Skip to main content
SpringerLink
Log in

A combined kinodynamic motion planning method for multisegment continuum manipulators in confined spaces

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Multisegment continuum manipulators exhibit broad application prospects for complex tasks in confined spaces due to their inherent compliance and dexterity. However, the dynamic behaviors of these manipulators are highly nonlinear, bringing great challenges to their obstacle-avoidance motion planning. In this paper, a combined kinodynamic motion planning method is proposed for cable-driven multisegment continuum manipulators in confined spaces. The kinodynamic motion planning problem for these manipulators is first transformed into a nonlinear optimization problem (NOP) with both obstacle-avoidance constraints and input limitation constraints. The workspace of the continuum manipulator is then divided into a safe subspace and a warning subspace. By introducing parameters, the transformed NOP for motion planning in the safe subspace is further reformulated as a mixed complementarity problem to solve, which can rapidly generate paths while strictly satisfying system constraints. In addition, based on normal distribution and adaptive parameters, an improved particle swarm optimization algorithm with great search performance is developed to address the motion planning problem in the warning subspace. The proposed path optimization framework can effectively address the highly nonlinear kinodynamic motion planning problem for multisegment continuum manipulators. Numerical simulations for obstacle-avoidance motion planning of multisegment continuum manipulators are conducted to illustrate the effectiveness and advantages of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Algorithm 1
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Data availability

The data generated or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

B :

Augmented system input matrix

\({\mathbf{c}}_{{{k}}}\) :

Obstacle-avoidance constraints at time \(t_{{{k}}}\)

d :

Vector of actual distances between potential collision points and obstacles

\(d_{s}\) :

Critical safety distance

\(d_{w}\) :

Warning distance

\(d_{i,j}\) :

Distance between the ith potential collision point on the manipulator and the jth obstacle

E :

Elastic potential energy of the system

G :

System input matrix

\(J_{{{k}}}\) :

Cost function of motion planning

m :

Number of system constraints

M :

System mass matrix

n :

Number of generalized coordinates

\({\mathbf{p}}_{j}\) :

Position of the jth particle

P :

Position set of the particle swarm

q :

Generalized coordinate

\({\dot{\mathbf{q}}}\) :

Generalized velocity

\({{\ddot{\mathbf{q}}}}\) :

Generalized acceleration

s :

Number of actuation forces

\({\mathbf{u}}_{{{k}}}\) :

Cable actuation force at time \(t_{{{k}}}\)

\({\mathbf{u}}_{\max }\) :

Upper bound of the actuation force

\({\mathbf{u}}_{\min }\) :

Lower bound of the actuation force

V :

Coupling matrix including the centrifugal-Coriolis and damping matrices

w :

Number of the system output variables

\( \mathbf{x}_{{{k}}} \) :

Vector of the generalized coordinates and the Lagrange multiplier

\( \mathbf{y}_{{{k}}} \) :

Actual output variable of the system at time \( {{t}}_{{{k}}} \)

\( \tilde{\mathbf{y}}_{{k}} \) :

Desired output variable of the system at time \( {{t}}_{{{k}}} \)

\(\varphi\) :

Number of particles updated by a chaotic map

\(\eta\) :

Time-step length

\({{\varvec{\uplambda}}}\) :

Vector of Lagrange multipliers

\({{\varvec{\upsigma}}}\) :

Standard deviation of normal distribution

\(\upsilon\) :

Penalty factor

\({{\varvec{\uppsi}}}\) :

System constraints

\(\Phi\) :

Penalty function

MiCP:

Mixed complementarity problem

NOP:

Nonlinear optimization problem

PSO:

Particle swarm optimization

References

  1. Rus, D., Tolley, M.T.: Design, fabrication and control of soft robots. Nature 521(7553), 467–475 (2015)

    Article  Google Scholar 

  2. Franco, E., Garriga-Casanovas, A.: Energy-shaping control of soft continuum manipulators with in-plane disturbances. Int. J. Robot. Res. 40(1), 236–255 (2021)

    Article  Google Scholar 

  3. Jing, X., Jiang, J., Xie, F., Zhang, C., Chen, S., Yang, L.: Continuum manipulator with rigid-flexible coupling structure. IEEE Robot. Autom. Lett. 7(4), 11386–11393 (2022)

    Article  Google Scholar 

  4. Hoang, T.T., Phan, P.T., Thai, M.T., Lovell, N.H., Do, T.N.: Bio-inspired conformable and helical soft fabric gripper with variable stiffness and touch sensing. Adv. Mater. Technol. 5(12), 2000724 (2020)

