Inverse Kinematic Control Research Articles

Intelligent Rock-Climbing Robot Capable of Multimodal Locomotion and Hybrid Bioinspired Attachment.

Rock-climbing robots have significant potential in fieldwork and planetary exploration. However, they currently face limitations such as a lack of stability and adaptability on extreme terrains, slow locomotion, and single functionality. This study introduces a novel multimodal and adaptive rock-climbing robot (MARCBot), which addresses these limitations through spiny grippers that draw inspiration from morpho-functionalities observed in beetles, arboreal birds, and hoofed animals. This hybrid bioinspired design enables high attachment strength, passive adaptability to different terrains, and quick attachment on rock surfaces. The multimodal functionality of the gripper allows for attachment during climbing and support during walking. A novel control strategy using dynamics and quadratic programming (QP) optimizes attachment wrench distribution, reducing cost-of-transport by 20.03% and 6.05% compared to closed-loop inverse kinematic (CLIK) and virtual model control (VMC) methods, respectively. MARCBot achieved climbing speeds of 0.15mmin-1 on a vertical discrete rock surface under gravity and trotting speeds of up to 0.21ms-1 on various complex terrains. It is the first robot capable of climbing on rock surfaces and trotting in complex terrains without the need for switching end-effectors. This study highlights significant advancements in climbing and multimodal locomotion for robots in extreme environments.

Inverse kinematics solution and control method of 6-degree-of-freedom manipulator based on deep reinforcement learning

The advent of Industry 4.0 has significantly promoted the field of intelligent manufacturing, which is facilitated by the development of new technologies are emerging. Robot technology and robot intelligence methods have rapidly developed and been widely applied. Manipulators are widely used in industry, and their control is a crucial research topic. The inverse kinematics solution of manipulators is an important part of manipulator control, which calculates the joint angles required for the end effector to reach a desired position and posture. Traditional inverse kinematics solution algorithms often face the problem of insufficient generalization, and iterative methods have challenges such as large computation and long solution time. This paper proposes a reinforcement learning-based inverse kinematics solution algorithm, called the MAPPO-IK algorithm. The algorithm trains the manipulator agent using the MAPPO algorithm and calculates the difference between the end effector state of the manipulator and the target posture in real-time by designing a reward mechanism, while considering Gaussian distance and cosine distance. Through experimental comparative analysis, the feasibility, computational efficiency, and superiority of this reinforcement learning algorithm are verified. Compared with traditional inverse kinematics solution algorithms, this method has good generalization and supports real-time computation, and the obtained result is a unique solution. Reinforcement learning algorithms have better adaptability to complex environments and can handle different sudden situations in different environments. This algorithm also has the advantages of path planning, intelligent obstacle avoidance, and other advantages in dynamically processing complex environmental scenes.

Trajectory Tracking Control of an Aerial Manipulator in the Presence of Disturbances and Model Uncertainties

The precise control of an aerial manipulator presents a formidable challenge due to the inherent mobility of its base, which is subject to both external disturbances and dynamic disturbances due to manipulator motions. In this paper, we introduce two Closed-Loop Inverse Kinematics (CLIK) control algorithms tailored to aerial manipulators. The first algorithm operates at the velocity level and uses the Generalized Jacobian for inverse kinematics, while the second one operates at the acceleration level. We evaluate their performance in a simulated environment, replicating real-world challenges such as the wind effect, sensors noise, uncertainty of the system inertial parameters, and impulsive forces at the end-effector. Trajectory tracking simulated experiments are carried out for a two- and three-degree-of-freedom (DOF) aerial manipulator tracking a circular trajectory with its end-effector. Both algorithms demonstrate promising results in coping with external disturbances and variations in the inertial parameters, enhancing the precision of the trajectory tracking control. The acceleration-level algorithm shows overall better performance compared to the velocity-level one in the face of greater implementation complexity and computational burden.

