Minimum Jerk Trajectory Research Articles

Robot Manipulator Minimum Jerk Trajectory Planning Based on the Improved Dung Beetle Optimizer Algorithm

Trajectory planning of robotic manipulators in complex environments involves generating smooth and collision-free paths, and key aspects to consider include dynamic environment perception, path planning, trajectory smoothing and optimization, and obstacle avoidance. This paper discusses different algorithms and finally proposes a fusion of the improved Dung Beetle Optimizer (IDBO) algorithm using chaotic mapping, sinusoidal random mutation, and nonlinear convergence strategies with the bidirectional Rapidly exploring Random Tree (RRT) algorithm to achieve manipulator trajectory planning and minimum jerk optimization trajectory. In the experiment, the IDBO algorithm was compared with other heuristic algorithms. The path obtained was shortened by 9.18% on average, and the calculation time was shortened by 33.81% on average. Then, the paper explored Cartesian coordinate space trajectory planning and joint space trajectory planning when the robot was working in 3D space, and verified the superiority of the latter. In controlling the movement of the robot, by combining the minimum angle jerk planning and the bidirectional RRT obstacle avoidance algorithm to drive the joint angle parameters obtained by the spatial trajectory planning, the trajectory of the robot manipulator can be smoother, more efficient, and avoid obstacles in complex 3D space. This research helps improve the performance, safety, and technical support of robots, and is of great research significance.

Long-distance optical-conveyor-belt transport of ultracold Cs133 and Rb87 atoms

We report on the transport of a thermal cloud of ultracold cesium and rubidium atoms over about 37 cm in under 25 ms using an optical conveyor belt formed by two counterpropagating beams with a controllable frequency difference that generate a movable optical lattice. By carefully selecting the waists and focus positions, we are able to use two static Gaussian beams for the transport, avoiding the need for a Bessel beam or variable-focus lenses. We characterize the transport efficiency for both species, including a comparison of different transport trajectories, gaining insight into the loss mechanisms and finding the minimum jerk trajectory to be optimum. Using the optimized parameters, we are able to transport up to 7×106 cesium or rubidium atoms with an efficiency up to 75%. To demonstrate the viability of our transport scheme for experiments employing quantum gas microscopy, we produce Bose-Einstein condensates of either species after transport and present measurements of the simultaneous transport of both species. Published by the American Physical Society 2024

Using principles of motor control to analyze performance of human machine interfaces

There have been significant advances in biosignal extraction techniques to drive external biomechatronic devices or to use as inputs to sophisticated human machine interfaces. The control signals are typically derived from biological signals such as myoelectric measurements made either from the surface of the skin or subcutaneously. Other biosignal sensing modalities are emerging. With improvements in sensing modalities and control algorithms, it is becoming possible to robustly control the target position of an end-effector. It remains largely unknown to what extent these improvements can lead to naturalistic human-like movement. In this paper, we sought to answer this question. We utilized a sensing paradigm called sonomyography based on continuous ultrasound imaging of forearm muscles. Unlike myoelectric control strategies which measure electrical activation and use the extracted signals to determine the velocity of an end-effector; sonomyography measures muscle deformation directly with ultrasound and uses the extracted signals to proportionally control the position of an end-effector. Previously, we showed that users were able to accurately and precisely perform a virtual target acquisition task using sonomyography. In this work, we investigate the time course of the control trajectories derived from sonomyography. We show that the time course of the sonomyography-derived trajectories that users take to reach virtual targets reflect the trajectories shown to be typical for kinematic characteristics observed in biological limbs. Specifically, during a target acquisition task, the velocity profiles followed a minimum jerk trajectory shown for point-to-point arm reaching movements, with similar time to target. In addition, the trajectories based on ultrasound imaging result in a systematic delay and scaling of peak movement velocity as the movement distance increased. We believe this is the first evaluation of similarities in control policies in coordinated movements in jointed limbs, and those based on position control signals extracted at the individual muscle level. These results have strong implications for the future development of control paradigms for assistive technologies.

Impedance characteristic of the human arm during passive movements

This paper describes the impedance characteristics of the human arm during passive movement. The arm was moved in the desired trajectory. The motion was actuated by a 1-degree-of-freedom robot system. Trajectories used in the experiment were minimum jerk (the rate of change of acceleration) trajectories, which were found during a human and human cooperative task and optimum for muscle movement. As the muscle is mechanically analogous to a spring-damper system, a second-order equation was considered as the model for arm dynamics. In the model, inertia, stiffness, and damping factor were considered. The impedance parameters were estimated from the position and torque data obtained from the experiment and based on the “Estimation of Parametric Model”. It was found that the inertia is almost constant over the operational time. The damping factor and stiffness were high at the starting position and became near zero after 0.4 seconds.

