Robot Dynamics Research Articles

Design and sequential jumping experimental validation of a musculoskeletal bipedal robot based on the spring-loaded inverted pendulum model.

To effectively control a robot's motion, it is common to employ a simplified model that approximates the robot's dynamics. Nevertheless, discrepancies between the actual mechanical properties of the robot and the simplified model can result in motion failures. To address this issue, this study introduces a pneumatic-driven bipedal musculoskeletal robot designed to closely match the mechanical characteristics of a simplified spring-loaded inverted pendulum (SLIP) model. The SLIP model is widely utilized in robotics due to its passive stability and dynamic properties resembling human walking patterns. A musculoskeletal bipedal robot was designed and manufactured to concentrate its center of mass within a compact body around the hip joint, featuring low leg inertia in accordance with SLIP model principles. Furthermore, we validated that the robot exhibits similar dynamic characteristics to the SLIP model through a sequential jumping experiment and by comparing its performance to SLIP model simulation.

Color-Based Object Tracking Using Forward and Inverse Kinematics

Nowadays, the current surge in diverse applications of robotic arms makes comprehending these concepts of paramount importance. Various studies have been conducted on the topic of robotic arms. However, little attention was paid to the coupling relationship between object tracking and kinematics. Therefore, this research paper delves into the intricacies of robotic arm dynamics, with a specific focus on the topics of Forward and Inverse Kinematics, alongside object tracking facilitated by color-based methodologies to deepen foundational insights into robotic arm functionality. Controlling the motion and movement of robotic arms is the initial step. Leveraging the capabilities of cutting-edge technologies such as OpenCV, Armpi, and Hiwonder, it becomes feasible to precisely rotate the servos to user-input degrees and accurately position the arm based on three-dimensional Cartesian coordinates. Additionally, cameras equipped in the system enable photographing and recognizing target objects. By analyzing various positions of the target object, the robotic arm can dynamically adjust multiple servos to maintain the object's relative position. This tracking mechanism relies on the Proportional-Integral-Derivative algorithm, incorporating a minimum valid area parameter to mitigate interferences. Harnessing these algorithms empowers the robotic arm to discern objects based on camera-detected colors, and is affected slightly by different angles or distances, meaning the system's error margin consistently resides within a favorable interval. The approach exhibits practical utility in daily life scenarios, such as drug classification and recognition.

Numerical Analysis of a Drop-Shaped Aquatic Robot

Finite-dimensional equations constructed earlier to describe the motion of an aquatic drop-shaped robot due to given rotor oscillations are studied. To study the equations of motion, we use the Poincaré map method, estimates of the Lyapunov exponents, and the parameter continuation method to explore the evolution of asymptotically stable solutions. It is shown that, in addition to the so-called main periodic solution of the equations of motion for which the robot moves in a circle in a natural way, an additional asymptotically stable periodic solution can arise under the influence of highly asymmetric impulsive control. This solution corresponds to the robot’s sideways motion near the circle. It is shown that this additional periodic solution can lose stability according to the Neimark–Sacker scenario, and an attracting torus appears in its vicinity. Thus, a quasiperiodic mode of motion can exist in the phase space of the system. It is shown that quasiperiodic solutions of the equations of motion also correspond to the quasiperiodic motion of the robot in a bounded region along a trajectory of a rather complex shape. Also, strange attractors were found that correspond to the drifting motion of the robot. These modes of motion were found for the first time in the dynamics of the drop-shaped robot.

MPMC-frame: Multiplatform migration control framework for manipulator control

Existing robot control models suffer from poor generalization performance due to varied tasks between manipulators, configuration differences, and physical limits of motion. To address this problem, a multiplatform migration control framework (MPMC-frame) based on a constrained dynamics model is proposed in this paper. First, a model of the robotic manipulator dynamics with configuration adjustment (CA) is constructed based on a neural network to unify the physical joint data of different manipulators. Second, the model-based controller that can be integrated into the framework is designed, and the constraint on the upper bound on the error of uncertain parameters in the control law to guarantee the control robustness and accuracy of the controller for different manipulator platforms. Final, the generic potential function is designed based on multiplatform task requirements, and a task parameter table is constructed to improve the joint motion control performance of MPMC-frame. The feasibility of the method proposed in this paper are verified through simulations and experiments based on the ABB_irb120 and AUBO_i5 robotic manipulators.

