## Article

# Path planning with obstacle avoidance for soft robots based on improved particle swarm optimization algorithm

Correspondence to: Prof. Xinbin Zhang, Academy of Sciences, Harbin Institute of Technology University, Building 2H, Harbin 150001, China. E-mail:

**Received:**28 Aug 2023 |

**First Decision:**21 Sep 2023 |

**Revised:**30 Sep 2023 |

**Accepted:**18 Oct 2023 |

**Published:**29 Oct 2023

**Academic Editor:**Simon X. Yang |

**Copy Editor:**Yanbin Bai |

**Production Editor:**Yanbin Bai

**Open Access**This article is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, sharing, adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Abstract

Soft-bodied robots have the advantages of high flexibility and multiple degrees of freedom and have promising applications in exploring complex unstructured environments. Kinematic coupling exists for the soft robot in a problematic space environment for motion planning between the soft robot arm segments. In solving the soft robot inverse kinematics, there are only solutions or even no solutions, and soft robot obstacle avoidance control is tough to exist, as other problems. In this paper, we use the segmental constant curvature assumption to derive the positive and negative kinematic relationships and design the tip self-growth algorithm to reduce the difficulty of solving the parameters in the inverse kinematics of the soft robot to avoid kinematic coupling. Finally, by combining the improved particle swarm algorithm to optimize the paths, the convergence speed and reconciliation accuracy of the algorithm are further accelerated. The simulation results prove that the method can successfully move the soft robot in complex space with high computational efficiency and high accuracy, which verifies the effectiveness of the research.

## Keywords

*,*particle swarm optimization

*,*path tracking

*,*tip growth type

## 1. INTRODUCTION

With the development of robotics, modern applications of robots have been extended to various complex situations and environments, such as medical surgery, search and rescue in confined spaces, industrial equipment maintenance^{[1-3]}, etc. In these complex environments, the flexibility, suppleness, joint limitations, and other properties of robots have high requirements, and traditional rigid robotic arms are difficult to use in these unstructured environments, while flexible robotic In contrast, flexible robotic arms are characterized by high self-load ratio, high flexibility, and lightweight structure, and thus can achieve bending motion in any shape within the elastic deformation range, thus enabling dexterous operation and strong adaptability in narrow spaces and spatial environments with complex obstacle distribution^{[4]}.

The main difference between soft robots and rigid robots is that the materials used to manufacture soft robots are mainly soft materials. However, the elasticity of soft actuators manufactured based on material deformation also makes their control strongly nonlinear, with an infinite number of degrees of freedom during large deformations, which makes it difficult to establish an accurate model^{[5]}. In recent years, scholars at home and abroad have conducted much research on the design, modeling, control, and obstacle avoidance of flexible robotic arms. IS Godage^{[6]}proposed a curve parametric (CP) kinematic model based on segmented constant curvature, which gives an accurate positive kinematic model by iterative methods and can simulate the bending motion of most of the flexible continuous arms. However, the Piecewise Constant curvature (PCC) method has numerical singularities when applied to the inverse solution of the soft body continuous arm, which cannot simulate the straight arm state of the continuous section to converge and takes a long time to compute. The inverse kinematics problem is also challenging, and conventional inverse methods are computationally overloaded or unsolvable for soft robots. Neppalli *et al.*^{[7,8]} finally obtained a multi-segment kinematic inverse solution by applying single-segment inverse kinematics to a multi-segment backbone for direction compensation. However, this method makes it difficult to avoid obstacles while maintaining access to known end joints and requires additional manual assistance to operate the robot arm movement.

At the same time, reliable obstacle avoidance algorithms are indispensable to make flexible robots better able to accomplish the corresponding tasks in tight spaces. Various practical obstacle avoidance planning methods have been proposed, such as artificial potential field methods^{[9]}, neural network algorithms^{[10]}, genetic algorithms^{[11]}, and machine learning^{[12]}, but the above obstacle avoidance algorithms are mainly used for traditional rigid robotic arms, and in order to enhance the ability of flexible robots to traverse obstacles, Khatib *et al.*^{[13]} implemented a multi-stage extended Kalman filter in a simulation for a flexible continuum. Palmer *et al.*^{[14]}. characterized the macroscopic features of the robot arm by constructing a spatial curve and optimized the path curve to make the soft robot follow the desired trajectory to the target point. However, this method makes the motion of the robot unsmooth.