Human-robot force cooperation analysis by deep reinforcement learning

PurposeThis study aims to realize natural and effort-saving motion behavior and improve effectiveness for different operators in human–robot force cooperation.Design/methodology/approachThe parameter of admittance model is identified by deep deterministic policy gradient (DDPG) to realize human–robot force cooperation for different operators in this paper. The movement coupling problem of hybrid robot is solved by realizing position and pose drags. In DDPG, minimum jerk trajectory is selected as the reward objective function, and the variable prioritized experience replay is applied to balance the exploration and exploitation.FindingsA series of simulations are implemented to validate the superiority and stability of DDPG. Furthermore, three sets of experiments involving mass parameter, damping parameter and DDPG are implemented, the effect of DDPG in real environment is validated and could meet the cooperation demand for different operators.Originality/valueDDPG is applied in admittance model identification to realize human–robot force cooperation for different operators. And minimum jerk trajectory is introduced into reward objective to meet requirement of human arm free movements. The algorithm proposed in this paper could be further extended in the other operation task.

Trajectory Planning and Optimization for Minimizing Uncertainty in Persistent Monitoring Applications

This paper considers persistent monitoring of environmental phenomena using unmanned aerial vehicles (UAVs). The objective is to generate periodic dynamically feasible UAV trajectories that minimize the estimation uncertainty at a set of points of interest in the environment. We develop an optimization algorithm that iterates between determining the observation periods for a set of ordered points of interest and optimizing a continuous UAV trajectory to meet the required observation periods and UAV dynamics constraints. The interest-point visitation order is determined using a Traveling Salesman Problem (TSP), followed by a greedy optimization algorithm to determine the number of observations that minimizes the maximum steady-state eigenvalue of a Kalman filter estimator. Given the interest-point observation periods and visitation order, a minimum-jerk trajectory is generated from a bi-level optimization, formulated as a convex quadratically constrained quadratic program. The resulting B-spline trajectory is guaranteed to be feasible, meeting the observation duration, maximum velocity and acceleration, region enter and exit constraints. The feasible trajectories outperform existing methods by achieving comparable observability at up to 47% higher travel speeds, resulting in lower maximum estimation uncertainty.

Study of Kinesthetic Negotiation Ability in Lightweight Comanipulative Decision-making Tasks: Design and Study of a Virtual Partner based on Human-human Interaction Observation

This article presents the results of an experiment on physical Human-Human Interaction (pHHI), where human dyads cooperate on a one-dimensional comanipulative task in a novel lightweight teleoperation setup. The results of this experiment show that humans are able to handle asymmetrical information about the task and solve conflicts using only the kinesthetic channel. Data from the pHHI experiment is used to design a virtual partner that can perform the task alongside a human. The virtual partner behavior is based on the observation that initiative is highly correlated to decision-making in our pHHI negotiation scenario. The virtual agent is then evaluated in a physical Human-Robot Interaction (pHRI) experiment. The results of the second experiment show that the virtual partner is able to perform the task without compromising the performances of the dyad and that a similar role distribution is observed in human-human and human-robot dyads. Moreover, the knowledge of the partner’s nature does not seem to influence the performances. The results obtained with the virtual partner are encouraging and could be used to design kinesthetic negotiation algorithms in pHRI settings. The main contributions of this article are: (1) supporting evidence of the possibility for humans to use the kinesthetic channel as mean of negotiation during physical Human-Human Interaction in the lightest known impedance negotiation tasks (with no virtual mass involved), (2) highlighting of the correlation between initiative and dyadic decision making, (3) design of a simple yet efficient virtual partner algorithm capable of realistic physical Human-Robot Interaction in the one-dimension tracking task used in the experimental setup. This design combines minimum jerk trajectory, switching role ability, decision criteria, and statistical parameters that are detailed in this article.