Research on Some Control Algorithms to Compensate for the Negative Effects of Model Uncertainty Parameters, External Interference, and Wheeled Slip for Mobile Robot

In this article, the research team systematically developed a method to model the kinematics and dynamics of a 3-wheeled robot subjected to external disturbances and sideways wheel sliding. These models will be used to design control laws that compensate for wheel slippage, model uncertainties, and external disturbances. These control algorithms were developed based on dynamic surface control (DSC). An adaptive trajectory tracking DSC algorithm using a fuzzy logic system (AFDSC) and a radial neural network (RBFNN) with a fuzzy logic system were used to overcome the disadvantages of DSC and expand the application domain for non-holonomic wheeled mobile robots with lateral slip (WMR). However, this adaptive fuzzy neural network dynamic surface control (AFNNDSC) adaptive controller ensures the closed system is stable, follows the preset trajectory in the presence of wheel slippage model uncertainty, and is affected by significant amplitude disturbances. The stability and convergence of the closed-loop system are guaranteed based on the Lyapunov analysis. The AFNNDSC adaptive controller is evaluated by simulation on the Matlab/simulink software R2022b and in a steady state. The maximum position error on the right wheel and left wheel is 0.000572 (m) and 0.000523 (m), and the angular velocity tracking error in the right and left wheels of the control method is 0.000394 (rad/s). The experimental results show the theoretical analysis’ correctness, the proposed controller’s effectiveness, and the possibility of practical applications. Orbits are set as two periodic functions of period T as follows.

Robot skill learning system of multi-space fusion based on dynamic movement primitives and adaptive neural network control

This article develops a robot skill learning system with multi-space fusion, simultaneously considering motion/stiffness generation and trajectory tracking. To begin with, surface electromyography (sEMG) signals from the human arm is captured based on the MYO armband to estimate endpoint stiffness. Gaussian Process Regression (GPR) is combined with dynamic movement primitive (DMP) to extract more skills features from multi-demonstrations. Then, the traditional DMP formulation is improved based on the Riemannian metric to encode the robot’s quaternions with non-Euclidean properties. Furthermore, an adaptive neural network (NN)-based finite-time admittance controller is designed to track the trajectory generated by the motion model and to reflect the learned stiffness characteristics. In this controller, a radial basis function neural network (RBFNN) is employed to compensate for the uncertainty of the robot dynamics. Finally, experimental validation is conducted using the ROKAE collaborative robot, confirming the effectiveness of the proposed approach. In summary, the presented framework is suitable for human-robot skill transfer method that require simultaneous consideration of position and stiffness in Euclidean space, as well as orientation on Riemannian manifolds.

Neural dynamics of robust legged robots.

Legged robot control has improved in recent years with the rise of deep reinforcement learning, however, much of the underlying neural mechanisms remain difficult to interpret. Our aim is to leverage bio-inspired methods from computational neuroscience to better understand the neural activity of robust robot locomotion controllers. Similar to past work, we observe that terrain-based curriculum learning improves agent stability. We study the biomechanical responses and neural activity within our neural network controller by simultaneously pairing physical disturbances with targeted neural ablations. We identify an agile hip reflex that enables the robot to regain its balance and recover from lateral perturbations. Model gradients are employed to quantify the relative degree that various sensory feedback channels drive this reflexive behavior. We also find recurrent dynamics are implicated in robust behavior, and utilize sampling-based ablation methods to identify these key neurons. Our framework combines model-based and sampling-based methods for drawing causal relationships between neural network activity and robust embodied robot behavior.

Exact linearization and control of a mobile robot for the inspection of soil resources in Solanum tuberosum crops.

