Research on Path Planning of Concrete Pouring Construction Robot Based on Online Obstacle Avoidance Algorithm

Abstract

Aiming at the problem of harsh concrete construction environment and low level automation of concrete pouring operation, this paper proposes an autonomous concrete pouring planning method based on real-time obstacle avoidance algorithm. A new 3-DoF articulated concrete pouring robot is designed and kinematically modeled. Rectangular fitting is adopted to simplify irregular obstacles. Then generate obstacle maps and apply intelligent obstacle avoidance algorithms based on the maps, which adopt the reward mechanism in reinforcement learning. The effectiveness of the proposed method in autonomous obstacle avoidance path planning for pouring robots is demonstrated through simulation and prototype experiments.

1 Introduction

Concrete pouring refers to the process of pouring concrete material into a designed mold until it is plasticized [1], and now concrete pump trucks and pumping pouring technology are mostly used for pouring operations [2]. In the real concrete pump truck pouring process, the cooperative control of the pump truck boom often depends on the rich experience of the construction site operators [3], through manual control of the end joint hose to ensure that the end of the boom pouring mouth in accordance with the expected trajectory to move, so as to better complete the concrete pouring [4]. However, under this operation method, there are certain safety troubles, which not only directly affect the quality of pouring, but also threaten personal safety. And as the scale of urban construction is expanding, in order to alleviate the situation of tense construction land, the development of high building is accelerating, and at the same time, the complexity of the building structure is also increasing, especially in the ultra-long, large-volume concrete pouring surface, ultra-high-rise buildings, the concrete pouring of underground steel sinkholes, the application of the traditional boom-type concrete pump trucks has a certain test [5, 6]. Therefore the robotization of the concrete pouring process is particularly urgent and important for the development of construction engineering and intelligent construction.

In the early stage, the research on concrete pump trucks mainly focused on the structural analysis and vibration suppression control of the boom. Guo et al. carried out a finite element analysis of the horizontal working condition of the material handling mechanism and obtained the dynamic response of the material handling system structure, as well as the distribution of the stress and deformation of the system at various moments of the time [7]. Khulief et al. designed a vibration control method of the boom by establishing a finite element model of a flexible arm and analyzing the dynamics characteristics [8]. Qiu et al. studied the synchronized positioning control and vibration suppression of a new type of flexible robotic arm [9]. Henikl et al. took the concrete pump truck boom as the research object, applied the modal control theory, and put forward the concept of active damping and decentralized control of the vibration of the flexible arm of the pump truck. Applications are ineffective and considered an active control method to suppress boom vibration [10]. Cazzulani et al. concluded that the method of vibration suppression through external passive compensating devices is not effective in concrete placing applications and considered an active control method to suppress boom vibration [11].

Concrete pouring construction robot is the latest improvement of intelligent construction machinery based on the truck mounted concrete pump which is now heavily used in the field of concrete pouring [12]. Recently, more and more researchers pay attention to the new construction machinery because it has both the practicality of the traditional concrete pouring machinery and the intelligence of the robot. Due to the complex and changing environment of concrete construction, the existence of pouring exclusion zones is often faced during the concrete pouring process, including the area where the pouring has been completed and the multiple construction equipments that exist in the construction site. Therefore, it is essential to plan the pouring path of this construction robot in real time, particularly with regard to construction safety. Huang et al. proposed a pseudo-distance based obstacle avoidance method for the end obstacle avoidance and boom joint limitation problems of concrete pouring robots, which is currently a more advanced research in obstacle avoidance of pouring robots [13]. In addition, in terms of path planning based on obstacle avoidance, reinforcement learning is currently a more advanced intelligent algorithm, and current applications have been able to achieve good autonomous planning performance, especially in the field of mobile robots [14].

Considering the impact of the construction environment on concrete pouring, an intelligent trajectory planning method based on grid map is proposed for a 3-DoF articulated concrete pouring construction robot, which applies an advanced real-time obstacle avoidance algorithm with improvements for the first time.

In this paper, we will combine the algorithmic ideas in reinforcement learning and the characteristics of concrete pouring construction to establish an autonomous path planning system for concrete pouring robots. The new designed robot is firstly analyzed for kinematics and a complete kinematic model with D-H parameter method is also developed. Then, the simplified pouring map with obstacles is building based on the construction environment. Aiming at the obstacle avoidance in the map, the Bellman equation in reinforcement learning is used as the obstacle avoidance policy.

