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Abstract In this paper a self modeling method based on a causal network is proposed for the tracking control of the Crawler Fire Fighting Robot CFFR The method mainly consists of two parts one is a motion model based on data driving learning to establish the correspondence between control signal sequence and vehicle motion estimating the motion state of the next moment from historical data eliminating complex CFFR modeling The other is the tracking network Based on the simulation data of the motion model the relationship between the target trajectory and the current control command is learned which simplifies the design and cumbersome tuning of the complex controller The effectiveness of the proposed method is verified in both simulated and real world environments Qualitative and quantitative experimental results verify the accuracy of the tracking I INTRODUCTION When a fire breaks out the scene is extremely harsh High temperature smoke toxic gases and other hazards pose a great threat to firefighters Therefore firefighters rush into the fire to carry out rescue sometimes not only the task cannot be completed but also increase casualties In this case the assistance of robots is important They belong to special robots mainly composed of water cannons sensors and other equipment CFFRs are characterized by high temperature resistance corrosion resistance and strong maneuverability they can not only extinguish fire in dangerous areas but also efficiently collect key information to support on site command 1 In different scenarios multiple types of robots participate in firefighting 2 3 Forests and indoor fires are usually detected by drones and then fired by ground vehicles by spraying air water or foam 4 5 In practice CFFR is a vital equipment because the medium required for firefighting is usually transported by a flexible pipe that is towed by the vehicle requiring a large traction of the robot while the rubber tires of the wheeled vehicle are not ideal for heat or explosion resistance The CFFR not only overcomes these shortcomings but also has the advantages of strong obstacle resistance With the on board sensors CFFR can already identify the location of the fire 6 7 and plan path in real time based on SLAM and obstacle avoidance algorithm 8 Even so most of the CFFRs are manually operated within the visible range of people and in a wide field making it difficult to rush into the This work is supported by the National Key R D Program of China grant 2017YFB1300202 Science and Technology on Space Intelligent Control Laboratory for National Defense No KGJZDSYS 2018 09 National Natural Science Foundation of China under Grant U1713222 61773378 81671854 Major Science and Technology Projects in Henan Province No 161100210900 The authors are with the State Key Laboratory of Management and Control for Complex Systems Institute of Automation Chinese Academy of Sciences Beijing 100190 China changwenkai2013 indoor fire In addition to the lack of perception the difficult accurate tracking control is another reason especially in the environment with obstacles manual operation is also difficult to pass smoothly The main reason is that the motion model of crawler vehicles is complicated The steering can only rely on the differential control of the caterpillar tracks and the sliding friction with the ground is difficult to accurately model Traditional methods focus on modeling and designing controllers Crawler vehicles are non holonomically constrained mechanical systems that lack a stable smooth and time invariant state feedback and require more nonlinear control Keiji 9 integrated odometer and inertial measurement unit IMU focusing on eliminating the cumulative error in the turning process Yang 10 utilized synovial control to obtain gradual convergence trajectory deviation Zhao 11 proposed a kinematics aware model based on online parameter identification for high speed crawler vehicles Adaptive fuzzy control 12 and robust adaptive control 13 14 15 are also applied to the tracking problem of crawler vehicle with uncertainty model and random interference although some effects have been achieved the modeling process is complicated Hoang 16 introduced a neural based adaptive controller to cope with the uncertainty of the non holonomic model which simplifies the construction of controller but the algorithm only has simulation results Unlike the single model described above Edwin 17 employed a layered approach several models such as motion model and control model were established and Tang 18 introduced more mechanical parameters to establish a high speed motion model Said 19 combined the soil parameters with the caterpillar track parameters to refine the motion model and control method in different soils but the model is complicated and the overall optimization is difficult As can be seen model based methods require careful parameters tuning In addition to the control problems of crawler vehicles CFFR has its own particularity The CFFR is heavy and driven by motors which are protected by limiting the acceleration but this results in a slow response further increasing the control difficulty And with the increasing demand for indoor firefighting 20 CFFR requires a more accurate and concise tracking control method In actual deployment the skilled operator can estimate the CFFR motion trajectory through the feel and improve the accuracy of the operation in advance Inspired by this we designed a similar process to learn the correspondence between control and motion response sequences The robot itself can self model the motion model based on the historical driving data and then estimate the current control command based on the future trajectory This overall modeling method has been involved in multi degree of freedom robots and achieved good results 21 22 Self modeling Tracking Control of Crawler Fire Fighting Robot Based on Causal Network Wenkai Chang Peng Li Caiyun Yang Tao Lu Yinghao Cai and Shuo Wang 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE3911 In view of the complexity of the crawler vehicle control this paper proposes to use the data driven self modeling algorithm to learn the CFFR motion model and control model respectively The motion model learns the vehicle motion state from historical data and the control model estimates the control command from the future trajectory Each model corresponds to a separate network which not only increases the interpretability of the learning process but also transforms the traditional complex tuning process into a self modeling process The following structure is as follows Section II introduces the characteristics of the experimental platform Section III describes the motion model learning method and Section IV introduces the self modeling process of the control model Section V is the experiment and finally in conclusion II STRUCTURAL CHARACTERISTICS The experimental platform is shown in Fig 1 a The water cannon and the electric control cabinet are installed on the crawler vehicle The CFFR is powered by battery and driven by servo motors The control