In recent years, the development of robots for agro-industrial applications, such as the cultivation of Solanum tuberosum potatoes, has aroused the interest of the academic and scientific communities. This is due, at least in part, to the complexity of modeling and robustly controlling some dynamics inherent to nonlinear behaviors normally attributed to the different technologies associated with the movement of these autonomous vehicles and their non-holonomic constraints. The different nonlinear dynamics of mobile robots are usually represented by state-space models. However, given some equilibrium and stability characteristics, the implementation of effective controllers for the robust parametric tracking and variation problem requires techniques that allow the operability of robots around regions of stable equilibrium. Feedback linearization control is one such technique that attempts to mathematically eliminate nonlinear expressions from the plant model. However, this technique requires an observable and controllable mathematical model. If there is some relationship between the model inputs and a controlled output that allows the relative degree of the control law to be determined, the controller design and implementation are posed as a linear issue. Flat filters developed from the generalized proportional integral control approach are an alternative that could facilitate the design of controllers for these linearized systems. From these flat filters, it is possible to obtain the transfer function of a controller without relying on the derivatives of the system output. This work proposes the design of a controller via exact linearization and its equivalent flat filter for a robot inspector of the soil resource of S. tuberosum crops in the department of Cundinamarca, Colombia. The actuator motion constraints resulted in a robot with two degrees of mobility and one non-holonomic constraint. Numerical validation of this system suggests that it can be an effective solution to the problem of tracking control at changing references by providing a system capable of navigating through crop rows. The results suggest correct tracking for linear and circular trajectories. However, the control lacks the ability to track spiral-type trajectories.

Model-free scheme using time delay estimation with fixed-time FSMC for the nonlinear robot dynamics

<abstract><p>This paper presents a scheme of time-delay estimation (TDE) for unknown nonlinear robotic systems with uncertainty and external disturbances that utilizes fractional-order fixed-time sliding mode control (TDEFxFSMC). First, a detailed explanation and design concept of fractional-order fixed-time sliding mode control (FxFSMC) are provided. High performance tracking positions, non-chatter control inputs, and nonsingular fixed-time control are all realized with the FxSMC method. The proposed approach performs better and obtains superior performance when FxSMC is paired with fractional-order control. Furthermore, a TDE scheme is included in the suggested strategy to estimate the unknown nonlinear dynamics. Afterward, the suggested system's capacity to reach stability in fixed time is determined by using Lyapunov analyses. By showing the outcomes of the proposed technique applied to nonlinear robot dynamics, the efficacy of the recommended method is assessed, illustrated, and compared with the existing control scheme.</p></abstract>

Adaptive Approximation Tracking Control of a Continuum Robot With Uncertainty Disturbances.

Continuum robot has certain compliance and intrinsic safety, which makes it an excellent substitute for the traditional rigid robot in the various tasks, such as human-robot interaction or medical surgery. However, due to the complex nonlinearities which are induced by the compliance, parameter uncertainties, and unknown disturbances, good performance control scheme for the continuum robot is always a challenging task for the practical applications. Thus, to overcome this challenge of the uncertain dynamics and unknown external disturbances, this article develops a novel adaptive control scheme for a continuum robot using the function approximation technique (FAT). Specifically, for the proposed continuum robot, an adaptive FAT control (AFATC) strategy with no update laws is proposed to handle the uncertain parameters of the robot dynamics and external disturbances. The control law is expressed as a finite linear combination of the orthogonal basis functions by the FAT. The proposed AFATC scheme uses a fixed control structure, and the weight matrices are not updated in time. Then, the stability of the proposed controller is proved based on the Lyapunov function. Afterwards, the simulation results indicate the proposed AFATC scheme has good control performance compared with the regressor-free adaptive control (RFAC) method. Finally, the effectiveness of the proposed AFATC scheme is demonstrated in a group of real-time experiments.

Port-Hamiltonian Neural ODE Networks on Lie Groups for Robot Dynamics Learning and Control

Port-Hamiltonian Neural ODE Networks on Lie Groups for Robot Dynamics Learning and Control

Online and Robust Intermittent Motion Planning in Dynamic and Changing Environments.

