Optimal Trajectory Planning of a Cable-Driven Parallel Robot by Direct Collocation Approaches
الموضوعات :
Milad Badrikouhi
1
,
Mahdi Bamdad
2
1 - Mechanical and Mechatronics Engineering School, Shahrood University of Technology, Iran
2 - Mechanical engineering department, Shahrood university of technology
الکلمات المفتاحية: B-Spline Interpolation Curves, Cable-Driven Parallel Robot, Direct Collocation, GPOPS-II, Trajectory Planning,
ملخص المقالة :
Trajectory planning in cable-driven robots is more challenging than rigid-link ones. To maintain the robot control, the cable tensions must be positive during motion. This paper presents a direct collocation approach to solve the optimal trajectory planning based on the minimization of a robot's tension and tension-rate objective functions. Besides, during robot motion, the cables must be tensile. The configuration of a cable parallel robot composed of a 3-cable and a prismatic actuator neutralizes the moving platform’s weight while improving tensionability. To generate smooth trajectories, the proposed method is compared with two standard approaches: GPOPS-II software package which uses Legendre-Gauss-Radu quadrature orthogonal collocation polynomials and direct collocation by using B-spline interpolation curves. Despite the efficiency of using B-spline functions in trajectory planning, numerical simulations demonstrate that the Hermite-Simpson direct collocation approach has a substantial benefit in the computation cost and accuracy for trajectory planning of a cable-driven parallel robot. Also, by choosing appropriate constraints and cost functions, the cable forces in the parallel robot can be well managed.
[1] Sohrabi, S., Mohammadi Daniali, H., and Fathi, A., Trajectory Path Planning of Cable Driven Parallel Manipulators, Considering Masses and Flexibility of The Cables, ADMT Journal, Vol. 9, No. 3, 2017, pp. 57-64.
[2] Shahabi, E., Hosseini, M., Kinematic Synthesis of a Novel Parallel Cable Robot as Artificial Leg, ADMT Journal, Vol. 9, No. 3, 2017, pp. 1-10.
[3] Hussein, H., Santos, J. C., and Gouttefarde, M., Geometric Optimization of a Large Scale Cdpr Operating on A Building Facade, In 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018: IEEE, pp. 5117-5124.
[4] Phuoc Tho, T., Truong Thinh, N., Evaluating Cable Tension Distributions of CDPR for Virtual Reality Motion Simulator, Mechanics Based Design of Structures and Machines, 2023, pp. 1-19.
[5] H. D. Taghirad, Parallel Robots: Mechanics and Control, CRC press, 2013.
[6] Behzadipour, S., and Khajepour, A., Design of Reduced Dof Parallel Cable-Based Robots, Mechanism and Machine Theory, Vol. 39, No. 10, 2004, pp. 1051-1065.
[7] Zhao, X., Zi, B., and Qian, L., Design, Analysis, And Control of a Cable-Driven Parallel Platform with A Pneumatic Muscle Active Support, Robotica, Vol. 35, No. 4, 2017, pp. 744-765.
[8] Korayem, M. H., Bamdad, M., Tourajizadeh, H., Korayem, A. H., and Bayat, S., Analytical Design of Optimal Trajectory with Dynamic Load-Carrying Capacity for Cable-Suspended Manipulator, The International Journal of Advanced Manufacturing Technology, Vol. 60, No. 1, 2012, pp. 317-327.
[9] Badrikouhi, M., Bamdad, M., Novel Manipulability for Parallel Mechanisms with Prismatic-Revolute Actuators, GA-DP Trajectory Planning Application, Mechanics of Solids, Vol. 56, No. 2, 2021, pp. 278-291.
[10] Riyahi Vezvari, M., Nikoobin, A., Optimal Balancing of Spatial Suspended Cable Robot in Point-To-Point Motion Using Indirect Approach, ADMT Journal, Vol. 10, No. 3, 2017, pp. 87-96.
[11] Alibakhshi, R., Trajectory Optimization of Spherical Parallel Robots Using Artificial Neural Network, ADMT Journal, Vol. 7, No. 1, 2014.
[12] Betts, J. T., Survey of Numerical Methods for Trajectory Optimization, Journal of Guidance, Control, and Dynamics, Vol. 21, No. 2, 1998, pp. 193-207.
[13] Bamdad, M., Time-Energy Optimal Trajectory Planning of Cable-Suspended Manipulators, in Cable-Driven Parallel Robots: Springer, 2013, pp. 41-51.
[14] Hereid, A., Cousineau, E. A., Hubicki, C. M., and Ames, A. D., 3D Dynamic Walking with Underactuated Humanoid Robots: A Direct Collocation Framework for Optimizing Hybrid Zero Dynamics, in 2016 IEEE International Conference on Robotics and Automation (ICRA), 2016: IEEE, pp. 1447-1454.
[15] Kolathaya, S., Guffey, W., Sinnet, R. W., and Ames, A. D., Direct Collocation for Dynamic Behaviors with Nonprehensile Contacts: Application to Flipping Burgers, IEEE Robotics and Automation Letters, Vol. 3, No. 4, 2018, pp. 3677-3684.
[16] Patterson, M. A., and Rao, A. V., GPOPS-II: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using Hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming, ACM Transactions on Mathematical Software (TOMS), Vol. 41, No. 1, 2014, pp. 1-37.
[17] Freeman, P., Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots, Washington University in St. Louis ProQuest Dissertations Publishing, 2012.
[18] Campbell, S., Kunkel, P., General Nonlinear Differential Algebraic Equations and Tracking Problems: A Robotics Example, Applications of Differential-Algebraic Equations: Examples and Benchmarks, 2018, pp. 1.
[19] Qian, S., Bao, K., Zi, B., and Zhu, W., Dynamic Trajectory Planning for A Three Degrees-of-Freedom Cable-Driven Parallel Robot Using Quintic B-Splines, Journal of Mechanical Design, Vol. 142, No. 7, 2020, pp. 073301.
[20] Li, Y., T. Huang, T., and Chetwynd, D. G., An Approach for Smooth Trajectory Planning of High-Speed Pick-and-Place Parallel Robots Using Quintic B-Splines, Mechanism and Machine Theory, Vol. 126, 2018, pp. 479-490.
[21] Santos, J. C., Chemori, A., and Gouttefarde, M., Redundancy Resolution Integrated Model Predictive Control of Cdprs: Concept, Implementation and Experiments, in 2020 IEEE International Conference on Robotics and Automation (ICRA), 2020: IEEE, pp. 3889-3895.
[22] Ueland, E., Sauder, T., and Skjetne, R., Optimal Force Allocation for Overconstrained Cable-Driven Parallel Robots: Continuously Differentiable Solutions with Assessment of Computational Efficiency, IEEE Transactions on Robotics, Vol. 37, No. 2, 2020, pp. 659-666.
[23] Dal Bianco, N., Bertolazzi, E., Biral, F., and Massaro, M., Comparison of Direct and Indirect Methods for Minimum Lap Time Optimal Control Problems, Vehicle System Dynamics, Vol. 57, No. 5, 2019, pp. 665-696.
[24] Rahaghi, M. I., Barat, F., Solving Nonlinear Optimal Path Tracking Problem Using a New Closed Loop Direct–Indirect Optimization Method: Application on Mechanical Manipulators, Robotica, Vol. 37, No. 1, 2019, pp. 39-61.