Moreover, experiments were conducted on a prototype robot based on the obstacle avoidance method. Finally, the results of simulation and experiment show that the presented method in this research is well performed to avoid obstacles autonomously, and this research has a prospective impact on the field of autonomous concrete construction machinery.

2 Robot Modeling and Analysis

In order to better achieve the intelligence of concrete pouring construction, in this study, a 3-DoF articulated concrete pouring construction robot is designed according to the existing structure of the concrete pouring boom, and it is used as the research object of pouring trajectory planning.

2.1 Design of Robot Structure

As shown in Fig. 1, the robot structure refers to the design of simple rotary joints for concrete pouring boom to simplify motion control, reduce the complexity of the combined motion of arm stretching and rotating in traditional concrete pouring machinery. It is suitable for later integration with intelligent platforms and the application of algorithms to facilitate the control of multiple robots. The robot structure consists of 4 parts, including: 1-column, 2-pouring pipeline, 3-horizontal support part, 4-slewing ring bearing. The column assembly adopts lightweight truss structure, which plays a reinforcing role, and it is easy to disassemble and adapt to pouring planes of different heights, especially for ultra-high level planes which cannot be reached by traditional concrete pump trucks. Concrete and fluid are transported to the pipeline section through the pump and output pouring at the end of the pipeline. The pipe section is supported by part 3 and part 4 and connected by part 4, which is equivalent to the robot rotary joints and driven by servo motors.

Fig. 1

The structure of concrete pouring construction robot

Figure 2 shows the working range of the concrete pouring construction robot, with 2 degrees of freedom in the pouring plane x–y and 3 degrees of freedom for the 3-joint pouring robot. Therefore, an additional redundant degree of articulation increases the number of possible pouring path solutions and simplifies the structural complexity of the robot. It is suitable for the more complex construction environment and working conditions, which can further improve the construction efficiency and reduce the construction cost by enhancing the operational flexibility of the pouring robot and strengthening the stability of the mechanism under the adverse working conditions.

Fig. 2

The working range of the concrete pouring construction robot

2.2 Kinematic Modeling and Analysis

Considering that the robot concrete pouring work is done in Cartesian space and the motion control of the robot is based on Joint space, kinematic modeling of the robot is needed to complete the conversion from Cartesian space to Joint space. Based on the above new designed robot structure and D-H parameter representation, the model under the Cartesian space is established in the Robotics Toolbox in MATLAB, as shown in Fig. 3.

Fig. 3

The corresponding structure in MATLAB

The robot has four coordinate systems, which are including a base coordinate system and three joint coordinate systems. Then the positive kinematic model of the robot is established based on the coordinate systems, and the relationship between neighboring coordinates is deduced as formula (1).

$${}_{i}^{i - 1} T = \left[ {\begin{array}{*{20}c} {\cos \theta_{i} } & { - \sin \theta_{i} } & 0 & 0 \\ {\sin \theta_{i} } & {\cos \theta_{i} } & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} } \right] \times \left[ {\begin{array}{*{20}c} 1 & 0 & 0 & {l_{i} } \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} } \right]$$

(1)

i is the number of joints of the robot, here i = 3. To simplify the equation, ci and si denote a and b respectively. Substitution can be made to obtain the relationship between the pouring actuator of the robot and the fixed base as formula (2).

$$\begin{aligned} {}_{3}^{0} T & = {}_{1}^{0} T \times {}_{2}^{1} T \times {}_{3}^{2} T \\ & { = }\left[ {\begin{array}{*{20}c} {{\text{n}}_{x} } & {{\text{o}}_{x} } & {a_{x} } & {{\text{p}}_{x} } \\ {{\text{n}}_{y} } & {{\text{o}}_{y} } & {a_{y} } & {{\text{p}}_{y} } \\ {{\text{n}}_{x} } & {{\text{o}}_{z} } & {a_{z} } & {{\text{p}}_{z} } \\ 0 & 0 & 0 & 1 \\ \end{array} } \right]{ = }\left[ {\begin{array}{*{20}c} {{\text{c}}_{123} } & { - {\text{s}}_{123} } & 0 & {l_{1} {\text{c}}_{1} + l_{2} {\text{c}}_{12} + l_{3} {\text{c}}_{123} } \\ {{\text{s}}_{{{123}}} } & {{\text{c}}_{123} } & 0 & {l_{1} {\text{s}}_{{1}} + l_{2} {\text{s}}_{12} + l_{3} {\text{s}}_{123} } \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} } \right] \\ \end{aligned}$$