In this paper, based on the above-mentioned research, the kinematic coupling problem of the soft robot is addressed by deriving the forward and inverse kinematic models of the soft robot and proposing a self-growing control method based on the bionic vine tip, which avoids the kinematic coupling by discrete the soft robot body into several joint segments and only controls the motion of the soft robot tip joints. In order to avoid obstacles and smooth the motion of the soft robot, this paper uses the particle swarm algorithm to plan the path of the soft robot tip joints, and the planned path is used as the tracking path of the soft robot tip joints, and the rest of the joints use the information of the previous moment of the tip joints to complete the action so that the soft robot can pass the obstacles in the restricted space, and finally, the end-fitting strategy is designed to make the soft robot accurately reach the target point. Finally, the end fitting strategy is designed to make the soft robot reach the target point accurately and realize the trajectory planning of the soft robot in a complex environment. The main contributions are as follows: 1. The second section introduces the structure of the soft robot, establishes a kinematic model of the soft robot based on segmented constant curvature, and verifies the correctness of the model in the Matlab simulation environment; 2. In the third section, an improved particle swarm optimization (PSO) path planning algorithm was constructed to design the optimal planning path, and random peaks and bubbles were set to model obstacles; 3. The fourth section proposes a path tracking algorithm based on tip self-growth, which uses tip joint self-growth control software robots to track the planned path in the third section, thereby avoiding kinematic coupling and improving algorithm efficiency; 4. In the fifth section, the above algorithm was validated through Matlab simulation experiments. The experiments showed that the improved PSO algorithm proposed in this paper can effectively avoid obstacles. The path tracking algorithm based on tip self-growth further improves the algorithm efficiency in path following and can be used for obstacle avoidance planning of soft robots.

## 2. SOFT BODY ROBOT MODELING

### 2.1. Soft robot structure

#### 2.1.1. Soft robot structure

The design of the tip-growing soft robot designed in this paper is inspired by the principle of tip growth of vines and other plant rhizomes^{[15]}. In this approach, the tip extends outward and grows, based on the environment, allowing it to actively control the movement. In the process of movement, it does not rely on its previous posture but constantly growing new tissue structures to adapt to the changing environment; its growth principle is shown in Figure 1. The front end of the flexible body is driven by air pressure to continuously grow a new structure; the movement process does not depend on the environmental structure. The first generation of soft robots is shown in Figure 2(a). The overall structure of the flexible robot arm is shown in Figure 2(b), mainly composed of a control box base, flexible body, and steering module. The flexible body is made of flexible film material. The drive mechanism is in the drive box and drives the flexible body to grow in space by turning outward through air pressure, and three micro motors control each steering module. The theoretical bending angle of this structure ranges from 0 to 60 degrees.

#### 2.1.2. Kinematic modeling of soft robots

Soft robots do not have the traditional linkages and joints of rigid robots; they cannot be modeled using the traditional D-H parametric method of rigid robots^{[16]}. In 2006, Jones *et al.* proposed a theoretical kinematic model based on segmented constant curvature^{[17]}. This paper uses the segmented constant curvature method for the kinematic analysis of soft robots. In order to realize the kinematic modeling of the self-growing soft robot, the model is appropriately simplified, and the following basic assumptions are made: (1) The self-growing soft body robot maintains a smooth curve with the same curvature at the steering joints during the steering process. (2) The self-grown soft body robot only changes along the length of the neutral axis, and the radial dimension remains unchanged. (3) Neglecting the effect of gravity of controllers such as servos in the steering motion module on the motion characteristics of the model; As shown in Figure 3, for the soft robot arm with multiple joints, there are multi-level mapping relationships for motion control, including soft drive space to configuration space mapping and configuration space to task space mapping.