    Article  Google Scholar 

  5. Wallin, T.J., Pikul, J., Shepherd, R.F.: 3D printing of soft robotic systems. Nat. Rev. Mater. 3(6), 84–100 (2018)

    Article  Google Scholar 

  6. Zhang, J., Wang, B., Chen, H., Bai, J., Wu, Z., Liu, J., Peng, H., Wu, J.: Bioinspired continuum robots with programmable stiffness by harnessing phase change materials. Adv. Mater. Technol. 8(6), 2201616 (2023)

    Article  Google Scholar 

  7. Wang, J., Hu, C., Ning, G., Ma, L., Zhang, X., Liao, H.: A novel miniature spring-based continuum manipulator for minimally invasive surgery: design and evaluation. IEEE/ASME Trans. Mechatron. 28(5), 2716–2727 (2023)

  8. Yang, J., Peng, H., Zhang, J., Wu, Z.: Dynamic modeling and beating phenomenon analysis of space robots with continuum manipulators. Chin. J. Aeronaut. 35(9), 226–241 (2022)

    Article  Google Scholar 

  9. Chen, X., Zhang, X., Huang, Y., Cao, L., Liu, J.: A review of soft manipulator research, applications, and opportunities. J. Field Robot. 39(3), 281–311 (2021)

    Article  Google Scholar 

  10. Wang, H., Wang, C., Chen, W., Liang, X., Liu, Y.: Three-dimensional dynamics for cable-driven soft manipulator. IEEE/ASME Trans. Mechatron. 22(1), 18–28 (2017)

    Article  Google Scholar 

  11. Yang, J., Peng, H., Zhou, W., Zhang, J., Wu, Z.: A modular approach for dynamic modeling of multisegment continuum robots. Mech. Mach. Theory 165, 104429 (2021)

    Article  Google Scholar 

  12. Lai, J., Huang, K., Lu, B., Zhao, Q., Chu, H.K.: Verticalized-tip trajectory tracking of a 3D-printable soft continuum robot: enabling surgical blood suction automation. IEEE/ASME Trans. Mechatron. 27(3), 1545–1556 (2022)

    Article  Google Scholar 

  13. George Thuruthel, T., Ansari, Y., Falotico, E., Laschi, C.: Control strategies for soft robotic manipulators: a survey. Soft Robot. 5(2), 149–163 (2018)

    Article  Google Scholar 

  14. Seleem, I.A., El-Hussieny, H., Ishii, H.: Imitation-based motion planning and control of a multi-section continuum robot interacting with the environment. IEEE Robot. Autom. Lett. 8(3), 1351–1358 (2023)

    Article  Google Scholar 

  15. Till, J., Aloi, V., Rucker, C.: Real-time dynamics of soft and continuum robots based on cosserat rod models. Int. J. Robot. Res. 38(6), 723–746 (2019)

    Article  Google Scholar 

  16. Renda, F., Boyer, F., Dias, J., Seneviratne, L.: Discrete cosserat approach for multisection soft manipulator dynamics. IEEE Trans. Robot. 34(6), 1518–1533 (2018)

    Article  Google Scholar 

  17. Peng, J., Xu, W., Yang, T., Hu, Z., Liang, B.: Dynamic modeling and trajectory tracking control method of segmented linkage cable-driven hyper-redundant robot. Nonlinear Dyn. 101(1), 233–253 (2020)

    Article  Google Scholar 

  18. Franco, E., Ayatullah, T., Sugiharto, A., Garriga-Casanovas, A., Virdyawan, V.: Nonlinear energy-based control of soft continuum pneumatic manipulators. Nonlinear Dyn. 106(1), 229–253 (2021)

    Article  Google Scholar 

  19. Ghorbani, S., Samadikhoshkho, Z., Janabi-Sharifi, F.: Dual-arm aerial continuum manipulation systems: modeling, pre-grasp planning, and control. Nonlinear Dyn. 111(8), 7339–7355 (2023)

    Article  Google Scholar 

  20. Wang, X., Deng, Z., Peng, H., Wang, L., Wang, Y., Tao, L., Lu, C., Peng, Z.: Autonomous docking trajectory optimization for unmanned surface vehicle: a hierarchical method. Ocean Eng. 279, 114156 (2023)

    Article  Google Scholar 

  21. Wang, X., Li, B., Su, X., Peng, H., Wang, L., Lu, C., Wang, C.: Autonomous dispatch trajectory planning on flight deck: a search-resampling-optimization framework. Eng. Appl. Artif. Intell. 119, 105792 (2023)

    Article  Google Scholar 

  22. Ouyang, B., Liu, Y., Tam, H.-Y., Sun, D.: Design of an interactive control system for a multisection continuum robot. IEEE/ASME Trans. Mechatron. 23(5), 2379–2389 (2018)

