Statistical Model

Statistical methods are utilized to build the mapping functions between different variable spaces with only data, and physical relationships among these spaces are unnecessary. There are many regression approaches utilized in soft robots, like linear regression, local weight regression (LWR), support vector regression (SVR), Gaussian process regression (GPR), and local weight projection regression (LWPR). Other than the regression methods, the Gaussian mixture model (GMM) summarizes collected data with a joint data distribution, and the extended Kalman filter (EKF) estimates robot states as an observer.

Statistical methods make data distribution assumptions from the perspective of statistics. They can attain an acceptable performance even with a small amount of data and become more effective with more data. Moreover, most of them can be leveraged for both modeling and control.

Paper List:

SVR:

17AM: Melingui A, Ahanda J J B M, Lakhal O, et al. Adaptive algorithms for performance improvement of a class of continuum manipulators[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017, 48(9): 1531-1541.

SVR is applied in this paper for both control and modeling. Due to its lightweight, the SVR controller and model are trained offline and updated online to achieve adaptability.

20IL: Loutfi I M, Boutchouang A H B, Melingui A, et al. Learning-based approaches for forward kinematic modeling of continuum manipulators[J]. IFAC-PapersOnLine, 2020, 53(2): 9899-9904.

Various methods, like MLP, RBF, SVR, and CANFIS, are compared in this paper. SVR gets better approximation accuracy than NN on a simple function, but this model requires more convergence time than NN on a large amount of data (15625 samples), which may be caused by the different optimization strategies or mature NN optimization software.

GPR:

19GF: Fang G, Wang X, Wang K, et al. Vision-based online learning kinematic control for soft robots using local gaussian process regression[J]. IEEE Robotics and Automation Letters, 2019, 4(2): 1194-1201.

Multiple GPR controller is applied for control with weighting according to similarity.

20ZT: Tang Z Q, Heung H L, Tong K Y, et al. A probabilistic model-based online learning optimal control algorithm for soft pneumatic actuators[J]. IEEE Robotics and Automation Letters, 2020, 5(2): 1437-1444.

GPR is applied for pneumatic actuator modeling, and a controller based on this model and optimization is utilized.

LWPR:

16GF: Fagogenis G, Bergeles C, Dupont P E. Adaptive nonparametric kinematic modeling of concentric tube robots[C]//2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2016: 4324-4329.

LWPR is applied for concentric tube robot kinematic modeling.

22ZTb: Tang Z, Wang P, Xin W, et al. Learning-based approach for a soft assistive robotic arm to achieve simultaneous position and force control[J]. IEEE Robotics and Automation Letters, 2022, 7(3): 8315-8322.

LWPR is applied as a feedback controller for feedforward controller online compensation.

18JH: Ho J D L, Lee K H, Tang W L, et al. Localized online learning-based control of a soft redundant manipulator under variable loading[J]. Advanced Robotics, 2018, 32(21): 1168-1183.

LWPR is utilized by selecting null-space behavior with constrained optimization to minimize the overall inflated chamber pressures, and this controller is adaptive to variable fluid tip loads.

GMM:

19BY: Yu B, Fernández J G, Tan T. Probabilistic kinematic model of a robotic catheter for 3D position control[J]. Soft robotics, 2019, 6(2): 184-194.

The controller and modeling method of one soft robot is derived from the same GMM considering different priors.

16HW: Wang H, Chen J, Lau H Y K, et al. Motion planning based on learning from demonstration for multiple-segment flexible soft robots actuated by electroactive polymers[J]. IEEE Robotics and Automation Letters, 2016, 1(1): 391-398.

The pose and temporal value from human demonstrations are encoded into a GMM for robot planning in the navigation through narrow holes.

16MM: Malekzadeh M, Queißer J, Steil J J. Learning the end-effector pose from demonstration for the bionic handling assistant robot[J]. 2016.

The rotation matrix of the coordinate system is included in the GMM for full pose control.

EKF:

16AA: Ataka A, Qi P, Shiva A, et al. Real-time pose estimation and obstacle avoidance for multi-segment continuum manipulator in dynamic environments[C]//2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2016: 2827-2832.

This paper maps actuator variables and segment parameters into the robot pose to build the nonlinear forward modeling with the transformation matrices. EKF estimates tendon length with tip positions for correction.

16CJ: Jang C, Ha J, Dupont P E, et al. Toward on-line parameter estimation of concentric tube robots using a mechanics-based kinematic model[C]//2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2016: 2400-2405.

EKF estimates robot poses and physical parameters of CTR. Pose measurement is applied for correction.

19JL: Loo J Y, Kong K C, Tan C P, et al. Non-linear system identification and state estimation in a pneumatic based soft continuum robot[C]//2019 IEEE Conference on control technology and applications (CCTA). IEEE, 2019: 39-46.

Wavelet networks are included in EKF as forward models for curvature angle estimation and correction with flex sensor signals.

20JL: Loo J Y, Ding Z Y, Davies E, et al. Curvature and force estimation for a soft finger using an EKF with unknown input optimization[J]. IFAC-PapersOnLine, 2020, 53(2): 8506-8512.

Based on 19JL, the external force is also estimated.

11ST: Tully S, Kantor G, Zenati M A, et al. Shape estimation for image-guided surgery with a highly articulated snake robot[C]//2011 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 2011: 1353-1358.

Due to the modular structure of the snake robot, the EKF is adapted by changing the dimension of state variables according to the advancing or retracting motion for shape estimation.