Model-Free Intelligent Control for Space Soft Robotic Manipulators

Given the advantages of softness, lightness, low cost, and interaction safety, inverse kinematic modeling and control of soft actuators has caused a research boom. However, in realizing dexterous manipulation of space large soft manipulators, it is much more difficult to achieve precise control not only because of the greater accumulation of errors in the multiple degrees of freedom and nonlinear properties of soft materials at large scales but also because of the inability of directly solving the inverse kinematics in the cases of singular pure elongation. In this work, a model-free intelligent kinematic control strategy is proposed for these problems that exhibit a mapping relationship between the output end-effector position and the input pressure. For multiple-degree-of-freedom robots, especially pneumatic soft manipulators, traditional inverse kinematic modeling methods are complex and inverse Jacobian matrix solution often encounters geometric singularities. To address this issue, this paper proposes an inverse kinematics–multilayer perceptron (IK-MLP) method for soft manipulators. In this strategy, the trained intelligent controller can be applied to control pneumatic manipulators without establishing a traditional inverse kinematic model. The control algorithm is experimentally tested based on the ground experiment system of the space soft manipulator. Simulations and experiments are carried out to validate the given model-free intelligent controller, proving that the IK-MLP method can effectively solve the singularity of inverse kinematics.

Parametric configuration and programming of flexible robotic cells producing biotechnology experiments

In the last decades there has been an ever-increasing trend of accelerated scientific research in the biotechnology sector and the COVID-19 pandemic has further emphasized the need for high-throughput yet flexible processes. Even though automation has gained significant popularity to deal with this problem, the focus has been placed at laboratory level and for specific type of processes only. The aim of these automation applications is to offset the increasing costs of clinical trials, automate tedious laboratory work, run experiments in parallel and make scientific testing efficient and programmable. This paper investigates the application of robotic systems at a larger scale that will allow the automated execution of even custom defined biotechnology experiments so that these can be offered as a service to any interested stakeholder. A digital model of the proposed robotic biotechnology workcell is developed and the necessary methodology is investigated to showcase the feasibility of this approach. The goal is to use the digital model for evaluating different design considerations, such as equipment layout and robot types, as well as for planning and simulating the robot operation under various offline programming strategies. To achieve this goal, the Damped Least Squares Method is used for inverse kinematics control and a robotic arm trajectory planner is developed parametrically using characteristic intermediate points so as to create a motion plan that can be used for any robotic manipulator and any experiment within a family of facility setups. Two experiments are simulated using a SCARA robot and an articulated arm robot, each with an alternative cell layout to show the flexibility and robustness of the proposed approach. The obtained results show that the trajectory planner can consistently generate appropriate motion plans.

An error compensation controller for milling robots

This paper presents a method of controlling a serial robot for milling by an inverse kinematic controller combined with an outer PD loop (Inverse Dynamics + PD controller), with calibration and compensation of errors in calculating the cutting forces. Because the cutting forces are generated at the time of cutting, at the contact area between the workpiece and the cutting tool, the generalized forces of the cutting forces in the differential equations of motion of robot is always variable and difficult to determine precisely. The cutting forces depend on the cutting mode, the geometric parameters of the cutting layer, the cutting conditions, etc. This study shows an inverse dynamic controller with the outer PD loop and an additional calibration block to compensate the differences between the actual cutting forces and calculated cutting forces (which are caculated by the empirical formula). The cutting forces at each machining time of the calibration block is determined based on the differential equation of motion. The efficiency (convergence time and accuracy) of the proposed controller is evaluated by comparison between the numerical simulation results of the controller with cutting force calibration and the conventional PD controller. In the conventional PD controller, the dynamic model of the robot is assumed to define precisely. The results contribute to design and manufacture the controllers for robotic milling, and to improve the quality of the machined surface.