    Article  Google Scholar 

  23. Lai, J., Lu, B., Zhao, Q., Chu, H.K.: Constrained motion planning of a cable-driven soft robot with compressible curvature modeling. IEEE Robot. Autom. Lett. 7(2), 4813–4820 (2022)

    Article  Google Scholar 

  24. Meng, B.H., Godage, I.S., Kanj, I.: RRT*-based path planning for continuum arms. IEEE Robot. Autom. Lett. 7(3), 6830–6837 (2022)

    Article  Google Scholar 

  25. Donald, B., Xavier, P., Canny, J., Reif, J.: Kinodynamic motion planning. J. ACM 40(5), 1048–1066 (1993)

    Article  MathSciNet  Google Scholar 

  26. Allen, R.E., Pavone, M.: A real-time framework for kinodynamic planning in dynamic environments with application to quadrotor obstacle avoidance. Robot. Auton. Syst. 115, 174–193 (2019)

    Article  Google Scholar 

  27. Sharma, B.N., Raj, J., Vanualailai, J.: Navigation of carlike robots in an extended dynamic environment with swarm avoidance. Int. J. Robust Nonlinear Control 28(2), 678–698 (2018)

    Article  MathSciNet  Google Scholar 

  28. Li, F., Peng, H., Yang, H., Kan, Z.: A symplectic kinodynamic planning method for cable-driven tensegrity manipulators in a dynamic environment. Nonlinear Dyn. 106(4), 2919–2941 (2021)

    Article  Google Scholar 

  29. Kar, A.K.: Bio inspired computing—a review of algorithms and scope of applications. Exp. Syst. Appl. 59, 20–32 (2016)

    Article  Google Scholar 

  30. Zhao, L., Li, R., Han, J., Zhang, J.: A distributed model predictive control-based method for multidifferent-target search in unknown environments. IEEE Trans. Evol. Comput. 27(1), 111–125 (2023)

    Article  Google Scholar 

  31. Ekrem, Ö., Aksoy, B.: Trajectory planning for a 6-axis robotic arm with particle swarm optimization algorithm. Eng. Appl. Artif. Intell. 122, 106099 (2023)

    Article  Google Scholar 

  32. Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer, New York (2003)

    Google Scholar 

  33. Arnold, M., Brüls, O.: Convergence of the generalized-α scheme for constrained mechanical systems. Multibody Sys. Dyn. 18(2), 185–202 (2007)

    Article  MathSciNet  Google Scholar 

  34. Peng, H., Li, F., Liu, J., Ju, Z.: A symplectic instantaneous optimal control for robot trajectory tracking with differential-algebraic equation models. IEEE Trans. Ind. Electron. 67(5), 3819–3829 (2020)

    Article  Google Scholar 

  35. Yang, J., Peng, H., Zhou, W., Wu, Z.: Integrated control of continuum-manipulator space robots with actuator saturation and disturbances. J. Guid. Control. Dyn. 45(12), 2379–2388 (2022)

    Article  Google Scholar 

  36. Li, M., Peng, H., Zhong, W.: Optimal control of loose spacecraft formations near libration points with collision avoidance. Nonlinear Dyn. 83(4), 2241–2261 (2015)

    Article  MathSciNet  Google Scholar 

  37. Bratton, D., Kennedy, J.: Defining a standard for particle swarm optimization. In: 2007 IEEE Swarm Intelligence Symposium, Honolulu, USA, pp. 120–127 (2007)

  38. Liu, B., Wang, L., Jin, Y.H., Tang, F., Huang, D.X.: Improved particle swarm optimization combined with chaos. Chaos Solitons Fract. 25(5), 1261–1271 (2005)

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 12302063, No. 12202509 and No. U2241263), and the Fundamental Research Funds for the Central Universities, Sun Yat-Sen University (Grant No. 23qnpy81).

Author information

Authors and Affiliations

  1. School of Aeronautics and Astronautics, Sun Yat-Sen University, Shenzhen, 518107, People’s Republic of China

    Jinzhao Yang, Shunan Wu, Jie Zhang, Zhigang Wu & Jianing Wu

  2. Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Haijun Peng

  3. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Haijun Peng

  4. School of Advanced Manufacturing, Sun Yat-Sen University, Shenzhen, 518107, People’s Republic of China

    Jianing Wu

Authors
  1. Jinzhao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haijun Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shunan Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jie Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhigang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jianing Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinzhao Yang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, J., Peng, H., Wu, S. et al. A combined kinodynamic motion planning method for multisegment continuum manipulators in confined spaces. Nonlinear Dyn 112, 2721–2744 (2024). https://doi.org/10.1007/s11071-023-09190-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-09190-3

Keywords

Search

Navigation