perceptron is proposed to solve FKP problem in real time. Secondly, a universal interpolator based on Non-Uniform Rational B-Splines (NURBS) is developed, capable of handling any geometric shape to ensure smooth and flexible motion trajectories. Finally, we developed a generalized momentum observer to detect external collisions, eliminating the need for external sensors and thereby reducing mechanical complexity and cost. The experiments verify the effectiveness of the kinematics solution and trajectory planning, demonstrating that the improved momentum torque observer can significantly reduce system overshoot, enabling the two-arm surgical robot to perform precise and safe surgical tasks under algorithmic guidance.

An Efficient Quadratic Programming Method for Kinematic Control of Redundant Manipulators under Joint Velocity Constraints

This paper presents an efficient inverse kinematics solution for redundant robotic arms. The proposed method combines the principles of continuation methods, improves the instability of the computation time by increasing the convergence of the kinematics function, and improves the efficiency of traditional numerical methods. The effectiveness and efficient performance of the method are demonstrated through comparative experiments. The computational speed of the method is twice as fast as the Newton–Raphson method under joint limit constraints and equal solution accuracy.

Development of Standalone Extended-Reality-Supported Interactive Industrial Robot Programming System

Extended reality (XR) is one of the most important technologies in developing a new generation of human–machine interfaces (HMIs). In this study, the design and implementation of a standalone interactive XR-supported industrial robot programming system using the Unity game engine is presented. The presented research aims to achieve a cross-platform solution that enables novel tools for robot programming, trajectory validation, and robot programming debugging within an extended reality environment. From a robotics perspective, key design tasks include modeling in the Unity environment based on robot CAD models and control design, which include inverse kinematics solution, trajectory planner development, and motion controller set-up. Furthermore, the integration of real-time vision, touchscreen interaction, and AR/VR headset interaction are involved within the overall system development. A comprehensive approach to integrating Unity with established industrial robot modeling conventions and control strategies is presented. The proposed modeling, control, and programming concepts, procedures, and algorithms are verified using a 6DoF robot with revolute joints. The benefits and challenges of using a standalone XR-supported interactive industrial robot programming system compared to integrated Unity–robotics development frameworks are discussed.

Kinematic Modelling of Humanoid Robot Based on Vectorial Approach

The present work is dedicated to the study of the inverse kinematics solution of a humanoid bipedal robot with 30 degrees of freedom using a newly approach based on vectors that generated from the geometric space of the robot. The solutions of the inverse kinematics problem for all joints articulations are carried out through a simple and linear equations. Finally, simulations of results are performed through harmonization of trajectories of end effectors of the robot's members.

Closed-Form Kinematics Solutions for Redundant Medical Robots with Joint Limits and Singularity Avoidance

Closed-form forward and inverse position, velocity and acceleration kinematics problems solutions are developed for a redundant medical robot family. Developed solutions allow one to choose a specific joint as a set one. Solutions work in constant time, suitable for real-time operation. Methods for joint limit and singularity avoidance are proposed. Simulation experiments are performed on simulated KUKA MED 14 r820 robot.

Structural design and control strategy of a cable-driven robot under high-altitude facade conditions with large span and multiple constraints

Purpose This paper explores the challenges of using cable-driven parallel robots on high-altitude, large-span facades, where redundancy in multicable systems and the elastic deformation of the cables are significant issues. This study aims to improve the accuracy and stability of the work platform through enhanced control strategies. These strategies address the redundancy in multicable systems and reduce the risks associated with cable deformation and mechanical failures during large-span movements. Design/methodology/approach The paper proposes a dynamic model for a four-rope parallel robot designed explicitly for large-span applications. The study introduces a position–force control strategy incorporating kinematic inverse solutions and a rope dynamics model to account for rope elasticity and its effects. This approach increases the number of system equations to match the unknowns, effectively solving the redundancy problem inherent in multicable systems. In addition, the tension changes of ropes and the stability of the working platform are examined under different motion distances (X = 50 m and X = 100 m) and varying Young’s modulus values (K = 5000 MPa and K = 8000 MPa). Findings This study’s large-span rope force–position control strategy successfully resolves the typical nonlinear characteristics and external disturbances in multicable parallel systems. By continuously monitoring and adjusting cable tension and end positions, this strategy ensures precise control over each cable’s tension, optimizes the distribution of cable tensions and maintains the system’s stability and response speed. The analysis in this paper indicates that this control strategy significantly improves the motion accuracy of robots operating on large-span high-altitude facades. Practical implications Industry adoption: The design and control strategies developed for the four-cable-driven parallel robot can be adopted by companies specializing in facade maintenance, construction or inspection. This could lead to safer, more efficient and cost-effective operations, especially in challenging environments like high-rise buildings. Innovation in robotic solutions: The research can inspire innovation within the field of robotics, particularly in developing robots for specific applications such as large surface maintenance. It showcases how adaptive control and stability can be achieved in complex operational scenarios. Safety improvements: By demonstrating a more stable and precise control mechanism for navigating large facades, the study could contribute to significant safety improvements, reducing the risk of accidents associated with manual facade maintenance and inspection tasks. Originality/value This paper combines the force/position hybrid control method with actual robotic applications, offering a novel solution to the complex issue of controlling cable-driven parallel robots in challenging environments. Thus, it contributes to the field. The proposed method significantly enhances the precision and stability of such systems and provides robust technical support for high-precision tasks in complex mechanical settings.

A heuristic solution-based motion planning framework for redundant manipulators

Motion planning and optimization are the key and challenging problems for redundant manipulators operating in cluttered environments. This paper proposes a motion planning framework based on the heuristic solution that explores the optimal solutions for path planning and kinematic solutions by estimating the cost of target configurations via dynamic programming methods. A heuristic function model based on artificial neural networks (ANN) is constructed in the path planning structure and rapidly trained through the RRT* algorithm, leveraging value iteration concepts to search the state space. This structure can utilize previous experience to guide future exploration behavior with significant improvements in path quality and algorithm efficiency. The kinematic solving structure is unified with path planning by building a global energy optimal heuristic function. K-means is employed to determine the initial policy, avoid ineffective searches in non-critical spaces, and introduce gradient concepts to explore the optimal policy rapidly. The proposed method can obtain better energy optimization results while ensuring solving efficiency. The optimal joint angles of the manipulator are determined through collision detection and posture adjustment methods. Finally, the performance of the proposed framework is simulated and experimentally verified.