Perception-Aware Receding Horizon Trajectory Planning for Multicopters With Visual-Inertial Odometry

Visual inertial odometry (VIO) is widely used for the state estimation of multicopters, but it may function poorly in environments with few visual features or in overly aggressive flights. In this work, we propose a perception-aware collision avoidance trajectory planner for multicopters, that may be used with any feature-based VIO algorithm. Our approach is able to fly the vehicle to a goal position at high speed, avoiding obstacles in an unknown stationary environment while achieving good VIO state estimation accuracy. The proposed planner samples a group of minimum jerk trajectories and finds collision-free trajectories among them, which are then evaluated based on their speed to the goal and perception quality. Both the motion blur of features and their locations are considered for the perception quality. Our novel consideration of the motion blur of features enables automatic adaptation of the trajectory’s aggressiveness under environments with different light levels. The best trajectory from the evaluation is tracked by the vehicle and is updated in a receding horizon manner when new images are received from the camera. Only generic assumptions about the VIO are made, so that the planner may be used with various existing systems. The proposed method can run in real time on a small embedded computer on board. We validated the effectiveness of our proposed approach through experiments in both indoor and outdoor environments. Compared to a perception-agnostic planner, the proposed planner kept more features in the camera’s view and made the flight less aggressive, making the VIO more accurate. It also reduced VIO failures, which occurred for the perception-agnostic planner but not for the proposed planner. The ability of the proposed planner to fly through dense obstacles was also validated. The experiment video can be found at https://youtu.be/qO3LZIrpwtQ.

A recurrent neural network for variable admittance control in human–robot cooperation: simultaneously and online adjustment of the virtual damping and Inertia parameters

In this manuscript, a recurrent neural network is proposed for variable admittance control in human–robot cooperation tasks. The virtual damping and the virtual inertia of the designed robot’s admittance controller are adjusted online and simultaneously. A Jordan recurrent neural network is designed and trained for this purpose. The network is indirectly trained using the real-time recurrent learning algorithm and based on the velocity error between the reference velocity of the minimum jerk trajectory model and the actual velocity of the robot. The performance of the proposed variable admittance controller is presented in terms of the human required effort, the task completion time, the achieved accuracy at the target, and the oscillations during the movement. Its generalization ability is evaluated experimentally by conducting cooperative tasks along numerous straight-line segments using the KUKA LWR robot and by ten subjects. Finally, a comparison with previous developed variable admittance controllers, where only the variable damping or only the virtual inertia is adjusted, is presented.

Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation

This article aims to present a minimum-jerk trajectory planning approach to address the smooth trajectory generation problem of 3-prismatic-universal-universal translational parallel kinematic manipulator. First, comprehensive kinematics and dynamics characteristics of this 3-prismatic-universal-universal parallel kinematic manipulator are analyzed by virtue of the accepted link Jacobian matrices and proverbial virtual work principle. To satisfy indispensable continuity and smoothness requirements, the discretized piecewise quintic polynomials are employed to interpolate the sequence of joints’ angular position knots which are transformed from these predefined via-points in Cartesian space. Furthermore, the trajectory planning problem is directly converted into a constrained nonlinear multi-variables optimization problem of which objective function is to minimize the maximum of the joints’ angular jerk throughout the whole trajectory. Finally, two typical application simulations using the reliable sequential quadratic programming algorithm demonstrate that this proposed minimum-jerk trajectory planning approach is of explicit feasibility and appreciable effectiveness.

A nonlinear control model of musculoskeletal systems with minimum jerk trajectories

A nonlinear control model of musculoskeletal systems with minimum jerk trajectories

A nonlinear control model of musculoskeletal systems with minimum jerk trajectories

A nonlinear control model of musculoskeletal systems with minimum jerk trajectories

Analysis of Velocity Pattern of a Power-Assisted Mobile Robot

This paper aims to analyze the velocity pattern of a power-assisted mobile robot when the operator performs operation without any discomfort. Power-assist systems for mobile robots such as wheelchairs and conveyance carriers are extremely effective in alleviating the physical burden on operators when they carry heavy objects. Although the velocity control based power-assist system has an advantage that it can be easily realized, the problem lies in that the system becomes unstable when the operator has high stiffness. Variable impedance control based on impedance estimation of the operator is effective at solving this problem. To realize operator impedance estimation, it is necessary to know the intended robot’s motion of a person. In this study, as a preliminary step to estimate the operator’s impedance, the velocity pattern when the operator performs natural operation of the robot through the power-assist system is analyzed. The results confirm that the natural velocity pattern can be approximated by a velocity pattern connecting two minimum jerk trajectories.