In this article, we propose RRT-Q X∞ , an online and intermittent kinodynamic motion planning framework for dynamic environments with unknown robot dynamics and unknown disturbances. We leverage RRT X for global path planning and rapid replanning to produce waypoints as a sequence of boundary-value problems (BVPs). For each BVP, we formulate a finite-horizon, continuous-time zero-sum game, where the control input is the minimizer, and the worst case disturbance is the maximizer. We propose a robust intermittent Q-learning controller for waypoint navigation with completely unknown system dynamics, external disturbances, and intermittent control updates. We execute a relaxed persistence of excitation technique to guarantee that the Q-learning controller converges to the optimal controller. We provide rigorous Lyapunov-based proofs to guarantee the closed-loop stability of the equilibrium point. The effectiveness of the proposed RRT-Q X∞ is illustrated with Monte Carlo numerical experiments in numerous dynamic and changing environments.

Sliding-mode control of a soft robot based on data-driven sparse identification

Soft robots are increasingly finding their way into many applications, especially those involving manipulation of sensitive and delicate objects or interaction with humans. However, their high-compliance characteristics pose considerable challenges in obtaining low-complexity yet accurate dynamical models that are suitable for advanced feedback control. This paper proposes a framework for end-effector positioning of a soft robot. First, physics-informed sparse regression is used for deriving a nonlinear mathematical model of the robot dynamics. Then, a control scheme comprising a super-twisting sliding mode controller and a nonlinear input estimator is designed for the positioning of the robot end-effector. Conditions for uniform asymptotic stability of the closed-loop system are given. Finally, experimental tests carried on a real soft robot show the efficacy of the proposed design and its tracking accuracy.

Adaptive passive admittance control of a compliant collaborative robot

Compliance of the collaborative robots plays an important role in human-robot interaction. Due to the complex nonlinearities caused by the compliance, and parameter uncertainties, good performance control method for the compliant collaborative robot is always a challenging task. Therefore, to overcome the challenge of the compliance, and uncertain dynamics, this paper develops an adaptive passive admittance control (APAC) approach for a novel compliant collaborative robot, whose compliant mechanism is constituted of the inerters, springs, and dampers. First, through force-current analogy between mechanical network and electrical network, the compliance of the proposed collaborative robot with the inerters, springs, and dampers, is represented by a novel and simplified admittance matrix to facilitate dynamics model of the proposed collaborative robot. Then, for the proposed compliant collaborative robot, an APAC strategy is presented to dispose of the uncertain parameters of the dynamics. The inertial matrix, Coriolis matrix, admittance matrix, and gravity vector of the compliant collaborative robot are expressed as linear representation of orthogonal basis functions by using function approximation technique (FAT). The boundedness of the robot dynamics is proved by detailed stability analysis which uses Lyapunov function. Finally, simulation results indicate that the proposed APAC of the compliant collaborative robot is effective.

Dual quaternion operations for rigid body motion and their application to the hand–eye calibration

The dual quaternion plays an advantageous role in the field of robotic kinematics and dynamics due to its compact expression. It is well known that quaternion can be easily implemented as algebraic operations on vectors through matrix operators. Similarly, the dual matrix operators can convert dual quaternion operations to matrix operations. However, it has not received adequate attention, and thus there are very few applications at present. With the dual matrix operators of dual quaternion, this paper re-verifies the equivalency between the conjugate formula of unit dual quaternion and dual Euler–Rodrigues formula. To combine this equivalence with the homomorphic mapping of Lie groups, a theoretical correlation of the current hand-eye calibration methods is established. Motivated by the attempt to establish a more complete scheme for hand-eye calibration, a new simultaneous method based on the conjugate formula of dual quaternion is proposed. The method verifies that the rotation problem can be extended to the rigid-body transformation problem via the dual algebra. Finally, the simulation and experimental validations for the hand–eye calibration method are given.