#### 2.1.3. Mapping of soft unit drive and configuration space

The geometric model of the Paragraph i segment of the soft body cell is given by drawing on the soft body robot kinematic model of Professor Walker, as shown in Figure 4. During the motion of the soft robot cell, it is driven by three drive lines at 120°, thus changing its soft arm bending angle

The bending angle

where the relationship between the driver length and the bending and deflection angles is:

#### 2.1.4. Mapping of soft unit conformation and task space

The mapping relationship from the soft robot configuration space to the task space can be improved by combining the arc curve parameters with the D-H parameters, thus establishing the homogeneous transformation matrix (HTM) to describe the spatial relationship between adjacent coordinate systems, as shown in Figure 4. Through geometric analysis, the coordinate system

According to the above HTM transformation, the mapping of the soft body robot arm configuration space to the task space can be found. From equation (6), the joint position of the robot arm, [

#### 2.1.5. Inverse kinematic model of the soft body unit

To establish the mapping from the task space to the configuration space of a soft robot and thus the inverse kinematics model of a soft arm. However, it has been a challenging problem to realize the inverse kinematics solution of the soft robot arm by solving the nonlinear equations through HTM transformation. In order to improve the reliability of the solution and reduce the difficulty of the inverse kinematics solution so as to avoid the possible singular solution or even no solution in the inverse kinematics solution process. Assuming that the length of each segment of the flexible arm is equal, only two variables, bending and deflection, are considered, and the solution formula is as follows:

In order to improve the reliability of the solution and reduce the difficulty of the inverse kinematics solution, so as to avoid the possible singular solution or even no solution in the process of inverse kinematics solution. Assuming that each segment of the flexible arm is of equal length and only two variables, bending and deflection, to verify the correctness of the kinematic model, its single-joint kinematic algorithm is simulated in the Matlab simulation environment with the following relevant parameters: the joint length is 140 mm, the diameter of the circle where the drive line is located is 10 mm, the bending angle is [0,

## PATH PLANNING BASED ON PARTICLE SWARM ALGORITHM

### 3.1 Optimal path

In order to ensure the efficient operation of the soft body robot, the planned paths need to be optimized according to different application scenarios and purposes and, thus, need to be optimized under certain criteria^{[18]}. In this paper, we choose to minimize the path length, using the motion path

### 3.2. Obstacle environment modeling

Three-dimensional obstacles generally have irregular geometrical shapes, so this paper uses the regular body envelope of the obstacle to approximate the modeling. This modeling method enlarges the obstacle domain to a certain extent but makes the obstacle domain greatly simplified and effectively improves the efficiency of planning. At a certain moment, as shown in the red joint

A bubble film-wrapped obstacle modeling method is proposed to address the problems of the motion of soft robots. Due to the characteristics of soft body robots in the motion process, soft-body joints will certainly produce motion deflection. This paper is in the obstacle surrounded by another layer of bubble film attached as a non-collision point in particle swarm planning. The positions of joints

By considering constraints such as optimization, security, and feasibility of the path

where

### 3.3. Elementary particle swarm optimization for soft robot trajectory planning

In this paper, considering the structural characteristics of the robot itself and the working environment requirements, only three scatter points need to be designed to avoid the bending angle being too large during the tracking process, which leads to the soft robot posture not being reached. Here, the three scatter points are regarded as one particle, the three-dimensional path is obtained by fitting the three-dimensional spline curve function, and the three-dimensional path length from the starting point to the target point is further solved as the particle adaptation value. In this paper, the simulation is carried out by MATLAB, and the effect is shown in Figure 9. The algorithm first obtains the initial positions and velocities of the particles randomly. It calculates the fitness based on the three scatter points of many particles to obtain the individual and global optimal solutions. Finally, the particle swarm position is updated iteratively by updating the equation:

In the n-dimensional search space, the position of particle ^{[19,20]}. In order to solve these problems, this paper introduces an improved PSO algorithm with adaptive weights, referred to as (Adaptive Weighted PSO, AWPSO), aimed at enhancing the convergence of the speed and execution efficiency of algorithms.