Robust PID control of quadrotors with power reduction analysis

This paper presents a novel robust controller applied to a quadrotor vehicle for regulation and trajectory tracking tasks. In the proposed scheme, the quadrotor position is controlled by a proportional integral derivative (PID) controller, while the orientation control is achieved through a model-based controller. The proposed controller is combined with a power reduction methodology, which includes a controller-gains tuning stage using the cuckoo search algorithm, and a minimum jerk trajectory design stage. The performance of the new controller is assessed in a free-disturbance case and under the effect of parametric uncertainty and aero-dynamical disturbances. The new controller is compared against two linear PID controllers and a nonlinear sliding mode-based controller. Numerical simulations demonstrate the superiority of the proposed scheme as well as its robustness against different types of perturbations. Also, it is proven that the power demanded by any controller is reduced when using the power reduction methodology.

Kinematic Redundancy Analysis during Goal-Directed Motion for Trajectory Planning of an Upper-Limb Exoskeleton Robot.

The kinematic redundancy of human arm imposes challenges on joint space trajectory planning for upper-limb rehabilitation robot. This paper aims to investigate normal motion patterns in reaching and reach-to-grasp movements, and obtain the unique solution in joint space for a five-DOF exoskeleton. Firstly, a six-camera optical motion tracking system was used to capture participants' arm motion during goal-directed reaching or reach-to-grasp movements. Secondly, statistical analysis was executed to explore the characteristics of swivel angle, which revealed that the swivel angle can be approximated to the mean value (155° ± 5°) in resolving the arm redundancy problem. Thirdly, combined with the minimum-jerk trajectory of end-effector, the generated joint trajectory complied well with the joint trajectory captured in healthy humans. Consequently, the obtained results facilitate a new way for three-dimensional trajectory planning of the exoskeleton robot. Further, adaptive assist-as-needed control of the exoskeleton robot can be implemented based on the optimal reference trajectory, with aims to provide assistance according to the patient's performance, and in turn promote neural plasticity.

A Variational Approach to Minimum-Jerk Trajectories for Psychological Safety in Collaborative Assembly Stations

Collaborative robotics is one of the main drivers of the fourth industrial revolution, where robots and humans cooperate in a shared workspace. Such robots are distinguished from the traditional robots by several features that, if tuned correctly, ensure safe physical interaction. However, interaction with robots also represents a potential source of psychological stress. Indeed, it has been proven that working and sharing the workspace with robots can psychologically stress the operator. This drawback—in addition to the reduced speed operation imposed by safety standards—represents a constraint difficult to bear for small and medium-sized enterprises. In this letter, we propose a novel trajectory-planning methodology for collaborative robots able to ensure both psychological and physical safety. We rely on the available literature and the calculus of variations to identify a family of psychologically acceptable minimum-jerk trajectories. From the identified family, we compute the fastest trajectory that limits the physical danger represented by the robot. A numerical implementation of the method is discussed, and experimental results prove the effectiveness of the idea.

Evaluation of tremor interference with control of voluntary reaching movements in patients with Parkinson\u2019s disease

BackgroundA large population of patients with Parkinson’s disease (PD) displays the symptom of resting tremor. However, the extent that resting tremor may affect the performance of movement control has not been evaluated specifically. This study aims at establishing methods to quantitatively evaluate motor performance in PD patients with tremor, and at analyzing the interfering effects of tremor on control of reaching movements.MethodsTen PD patients with tremor and Ten healthy control subjects were recruited to participate in this study. All patients and healthy control subjects performed point-to-point reaching movements with their tremor affected arm or preferred arm. We verified that a smoothing model of minimum-jerk trajectory (MJT) can be used to extract voluntary movement trajectory from tremor-corrupted movement trajectory in the reaching tasks by the patients. Performance indices of reaction time (RT) and movement time (MT) of reaching movements by the PD subjects with tremor were evaluated using MJT trajectories. Differences of RT and MT between the recorded trajectories and MJT in PD and control subjects were calculated to investigate the extent that tremor may affect their motor performance. Linear mixed-effects model was used to identify the contributions of tremor, bradykinesia and rigidity to the performance indices of RT and MT based on UPDRS scores. The power spectrum densities (PSD) of tremor were also evaluated using hand velocities to represent tremor intensity and to analyze their correlations with RT and MT.ResultsThe MJT model demonstrated good fit to recorded trajectory with a more consistent estimation of motor performance for both PD and control subjects. The RT and MT of patients were found to be 43.4 and 79.5% longer respectively than those of healthy control subjects. Analysis of the linear mixed-effects model was not able to reveal that tremor, bradykinesia and rigidity each had a significant contribution to RT or MT in PD patients with tremor. However, the PSD of tremor was found to correlate significantly to RT, but not to MT, in both linear regression and linear mixed-effects model.ConclusionsThe minimum-jerk trajectory and power spectrum densities are effective quantitative tools for evaluating motor performance for PD patients with tremor. Resting tremor is one of the factors prolonging the initiation of voluntary reaching movement in these patients.