Kinetostatic Optimization for Kinematic Redundancy Planning of Nimbl’Bot Robot

AbstractIn manufacturing industry, computer numerical control (CNC) machines are often preferred over industrial serial robots (ISR) for machining tasks. Indeed, CNC machines offer high positioning accuracy, which leads to slight dimensional deviation on the final product. However, these machines have a restricted workspace generating limitations in the machining work. Conversely, ISR are typically characterized by a larger workspace. ISR have already shown satisfactory performance in tasks like polishing, grinding, and deburring. This paper proposes a kinematic redundant robot composed of a novel two degrees-of-freedom mechanism with a closed kinematic chain. After describing a task-priority inverse kinematic control framework used for joint trajectory planning exploiting the robot kinematic redundancy, the paper analyses the kinetostatic performance of this robot depending on the considered control tasks. Moreover, two kinetostatic tasks are introduced and employed to improve the robot performance. Simulation results show how the robot better performs when the optimization tasks are active.

Null-Space Minimization of Center of Gravity Displacementof a Redundant Aerial Manipulator

Displacements of the base during trajectory tracking are a common issue in the control of aerial manipulators. These are caused by reaction torques transferred to the base due to the manipulator motion and, in particular, to the motion of its center of gravity. We present a novel approach to reduce base displacements of a kinematically redundant aerial manipulator by using null-space projection in the inverse kinematic control. A secondary objective function minimizes the horizontal displacement of the manipulator center of gravity. We test this algorithm on different trajectories for both three and four degrees of freedom (DOF) manipulators in a simulation environment. The results comparing our algorithm with inverse kinematic control without the null-space projection show up to an 80% reduction in the end-effector position error and an average of about 56% reduction in maximum base displacement. The simulation implementation also runs faster than in real-time in our code implementation. We provide a workspace analysis based on multiple stopping criteria such as excessive base displacement, joint velocities and end-effector position error for the 3 and 4 DOF manipulators. As expected, the 4 DOF manipulator has a larger workspace.

Virtual UR5 Robot for Online Learning of Inverse Kinematics and Independent Joint Control Validated with FSM Position Control

Virtual remote laboratories have already been successfully implemented in educational centers for practical learning of mechatronics and robotic systems. This article presents the development of a virtual articulated UR-type robot, designed as an educational tool that is suitable for programming and evaluating both the inverse kinematics control of the robot and the independent control of the robot joints. The 3D model of the virtual robot was developed in the Blender V2.79 software and uses the Modbus TCP industrial communication protocol for the communication to an external controller implemented in CoDeSys V3.5 software. The developed system allows the students to generate and test their own control algorithm for the robot joints with the visualization of the achieved performance in 3D and real time. Tailored control systems can be compared on the virtual robot. In this study, a novel technique for the joint position control based on an FSM is proposed and verified with the virtual UR5 robots to prove that the developed system is a suitable platform to teach and learn the inverse kinematics control and independent joint control of the UR5 robotic arm.

Zero Reaction Torque Trajectory Tracking of an Aerial Manipulator through Extended Generalized Jacobian

Aerial manipulators are used in industrial and service robotics tasks such as assembly, inspection, and maintenance. One of the main challenges in aerial manipulation is related to the motion of the UAV base caused by manipulator disturbance torques and forces, which jeopardize the precision of the robot manipulator. In this paper, we propose two novel inverse kinematic control methods used to track a trajectory with an aerial manipulator while also considering resultant UAV base motions. The first method is adapted from the generalized Jacobian formulation used in space robotics and includes the change in system momentum resulting from gravity and UAV control forces in the inverse kinematic control equation. This approach is simulated for a 2 and 3 degree-of-freedom aerial manipulator tracking trajectories with the end-effector. Although the end-effector position error is approximately zero throughout the simulated task, we see significant undesired UAV base motions of several centimeters in magnitude. To ameliorate this by exploiting the kinematic redundancy, we modify the generalized Jacobian by adding an additional task constraint which minimizes the reaction torques from the manipulator, to form the extended generalized Jacobian. While the second approach results in improved precision and reduced base motion by an order of magnitude as compared to the generalized Jacobian, a drawback is the reduction in the available workspace as the solution seeks to minimize the manipulator center of gravity translation. We also demonstrate and compare both approaches in a load picking task. All the algorithms are completed computationally faster than real time in the MATLAB simulations, illustrating their potential for application in real-world experiments.