(2)

As shown in the simplified schematic of the robot in Fig. 4, the inverse kinematics model of the robot is solved based on the above positional relationship, so that the rotation joint angles of the robot $\theta_{1} ,\theta_{2} ,\theta_{3}$ can be obtained from the known coordinates of the pouring point ${\text{P}}_{x} ,{\text{P}}_{y}$, and the inverse kinematics model is calculated by the geometric method as formula (3).

$$\left\{ {\begin{array}{*{20}l} {P_{x} = l_{1} \times \cos \upalpha _{1} + l_{2} \times \cos \upalpha _{2} + l_{3} \times \cos \upalpha _{3} } \hfill \\ {P_{y} = l_{1} \times \sin \upalpha _{1} + l_{2} \times \sin \upalpha _{2} + l_{3} \times \sin \upalpha _{3} } \hfill \\ {\upalpha _{1} = \theta_{1} } \hfill \\ {\upalpha _{2} = \upalpha _{1} + \theta_{2} = \theta_{1} + \theta_{2} } \hfill \\ {\upalpha _{3} = \upalpha _{2} + \theta_{3} = \theta_{1} + \theta_{2} + \theta_{3} } \hfill \\ \end{array} } \right.$$

(3)

Fig. 4

Simplified schematic of robot

After solve the equations simultaneously, the following joint angles are obtained for each pouring point.

3 Concrete Pouring Path Planning

In the construction site, the pouring exclusion zone is usually irregular, considering that the precision requirement of concrete pouring operation is not high, in order to facilitate the faster application of obstacle avoidance algorithms, irregular obstacles are fitted into rectangles, as shown in Fig. 5a, and the orange part is the irregular obstacle. The input obstacle is subjected to image processing, using MATLAB Image Processing Toolbox to obtain the edge contour of the irregular obstacle, dispersing it into a series of coordinate points ($x_{bi} ,y_{bi}$) and seeking its extreme value, and then, as in formula (4), the difference of the extreme value obtained in its x and y coordinates respectively is used as the length a and width b to automatically fit a rectangular obstacle enclosing all coordinate points.

$$\left\{ {\begin{array}{*{20}c} {{\text{a}}_{j} = \left| {\max ({\text{x}}_{bi} ) - \min ({\text{x}}_{bi} )} \right|} \\ {{\text{b}}_{j} = \left| {\max ({\text{y}}_{bi} ) - \min ({\text{y}}_{bi} )} \right|} \\ \end{array} } \right.$$

(4)

Fig. 5

Simplified fitting obstacle

For obstacles with a certain height, the mid-arm avoidance also needs to be considered. In order to simplify the pouring path computational solution, the concept of safety margin is utilized to form a safe avoidance area outside the simplified obstacle, as shown in Fig. 5b. The width s of the margin area consists of the reaction distance $s_{re}$ and braking distance of the robot $s_{{{\text{br}}}}$, and since each arm may not have the same motion speed, the maximum value of the all arms width is taken as s as shown in formula (5).

$$\left\{ {\begin{array}{*{20}l} {{\text{s}} = \max \left( {{\text{s}}_{re} + {\text{s}}_{br} } \right)} \hfill \\ {{\text{s}}_{re} = \left| {{\text{v}}_{cui} \cdot {\text{t}}} \right|} \hfill \\ {{\text{s}}_{br} = \left| {\frac{{{\text{v}}_{cui} }}{{2 \cdot\upmu \cdot {\text{a}}_{bri} }}} \right|} \hfill \\ \end{array} } \right.$$

(5)

In the above formula, ${\text{v}}_{cui}$ is the current end running speed of robot arm i, t is the reaction time, ${\text{a}}_{bri}$ is the braking acceleration, and μ is the braking damping coefficient. Based on the above method, obstacle fitting is performed to obtain a simplified construction environment map with obstacles as shown in Fig. 6.