A novel approach to estimate the upper limb reaching movement in three-dimensional space

In spite of the complexity that the number of redundancy levels suggests, humans show amazingly regularities when generating movement. When moving the hand between pairs of targets, subjects tended to generate roughly straight hand trajectories with single-peaked, bell-shaped speed profiles. The original minimum-jerk model, in which limb displacement is represented by a fifth order polynomial, has been shown to predict qualitative features of experimental trajectories recorded in monkeys performing intermediate speed one-joint elbow movements to a target. However, it is difficult to compare a real (experimentally measured) movement to its equivalent minimum-jerk trajectory (MJT) because the exact start and end times and positions of real movements are usually not well defined: even discrete movements usually exhibit an extended period of low (but non-zero) velocity and acceleration before and after a movement, making estimation of the exact start and end times inaccurate. The purpose of this study was to describe a method used for correctly fitting the minimum jerk trajectory to real movement data assuming that the minimum-jerk trajectory satisfies the same threshold condition as the real movement (the same position and the same percentage of maximum velocity), rather than the movements start and end at full rest. Thus, the original minimum-jerk model was revised. Starting from the original minimum-jerk model, in this work is proposed a method used for correctly fitting the minimum jerk trajectory to real movement data defined by a threshold condition. This method enables users to accurately compare a minimum-jerk trajectory to real movements. The latter were recorded using APDM inertial sensors. To estimate if the ideal model fits adequately the real reaching movements we consider three kinematic indexes. and Discussion: A total of 100 upper arm straight line reaching movements executed by healthy subjects were acquired. MJTs follow closely to the reaching movements when they have been computed considering the revised model. On the contrary, the MJTs do not follow the real profiles when considering the original formulation. This behaviour is confirmed when we consider the three kinematic indexes. These findings help us better understand important characteristics of movements in health. Future works will focus on the investigation of the performance of the upper arm straight line reaching movements in a larger healthy subjects sample and then in pathological conditions.

DirCol5i: Trajectory Optimization for Problems With High-Order Derivatives

In this technical brief, we focus on solving trajectory optimization problems that have nonlinear system dynamics and that include high-order derivatives in the objective function. This type of problem comes up in robotics—for example, when computing minimum-snap reference trajectories for a quadrotor or computing minimum-jerk trajectories for a robot arm. DirCol5i is a transcription method that is specialized for solving this type of problem. It uses the fifth-order splines and analytic differentiation to compute higher-derivatives, rather than using a chain-integrator as would be required by traditional methods. We compare DirCol5i to traditional transcription methods. Although it is slower for some simple optimization problems, when solving problems with high-order derivatives DirCol5i is faster, more numerically robust, and does not require setting up a chain integrator.

Intelligent Control for Human-Robot Cooperation in Orthopedics Surgery.

Cooperation between surgeon and robot is one of the key technologies that limit the robot to be widely used in orthopedic clinics. In this study, the evolution of human-robot cooperation methods and the control strategies for typical human-robot cooperation in robot-assisted orthopedics surgery were reviewed at first. Then an intelligent admittance control method, which combines the fuzzy model reference learning control with the virtual constraint control, is proposed to solve the requirements of intuitive human-robot interaction during orthopedics surgery. That is, a variable damping parameter model of the admittance control based on fuzzy model learning control algorithm is introduced to make the robot move freely by using the reference model of surgeon's motion equation with the minimum jerk trajectory. And the virtual constraint control method based on the principle of virtual fixture is adopted to make the robot move within the pre-defined area so as to perform more safe surgery. The basic principle and its realization of this intelligent control method are described in details. At last, a test platform is built based on our designed 6 DOF articulated robot. Experiments of safety and precision on acrylic model with this method show that the robot has the ability of better intuitive interaction and the high precision. And the pilot experiment of bone tumor resection on sawbone model shows the effectiveness of this method.