Singularity Analysis and Complete Methods to Compute the Inverse Kinematics for a 6-DOF UR/TM-Type Robot

Improving the strategies employed to control robotic arms is of great importance because of the increase in their use in advanced supervisory control strategies, such as digital twins. The inverse kinematic (IK) control of manipulators requires an IK solution and an awareness of the singular configurations. This work presents a complete IK calculation system with singularity analysis for the UR5 robotic arm created by Universal Robots. For a specific robot pose, different angle solution sets are obtained, and one of these solution sets has to be selected to achieve movement continuity and avoid singularities. Two methods for this double purpose are proposed: one calculates all the solution possibilities, and the other obtains only one solution set by following a sequence of decisions and calculations clearly stated by a finite state machine (FSM). Both methods are effective in managing singularities. The FSM-based method complements the IK solution procedure with advantages in the number of computations and performance by producing results that would not lead the joints to move abruptly. The results prove that the presented methods select an IK solution that does not result in a singular configuration, and that most of the time, they lead to the same valid IK solution.

Digital Twin for a Multifunctional Technology of Flexible Assembly on a Mechatronics Line with Integrated Robotic Systems and Mobile Visual Sensor-Challenges towards Industry 5.0.

A digital twin for a multifunctional technology for flexible manufacturing on an assembly, disassembly, and repair mechatronics line (A/D/RML), assisted by a complex autonomous system (CAS), is presented in the paper. The hardware architecture consists of the A/D/RML and a six-workstation (WS) mechatronics line (ML) connected to a flexible cell (FC) and equipped with a six-degree of freedom (DOF) industrial robotic manipulator (IRM). The CAS has in its structure two driving wheels and one free wheel (2DW/1FW)-wheeled mobile robot (WMR) equipped with a 7-DOF robotic manipulator (RM). On the end effector of the RM, a mobile visual servoing system (eye-in-hand MVSS) is mounted. The multifunctionality is provided by the three actions, assembly, disassembly, and repair, while the flexibility is due to the assembly of different products. After disassembly or repair, CAS picks up the disassembled components and transports them to the appropriate storage depots for reuse. Disassembling or repairing starts after assembling, and the final assembled product fails the quality test. The virtual world that serves as the digital counterpart consists of tasks assignment, planning and synchronization of A/D/RML with integrated robotic systems, IRM, and CAS. Additionally, the virtual world includes hybrid modeling with synchronized hybrid Petri nets (SHPN), simulation of the SHPN models, modeling of the MVSS, and simulation of the trajectory-tracking sliding-mode control (TTSMC) of the CAS. The real world, as counterpart of the digital twin, consists of communication, synchronization, and control of A/D/RML and CAS. In addition, the real world includes control of the MVSS, the inverse kinematic control (IKC) of the RM and graphic user interface (GUI) for monitoring and real-time control of the whole system. The "Digital twin" approach has been designed to meet all the requirements and attributes of Industry 4.0 and beyond towards Industry 5.0, the target being a closer collaboration between the human operator and the production line.

FEA-Based Inverse Kinematic Control: Hyperelastic Material Characterization of Self-Healing Soft Robots

Recent advances in soft continuum robots revealed the need for accurate models, required to develop advanced control strategies. In this article, a general methodology is presented that allows to create an accurate inverse kinematic control based on hyperelastic models, fitted on mechanical material properties. This methodology is based on finite element analysis (FEA) and links the mechanical properties of the material to the simulated behavior of a Pneunet actuator. This procedure is valid for any sort of hyperelastic material used in soft robotics, however, as a case study, a specific material with a self-healing ability is considered. This elastomeric polymer can recover from macroscopic damages without losing its mechanical performances, after undergoing a heat treatment. In this article, an accurate characterization of the mechanical behavior of this material is provided, involving mechanical testing, both in tensile and compression. On this experimental characterization data constitutive laws are fitted, using a FEA simulator. The robustness of this material modeling is shown, refitting the curve for material samples that were exposed to multiple damage-healing cycles. With this obtained constitutive model, a FEA simulation of a bending soft pneumatic actuator is developed. The simulation results are experimentally validated with a dedicated test bench consisting of a pressure control unit and a motion tracking camera. Using this validated model, an inverse kinematic control is developed, including the FEA simulation in the control scheme.

