Algebraic Method-Based Point-to-Point Trajectory Planning of an Under-Constrained Cable-Suspended Parallel Robot with Variable Angle and Height Cable Mast

Abstract

To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots (CSPRs), point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot (UCPR) with variable angle and height cable mast as described in this paper. The end-effector of the UCPR with three cables can achieve three translational degrees of freedom (DOFs). The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed. The motion trajectory of the end-effector comprising six segments is given. The connection points of the trajectory segments (except for point P3 in the X direction) are devised to have zero instantaneous velocities, which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition. The trajectory is respectively planned using three algebraic methods, including fifth degree polynomial, cycloid trajectory, and doubleS velocity curve. The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector. Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning. At the points where the velocity suddenly changes, the length and tension variation curves of the planned and unplanned three cables are compared and analyzed. The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment. The effectiveness and feasibility of fifth degree polynomial planning are validated.

A Real-time Look-ahead Trajectory Planning Methodology for Multi Small Line Segments Path

“…( 20) simultaneously, and Eq. ( 20) can be rewritten as: (18 Therefore, the quadratic equation for ε can be expressed as:…”

“…The kinematic limitations of machine tools have been fully considered to obtain a time-optimal feed rate curve [17]. Various of acceleration and deceleration trajectory planning algorithms, such as polynomial, trapezoidal, and S-shaped jerk-limited methods [18][19][20] and the jerk-continuous methods [21][22][23], are available, and the S-shaped acceleration and deceleration algorithm is widely used [24][25][26]. After the path-smoothing and trajectory planning methods are selected, the look-ahead function that calculates the velocity at each point should be determined.…”

Pick–and–Place Trajectory Planning and Robust Adaptive Fuzzy Tracking Control for Cable–Based Gangue–Sorting Robots with Model Uncertainties and External Disturbances

“…Qian [22] proposed a new trajectory planning method based on the improved quintic B-splines curves for a 3-DOF CBPR, and furthermore, the effectiveness of this method was verified through the experiments. Zhao et al [23] presented point-to-point trajectory planning for UCPR with variable angles and height cable mast by using three algebraic methods, while the effectiveness and feasibility of the method were validated with numerical simulation and experiments. The improved rapidly exploring random tree method was proposed to address moving obstacle avoidance for CDPRs, and the suggested method was verified with the experiment [24].…”

Safety Evaluation and Experimental Study of a New Bionic Muscle Cable-Driven Lower Limb Rehabilitation Robot

“…Barbosa, AM et al [ 17 ] designed a CDLR for which the movable platform can be respectively driven by one to six cables, which can independently complete the training of the hip joint, knee joint, and ankle joint. Zhao T. and Zi B. et al [ 18 ] designed a cable-driven parallel robot (CDPR) that can change the angle and height of the cable masts. Gallina, P. et al [ 19 , 20 ] designed a variable radius drum mechanism for the cable robot.…”