### 3.4. Improved particle swarm optimization for soft robot trajectory planning

The inertia weight of the general particle swarm algorithm is a fixed value. This treatment is simple but may lead to the initial particle distribution being insufficiently uniform and far away from the optimal solution. Consequently, this will cause a large number of unnecessary search operations, which seriously affects the algorithm's efficiency in its implementation. In this paper, we introduce the adaptive weights to strike a balance between the global search ability and the local search ability, thus accelerating the convergence speed of the algorithm. The speed change formula is as follows:

The state in which a particle moves is determined by its velocity, and the particle also adjusts its velocity and searches for optimal solutions based on the experience it has gained and the experience gained by other particles. The more the number of iterations, the more the particles may produce local optimums. Therefore, in order to make the convergence speed of the algorithm faster and avoid obtaining the local optimum, formula (17) is proposed as a new speed update formula. When the particle fails to find the global optimum solution, the speed of the global optimum particle at this time is slightly perturbed so that the convergence speed of the algorithm obtains an improvement.

## 4. PATH TRACKING ALGORITHM BASED ON THE IDEA OF TIP SELF-GROWTH

Path tracking means the soft robot follows a path into the obstacle space and reaches the target point. The required path is collision-free, so this paper studies a path-tracking algorithm based on the idea of "tip self-growth" to make the soft robot move collision-free in complex environments after obtaining the motion path by combining the particle swarm algorithm. The principle is to imitate the motion mechanism of self-growing vine tops in nature; during the path-tracking process, the tip of the soft robot keeps tracking the path while its body matches the path. The computational effort of the kinematic algorithm is significantly reduced.

Efficiently and accurately matching the soft body joints to the desired path at each step is the key problem in path tracking, and the essence of this problem is to efficiently find the points that precisely match the joints under the joint length constraints. This problem can be expressed as the equation:

In the equation, L is the joint length, and the length remains approximately unchanged in states such as bending during motion. The tip self-growth algorithm was developed to improve the efficiency of the planning process. The soft arm tip tracks the path movement, and the algorithm only needs to calculate the motion process of the tip joint

3) Tip self-growth process. After process 2), tip joint

(4) End position adjustment. When the tip joint reaches the target point of the previous interpolation moment

This method only needs to calculate the location point of the tip joint

## 5. SIMULATION EXPERIMENT

In order to verify the correctness and effectiveness of the soft continuous robot head traction algorithm proposed above, the algorithm is simulated and analyzed in the Matlab environment. First, the obstacle map is randomly generated using Matlab in a 3D space with a length and width of 100 cm and a height of 200 cm. The constrained space containing bubble film wrapping is generated by the method described in Section 3.2, as shown in Figure 18. The coordinates of the starting point are located at the point (0, 0, 20). Through the elementary particle swarm algorithm, the number of particles of the algorithm is set to 50, the number of iterations is 300, w=1.2,

At the moment of

Algorithm data comparison ^{[21]}

Algorithm |
1) |
2) |
3) |
4) |
5) |

Time/ms | 10 | 14 | 254 | 490 | 761 |

The next step of the research can be carried out in the following aspects: 1) to build a physical prototype and apply the obstacle avoidance planning algorithm to the real object for the mutual verification of simulation and physical experiments; 2) to consider the error in the physical prototype in the process of movement, design a closed-loop control system with feedback, and optimize it so as to reduce the error; 3) to study and analyze the dynamics model of the soft body robot so as to make the control effect better.