Geometrically-Exact Inverse Kinematic Control of Soft Manipulators With General Threadlike Actuators’ Routing

The inverse kinematic control of soft robots appears as an open challenge that has been the subject of a number of letters presented in the last decade. Some solutions have been provided based on specific assumptions on the robot’s shape or the actuation mechanism. Other more generic approaches are characterized by a significant computational cost or by a low level of accuracy for very high deformations. In the effort to overcome some of these limitations, here we present a Geometrically-Exact (GE) inverse kinematics controller, which can be applied to soft manipulators having general threadlike actuators’ routing. Being GE, the approach is suitable to applications involving arbitrarily large bending and twisting, and, on the other side, it relies on a reduced number of Degrees of Freedom (DOFs). We prove the feasibility of the proposed Jacobian-based inverse kinematic control in simulation for soft manipulators with complex and discontinuous actuators’ routing.

Indirect Force Control of a Cable-Suspended Aerial Multi-Robot Manipulator

We present the control in physical interaction with the environment of a Cable-suspended Aerial Multi-Robot Manipulator (CS-AMRM) called the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Fly-Crane</i> , composed of three aerial vehicles towed to a platform by means of six cables. The control strategy enables the system to accurately and safely perform tasks involving expected or unexpected interactions between the platform and the environment, in the absence of dedicated force/torque sensors. A previously developed Inverse Kinematic Controller (IKC) is enhanced with an admittance framework, and contacts are estimated through a generalized momentum-based observer. To assess the validity of our approach, and to provide practical insights into the method, we perform extensive experimental tests, comprehending the admittance property shaping to modulate stiffness, damping, and virtual mass, as well as experiments in a more realistic scenario involving contacts between the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Fly-Crane</i> and the environment.

Modular modeling and coordination control scheme for an underwater cooperative transportation performed by two I-AUVs

Intervention Autonomous Underwater Vehicles (I-AUVs), also known as Underwater Vehicle Manipulator Systems (UVMSs), are an alternative for reducing costs and increasing safety in underwater operations which require dexterous manipulation. Beyond the well-posed and currently studied manipulation scenarios, the cooperative underwater transportation is a promising and challenging task, still not extensively explored. This paper aims to contribute to this latter problem by addressing the modeling and control system design of a cooperative underwater transportation performed by two planar I-AUVs, each of them composed by an AUV linked to a 2-Degrees of Freedom (DoFs) serial manipulator. A hierarchical approach for deriving the equations of motion through the Modular Modeling Methodology (MMM) is presented. Also, a complete coordination scheme composed of the Inverse Kinematics (IK) and motion control modules is proposed. A new IK control is formulated on the jerk level with the Super-Twisting Algorithm (STA) to prevent numerical drift and uncertainties while considering secondary objectives. The low-level motion control is synthesized within a continuous Sliding Mode Control (SMC) algorithm to compensate for the modeling errors and external disturbances. The coordination scheme is verified through numerical simulation considering a scenario in which an object is transported by the two I-AUVs over a predefined path. The analysis is made more realistic by considering the thrusters and motors dynamics along with sensors measurements, sampling effects and an optimal state estimator. Modeling errors and external disturbances are also considered in the analysis. The results reveal the suitability of the proposed modeling and coordination approaches for numerical simulation and control of the I-AUVs during underwater transportation.