Individual axis control for industrial robots by posture-variant dynamic compensation and feedback control using the FDTD method

Industrial robots experience posture-dependent inertial variation and interference forces between joints, which in turn generates undesired vibrations due to the inherent elasticity of the reduction gears, making it difficult to control each axis independently. Conventionally, dynamic compensation is used to compensate the robot dynamics and decouple each axis, while state feedback control based on a two-inertia model is used for dealing with the vibrations caused by the elasticity of the reduction gears. However, the control design for this approach usually assumes a fixed moment of inertia, so its performance is compromised when large and fast changes in the robot posture occurs. In this paper, a posture-variant approach that takes into account the posture-dependent inertial variation in real time is proposed to achieve exact dynamic compensation and independent control of each axis regardless of the robot posture. The state equations of the posture-variant two-inertia system model for each robot axis are discretized using the finite-difference time-domain (FDTD) method and adapted on both the dynamic compensation and feedback control parts, allowing to easily redesign the whole control system considering the inertial variation at each control cycle. The effectiveness of the method is confirmed by experimental verification on a 6-axis industrial robot.

Development and research of the model of a wheel-legged robot

BACKGROUND: The development of robots capable of moving in both walking and wheeled modes and distinguishing with a simple design from the already developed robots is a relevant task for some recent years. In order for such a robot to have scientific and commercial success, it is necessary for it to be as structurally complex, smooth, reliable and inexpensive as its wheeled equivalent and, in addition, to be able to move stably and quickly over terrain that is impassable for wheeled robots. The robot dynamics is modeled with the Universal Mechanism and the MATLAB/Simulink software packages. The results of virtual tests of the robot in main motion modes (straight-line motion, turning, step climbing) are given in the paper.
 AIM: Increasing the mobility of a wheel-legged robot, equipped with the pseudo-walking propulsion system, using reasonable control laws.
 METHODS: In order to evaluate ride performance of the studied robot, methods of numerical simulation of its motion based on the multibody dynamics software packages are used.
 RESULTS: The maximal velocity of stable straight-line motion, the turning velocity and the height of the largest climbed step were obtained for the robot with given power of engines.
 CONCLUSION: The model of the new mobile robot equipped with the simple-designed propulsion system has been developed. This model demonstrated high cross-country abilities and other mobility indicators according to the results of virtual tests.

Mathematical Models of Dynamics of Emotional Robots’ Interest in Media Projects

Mathematical Models of Dynamics of Emotional Robots’ Interest in Media Projects

A Circular Formation Method for Biomimetic Robotic Fish Inspired by Fish Milling.

Circular motion phenomena, akin to fish milling, are prevalent within the animal kingdom. This paper delineates two fundamental mechanisms underlying such occurrences: forward following and circular topological communication. Leveraging these pivotal concepts, we present a multi-agent formation circular model based on a second-order integrator. This model engenders the attainment of homogeneous intelligence convergence along the circumferential trajectory. The convergence characteristics are intricately linked to the number of agents and the model parameters. Consequently, we propose positive and negative solutions for ascertaining the convergent circle property and model parameters. Furthermore, by integrating our proposed formation control methodology with a robotic fish dynamics model, we have successfully implemented simulations and experiments, demonstrating the circular formation of multiple biomimetic robotic fish. This study provides a mathematical explication for the circular motion observed in animal groups and introduces a novel approach to achieving circular formation in multiple robots inspired by biological phenomena.

A system decomposition method for region tracking control of a non‐holonomic mobile robot with dynamic parameter uncertainties

AbstractThe tracking control problem of non‐holonomic mobile robot systems has been extensively investigated in the past decades, however, most of the existing control strategies were developed specifically for the fixed‐point tracking. This technical note focuses on the region tracking control for a non‐holonomic mobile robot system with parameter uncertainties in the robot dynamics. With the system decomposition and adaptive control method, some restrictions imposed on the angular and linear velocities of the non‐holonomic mobile robot in recent literature are removed, enabling to track dynamic trajectories with any values of the angular and line velocities. The proposed adaptive control scheme can simultaneously solve both the regulation and region tracking problems of a non‐holonomic mobile robot with one passive wheel and two actuated wheels. By utilizing the designed control laws, the mobile robot system is able to globally reach inside a moving region specified by potential functions whose path can be a circular curve, a straight line, or sinusoidal curve, by using a single adaptive controller. Since the dynamic region can be specified arbitrarily small, the fixed‐point tracking can be regarded as a special case of region tracking studied in this paper. Compared with the traditional fixed‐point tracking, region tracking has more flexibility and better robustness. Numerical results are presented to show the effectiveness of the designed strategy.