Next, the particle swarm algorithm with basic weights (PSO) and the improved PSO algorithm (AWPSO) are used for path planning of soft body robots to compare the actual results of the two algorithms. The improved PSO algorithm adopts the adaptive weighting PSO algorithm with

Algorithm execution time comparison

Algorithm name |
Starting population |
Number of iterations |
Iterative convergence |
Average value |
Variance |

PSO | 50 | 300 | 26 | 159.2765327 | 60.46499189 |

AWPSO | 50 | 300 | 16 | 154.6223124 | 39.61297271 |

## 6. CONCLUSIONS

The main contribution of this paper is to address the problem of obstacle avoidance planning for the tip self-growing soft robot. Firstly, the configuration and modeling of the soft robot are introduced, and the derivation between the multi-level kinematic mapping relations is completed. Further, the particle swarm algorithm is used to perform a path search in the free motion space of the robot to achieve collision-free path planning. Considering the position deviation of the real robot due to the flexible structure during the motion, the obstacle is modeled with a different design of bubble film wrapping to avoid a collision. The proposed tip self-growing path-following algorithm improves the algorithm's efficiency in path-following. It ensures that the flexible robot can reach the target position while passing through the restricted environment. The effect of the "tip self-growth" algorithm on path tracking is analyzed by MATLAB simulations. The feasibility of particle swarm algorithm-based obstacle avoidance planning for soft robots is verified.

Through theoretical analysis and simulation results to prove its effectiveness, particle swarm-based soft robot path planning can achieve effective obstacle avoidance, and the "tip self-growth" algorithm in the solution is also relatively simple. Therefore, this method can be used for soft robot obstacle avoidance planning while also establishing a foundation for real-time control of the soft robot.

The next step of the research can be carried out in the following aspects: 1) to build a physical prototype and apply the obstacle avoidance planning algorithm to the real object for the mutual verification of simulation and physical experiments; 2) to consider the error in the physical prototype in the process of movement, design a closed-loop control system with feedback, and optimize it so as to reduce the error; 3) to study and analyze the dynamics model of the soft body robot so as to make the control effect better.

## DECLARATIONS

### Acknowledgments

This research was supported by the Defense Basic Research Program (JCKY2020404C001).

### Authors' contributions

Authors' contributions Made substantial contributions to the research and investigation process, reviewed and summarized the literature, and wrote and edited the original draft: Liu H, Jiang Y

Performed oversight and leadership responsibility for the research activity planning and execution and developed ideas and evolution of overarching research aims: Liu M, Su H

Performed critical review, commentary, and revision and provided administrative, technical, and material support: Zhang X, Huo J

### Availability of data and materials

Not applicable.

### Financial support and sponsorship

This research was funded by the Defense Basic Research Program (JCKY2020404C001).

### Conflicts of interest

All authors declared that there are no conflicts of interest.

### Ethical approval and consent to participate

Not applicable.

### Consent for publication

Not applicable.

### Copyright

© The Author(s) 2023.

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## Cite This Article

**OAE Style**

Liu H, Jiang Y, Liu M, Zhang X, Huo J, Su H. Path planning with obstacle avoidance for soft robots based on improved particle swarm optimization algorithm. *Intell Robot* 2023;3(4):565-80. http://dx.doi.org/10.20517/ir.2023.31

**AMA Style**

Liu H, Jiang Y, Liu M, Zhang X, Huo J, Su H. Path planning with obstacle avoidance for soft robots based on improved particle swarm optimization algorithm. *Intelligence & Robotics*. 2023; 3(4): 565-80. http://dx.doi.org/10.20517/ir.2023.31

**Chicago/Turabian Style**

Liu, Hongwei, Yang Jiang, Manlu Liu, Xinbin Zhang, Jianwen Huo, Haoxiang Su. 2023. "Path planning with obstacle avoidance for soft robots based on improved particle swarm optimization algorithm" *Intelligence & Robotics*. 3, no.4: 565-80. http://dx.doi.org/10.20517/ir.2023.31

**ACS Style**

Liu, H.; Jiang Y.; Liu M.; Zhang X.; Huo J.; Su H. Path planning with obstacle avoidance for soft robots based on improved particle swarm optimization algorithm. *Intell. Robot.* **2023**, *3*, 565-80. http://dx.doi.org/10.20517/ir.2023.31

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