Quintic Pythagorean-Hodograph Curves Based Trajectory Planning for Delta Robot with a Prescribed Geometrical Constraint

Liang, Xu; Su, Tingting

doi:10.3390/app9214491

Cited by 10 publications

(3 citation statements)

References 34 publications

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“…The strain energy measures how much a curve is bent. And the jerk energy (Meier and Nowacki, 1987) measures the curvature variation of a curve. In this paper, we use the jerk energy to obtain continuous smooth axis kinematic profiles with low-harmonic content.…”

Section: Jerk Energy Functionmentioning

confidence: 99%

Low-harmonic trajectory synthesis using trajectory pattern method (TPM) for high-speed and high-precision machinery

Rastegar

Wang

2021

Mech. Sci.

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Abstract. In high-speed and high-precision machinery, trajectories with high-frequency harmonic content are one of the main sources of reduction of operational precision. Trajectories with high-frequency harmonic content generally demand even higher-harmonic actuating forces/torques due to the nonlinear dynamics of such systems, which may excite natural modes of vibration of the system and/or be beyond the dynamic response limitation of the actuation devices. In this paper, a global interpolation algorithm that uses the trajectory pattern method (TPM) for synthesizing low-harmonic trajectories is presented. The trajectory synthesis with the TPM is performed with a prescribed fundamental frequency and continuous jounce boundary condition, which would minimize the number of high-harmonic components in the required actuation forces/torques and avoid excitation of the system modes of vibration. The minimal curvature variation energy method, Lagrange multiplier method, and contour error control are used to obtain smooth kinematic profiles and satisfy the trajectory accuracy requirements. As an example, trajectory patterns that consist of a fundamental frequency sinusoidal time function and its first three harmonics are used to synthesize the desired trajectories for a selected dynamic system. The synthesized trajectories are shown to cause minimal system vibration during its operation. A comparison with a commonly used trajectory synthesis method clearly shows the superiority of the developed TPM-based approach in reducing vibration and demand on the actuator dynamic response, thereby allowing the system to operate at higher speeds and precision.

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Section: Jerk Energy Functionmentioning

confidence: 99%

Low-harmonic trajectory synthesis using trajectory pattern method (TPM) for high-speed and high-precision machinery

Rastegar

Wang

2021

Mech. Sci.

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“…Zhang et al [7] inserted a quintic Bezier curve between small adjacent line segments to achieve velocity and acceleration continuity at the connecting points, and a quartic polynomial was adopted to achieve a constant velocity at the velocity limitation. To solve the problem of trajectory continuity, some fitting curves were presented, such as quintic and cubic nonuniform rational NURBS curves [8,9], the quintic Pythagorean hodograph (PH) curve [10], combining cubic splines with a linear segment with parabolic blends [11], and the S-curve [12]. However, since the trajectory of the end effector in Cartesian space needs to be mapped to the joint space through the inverse kinematic equation, it is realized by the joint actuator through the torque control according to the calculated joint variable values.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space

Zhu,

He,

et al. 2023

Mathematics

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Delta parallel robots have been widely used in precision processing, handling, sorting, and the assembly of parts, and their high efficiency and motion stability are important indexes of their performance.Corners created by small line segments in trajectory planning cause abrupt changes in a tangential discontinuous trajectory, and the vibration and shock caused by such changes seriously affect the robot’s high-speed and high-precision performance. In this study, a trajectory-planning method combining Cartesian space and joint space is proposed. Firstly, the vector method and microelement integration method were used to establish the complete kinematic and dynamic equations of a delta parallel robot, and an inverse kinematic/dynamic model-solving program was written based on the MATLAB software R2020a. Secondly, the end-effector trajectory of the delta parallel robot was planned in Cartesian space, and the data points and inverse control points of the end effector’s trajectory were obtained using the normalization method. Finally, the data points and control points were mapped to the joint space through the inverse kinematic equation, and the fifth-order B-spline curve was adopted for quadratic trajectory planning, which allowed the high-order continuous smoothing of the trajectory planning to be realized. The simulated and experimental results showed that the trajectory-smoothing performance in continuous high-order curvature changes could be improved with the proposed method. The peak trajectory tracking error was reduced by 10.53%, 41.18%, and 44.44%, respectively, and the peak torque change of the three joints was reduced by 3.5%, 11.6%, and 1.6%, respectively.

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“…According to the characteristics of stroke and human limb movement function, it mainly uses the mechanical factors, based on the kinematics, sports mechanics, and neurophysiology, and selects appropriate functional activities and exercise methods to train the patients to prevent diseases and promote the recovery of physical and mental functions (Gassert and Dietz, 2018;D'Onofrio et al, 2019;Cespedes et al, 2021). The integration of artificial intelligence, bionics, robotics, and rehabilitation medicine has promoted the development of the rehabilitation robot industry (Su et al, 2018;Wu et al, 2018Wu et al, , 2020Wu et al, , 2021bLiang and Su, 2019). With the innovation of technology, the rehabilitation robot has the characteristics of precise motion and long-time repetitive work, which brings a very good solution to many difficult problems of reality, such as the difficulty of standardization of rehabilitation movement, the shortage of rehabilitation physicians, and the increasing number of stroke patients (Deng et al, 2021a,b;Wu et al, 2021a).…”

Section: Introductionmentioning

confidence: 99%

Measurement Method of Human Lower Limb Joint Range of Motion Through Human-Machine Interaction Based on Machine Vision

et al. 2021

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To provide stroke patients with good rehabilitation training, the rehabilitation robot should ensure that each joint of the limb of the patient does not exceed its joint range of motion. Based on the machine vision combined with an RGB-Depth (RGB-D) camera, a convenient and quick human-machine interaction method to measure the lower limb joint range of motion of the stroke patient is proposed. By analyzing the principle of the RGB-D camera, the transformation relationship between the camera coordinate system and the pixel coordinate system in the image is established. Through the markers on the human body and chair on the rehabilitation robot, an RGB-D camera is used to obtain their image data with relative position. The threshold segmentation method is used to process the image. Through the analysis of the image data with the least square method and the vector product method, the range of motion of the hip joint, knee joint in the sagittal plane, and hip joint in the coronal plane could be obtained. Finally, to verify the effectiveness of the proposed method for measuring the lower limb joint range of motion of human, the mechanical leg joint range of motion from a lower limb rehabilitation robot, which will be measured by the angular transducers and the RGB-D camera, was used as the control group and experiment group for comparison. The angle difference in the sagittal plane measured by the proposed detection method and angle sensor is relatively conservative, and the maximum measurement error is not more than 2.2 degrees. The angle difference in the coronal plane between the angle at the peak obtained by the designed detection system and the angle sensor is not more than 2.65 degrees. This paper provides an important and valuable reference for the future rehabilitation robot to set each joint range of motion limited in the safe workspace of the patient.

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Quintic Pythagorean-Hodograph Curves Based Trajectory Planning for Delta Robot with a Prescribed Geometrical Constraint

Cited by 10 publications

References 34 publications

Low-harmonic trajectory synthesis using trajectory pattern method (TPM) for high-speed and high-precision machinery

Low-harmonic trajectory synthesis using trajectory pattern method (TPM) for high-speed and high-precision machinery

Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space

Measurement Method of Human Lower Limb Joint Range of Motion Through Human-Machine Interaction Based on Machine Vision

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