Motion control for a differential vehicle with variable point of interest. Application: Smart cane control

This article addresses an unified solution to the trajectory tracking and path following problems for differential drive mobile robots (DDMR) considering a point of interest (PoI) with variable location relative to the vehicle. The mobile robot is modeled with an extended kinematic model avoiding typical singularities of this kind of vehicles, and allowing a straightforward definition of the corresponding inverse kinematics controller (IKC). This classical IKC fulfills the control objective with exponential error convergence but with the shortcoming of generating backward navigation when the PoI is located behind the DDMR, which is undesirable in some practical applications where the forward navigation must be preserved. This situation is theoretically analyzed, concluding that even though both forward and backward navigations correspond to equilibrium points of the closed loop, the stability of the forward navigation requires a PoI located in front of the DDMR, and the stability of the backward navigation requires a PoI located behind the DDMR. Finally, the article presents novel alternative controllers in order to always fulfill the motion objectives with stable forward navigation. Simulation results are presented to show the performance of the proposed controllers, and a real application of a robotic cane guiding its user is experimentally developed.

Velocity Following Control of a Pseudo-Driven Wheel for Reducing Internal Forces Between Wheels

The coordination of multiple driving wheels is an important issue in wheeled mobile robot design, for both maximizing tractive capability and optimizing energy consumption. This study converts a driving wheel into a pseudo-driven wheel (PDW), which is controlled to follow the motion of the robot body, in accordance with the kinematic constraints. To eliminate the internal force conflicts between wheels, a velocity following control (VFC) method is proposed to control the PDW in the presence of force disturbance caused by soil distortion during wheel-terrain interaction. The feasibility of the PDW conversion and the proposed control method are experimentally demonstrated. Compared with the inverse kinematics control (IKC) method, the rover using PDW with VFC is shown to be capable of more accurate straight and steering path following on soft terrain, reducing internal forces between wheels by more than 70% in the experiments.

Kinematic and Dynamic Control of Cooperating Underwater Vehicle-Manipulator Systems

Cooperative control of autonomous underwater robots can provide capabilities that exceed those of any single marine robot. In this paper, the cooperation between two different underwater vehicle-manipulator systems is considered. Cooperation is enabled through a control scheme which generates state-dependent reference signals to achieve synchronization of the end-effector positions of the robots. These references are tracked by the individual control systems, which consist of decoupled kinematic and dynamic controllers. Consequently, the control systems do not constrain the choice of cooperation scheme. Due to the kinematic redundancy of the robots, a task-priority inverse kinematics controller is used for velocity-level redundancy resolution, and several tasks are defined for each robot. Furthermore, the dynamics of the robots are controlled by a higher-order sliding mode controller, namely the generalized super-twisting algorithm with adaptive gains. The dynamic control approach provides robustness to model uncertainties and unknown disturbances. The effectiveness of the methods is verified in a simulation study on a heterogeneous pair of UVMSs.

Analysis and control of a Stewart platform as base motion compensators - Part I: Kinematics using moving frames

Kinematics and its control application are presented for a Stewart platform whose base plate is installed on a floor in a moving ship or a vehicle. With a manipulator or a sensitive equipment mounted on the top plate, a Stewart platform is utilized to mitigate the undesirable motion of its base plate by controlling actuated translational joints on six legs. To reveal closed loops, a directed graph is utilized to express the joint connections. Then, kinematics begins by attaching an orthonormal coordinate system to each body at its center of mass and to each joint to define moving coordinate frames. Using the moving frames, each body in the configuration space is represented by an inertial position vector of its center of mass in the three-dimensional vector space ℝ3, and a rotation matrix of the body-attached coordinate axes. The set of differentiable rotation matrices forms a Lie group: the special orthogonal group, SO(3). The connections of body-attached moving frames are mathematically expressed by using frame connection matrices, which belong to another Lie group: the special Euclidean group, SE(3). The employment of SO(3) and SE(3) facilitates effective matrix computations of velocities of body-attached coordinate frames. Loop closure constrains are expressed in matrix form and solved analytically for inverse kinematics. Finally, experimental results of an inverse kinematics control are presented for a scale model of a base-moving Stewart platform. Dynamics and a control application of inverse dynamics are presented in the part II-paper.