Fig. 6

Simplified construction environment map

Obstacle avoidance adopts an intelligent algorithm based on a reinforcement learning reward mechanism, where the core idea in reinforcement learning is the solution of the Bellman equation as shown in formula (6) [15].

$$V_{\uppi } \left( s \right) = \sum\limits_{a} {\pi \left( {a\left| s \right.} \right) \cdot \left[ {\sum\limits_{r} {p\left( {r\left| {s,a} \right.} \right) \cdot r +\upgamma \cdot \sum\limits_{s^{\prime}} {V_{\uppi } \left( {s^{\prime } } \right) \cdot p\left( {s^{\prime } \left| {s,a} \right.} \right)} } } \right]}$$

(6)

a, s, s′, r, π represent the important components of reinforcement learning action, state, next moment state, reward and policy respectively. The state value $V_{\uppi } \left( s \right)$ is obtained by solving the Bellman equation after substituting all the values of given quantity. The state space S of the pouring robot consists of the angle values of each joint of the robot and can be expressed as in formula (7).

$${\text{s}}_{i} = [\theta_{1i} ,\theta_{2i} ,\theta_{3i} ],{\text{s}}_{i} \in {\text{S}},{\text{S}} \in \left[ { - 360^{ \circ } ,360^{ \circ } } \right]$$

(7)

The action a of the pouring robot is composed of 3 actions, forward motion, stationary and backward motion, which has the value of unit joint rotation or 0. Since the robot has 3 joints, the action matrix has the specification of 3×3×3, which represents 27 states under all feasible actions of the robot. To prevent falling into a long term static state dead zone, state [0, 0, 0] are removed, thus the action matrix a includes 26 action states that are feasible for the concrete pouring robot. In the reward r setting, r consists of $r_{1}$, $r_{2}$, $r_{3}$ as shown in formula (8).

$${\text{r}} = r_{1} + r_{2} + r_{3}$$

(8)

In the setting of $r_{1}$, when the robot arm passes through the obstacle area, $r_{1} = - \infty$, and vice versa $r_{2} = 0$, which ensures the obstacle avoidance function of the robot arm. In the setting of $r_{2}$, $r_{2}$ is the sum of all unit joint rotation, which ensures the optimal energy target of the robot arm motion. In the setting of $r_{3}$, when the end of the robot arm reaches the target pouring position, a larger reward value scalar ${\text{R}}_{{{\text{tar}}}}$ is given to $r_{3}$, which ensures that the robot can reach the correct pouring area.

Then solve formula (6) after predefine discount factor γ, and iteratively update it to find the maximum state value and output the policy as the optimal solution. As shown in Fig. 7, after applying the obstacle avoidance algorithm based on the simplified obstacle map, the frobot can achieve good obstacle avoidance performance.

Fig. 7

Algorithm-based simulation demonstration

4 Experiment and Verification

According to the intelligent pouring path planning method proposed in this research, the planning system of the robot was established, as shown in Fig. 8, and experiments were carried out on the prototype of the concrete pouring robot.

Fig. 8

Algorithm-based concrete pouring construction robot planning system

The concrete pouring construction robot planning system is divided into 3 parts, including path planning, trajectory generation and prototype experiment of the robot. In the path planning part, the obstacles are first fitted into rectangles using the planning method proposed in this research, and it is used to build a simplified construction map. In the prototype experiments, colorful stickers are used to represent the fitting obstacles. The robot then generates a series of actions in the trajectory generation to conform to the optimally planned path and forms a joint angle curve $\theta_{i} \left( {\text{t}} \right)$ from the values of this action. The joint motion signal is transmitted to the servo controller, performs the servo motor control of the robot three rotary joints. Finally, the experimental results showed the feasibility of the planning method proposed in this research.

5 Conclusion

In this paper, a new 3-DoF articulated concrete pouring construction robot is designed, and a robot autonomous pouring path planning method is proposed based on this robot structure. For the complex and changeable construction environment, a simplified obstacle map is established, and an obstacle avoidance algorithm based on reinforcement learning idea is applied. In the simulation and prototype experiments, the method shows obstacle avoidance feasibility, which is a good reference value for the intelligence of concrete construction robots.