of current loop position loop and speed loop are included in the motor driver which is connected to the Beckhoff controller using EtherCAT The PLC program coordinates the two motor driven wheels in the controller and controls the orientation of the water cannon The industrial computer in the cabinet is the vehicle control unit VCU and the communication is maintained by Robot Operating System ROS Automation Device Specification ADS 23 is utilized for data exchange between the computer and the controller As shown in Fig 1 c the PID controller makes the motor follow the set speed After various nonlinear constraints and safety protection the motion control becomes even more difficult Such as the controller limits the maximum acceleration of the platform which in turn limits the maximum current of the driver as shown in Fig 1 d the vehicle needs up to 1 5s to stabilize at the target speed However the crawler vehicle relies on differential steering and the delay increases the complexity of automatic control Therefore the core of self modeling of motion model is to learn the corresponding between control command and the motion state and the motion state needs to be extracted from the motion trajectory The single line Laser Range Finder LRF and IMU on the experimental platform can be used to obtain the position and motion state with SLAM based method 24 In addition the slow response is another feature that requires self modeling the recording of control signal and position signal should be kept in synchronism For the convenience of description a coordinate system is shown in Figure 2 where represents the coordinate system of the vehicle and the global coordinate system represents initial vehicle position of trajectory The center of the vehicle is set to indicates the position of in and indicates the orientation in and is obtained in real time represents the control commands of the left and right motor They are sent by the remote controller during the sampling phase and are issued by the VCU during the automatic tracking Fig 1 The experiment platform a b illustrate the vehicle structure c is the control system logic and d shows the vehicle motion response curve Fig 2 Illustration of the coordinate system of platform III SELF MODELING MOTION MODEL The self modeling of motion is to establish a mapping between the control signal and the motion state sequence that is the model contains the complex frictional motion during the turning process and the response delay Training data is the basis of self modeling Therefore this section will first describe the input and output parameters and then introduce the self modeling network structure A Velocity or Location From control signals to vehicle motion electrical energy is changed into kinetic and thermal energy while velocity and angular velocity reflect the kinetic energy recorded as Considering the response delay the model needs 3912 to predict the current moment and from a series of historical control commands historical kinetic energy indicators and current control commands The relationship is abbreviated as which represents the dynamic characteristics of the vehicle based on the speed parameters The Learning can be implemented in complex models and neural networks However the original information obtained by the sensor is the position Velocity is usually calculated based on a series of position points In general the trajectory curve can be fitted and the length is obtained by integration and then the velocity can be estimated The tangential direction of the starting point can be used as the direction of the velocity and the angular velocity can also be obtained according to a similar calculation During this process the estimated velocity does not add new information compared to the position but increases the calculation Therefore the positional parameters are more suitable for modeling the motion model where is the position and orientation of the vehicle in the global coordinate system at time and the mapping in Equation 2 is denoted by indicating that the can be estimated from current control command and the position sequence before time Compared with eliminates the estimation of speed In this paper a neural network based on causal network is proposed to implement which estimates the motion model of the whole vehicle by learning how to estimate the next position from the known trajectory Fig 3 Illustration of the trajectory normalization For the operation of the neural network the input data needs to be normalized As shown in Figure 3 with reference to the coordinate a rectangular area with side length is defined as the field of view around the robot The trajectory points are mapped into and then normalized as where and the scope fits the activation function ReLU 25 in neural network Since the rectangular field of view is established with reference to the robot direction is specified as the angle is distributed counterclockwise from 0 to and the orientation of other trajectory points are normalized to A continuous trajectory is intercepted from the normalized trajectory and the goal of self modeling is to predict from the sequence It is worth noting that the point in can only infer the speed information from while in also contains the information before But the effect is weak because the next motion state is most closely related to the state of the current moment and its neighboring moments The farther the distance is the weaker the impact B The Network Structure Inspired by causal network 26 a multi channel input network is proposed which contains trajectory segment and instructions that needed to predict the motion state The structure of the network is shown in Fig 4 Fig 4 Illustration of the motion model network a is a thumbnail of the entire network b data flow structure c multi channel data merge structure The descriptions and structures of layers nodes b c are corresponding The input of the network needs to consider both the pose and the control command These heterogeneous signals contain different noises and features Before inputting the causal network the signal sequences pass through 2 layers of convolution see Fig 4 b c and the convolution takes only the valid bits The input sequence therefore loses 4 positions before entering the causal network The output feature map is then input into the 9th 8th 7th 6th layer causal network At 5th layer channels add together The predicted vehicle state information is output separately through three convolution The input is 512 and output is 1 3913 Causal convolution relies solely on historical data and the field of view needs to be considered Since the vehicle trajectory sampling rate is 25Hz far less than the 16 kHz audio information in the original literature the 9 layer causal convolution can obtain a field of view of 29 1 256 points which corresponds to 256 25 10 24s driving trajectory CFFR has been driving a long distance Larger fields of view also attempt to allow the network to learn the current frictional characteristics of the caterpillar track and the ground as this characteristic is critical to the motion model The step of the dilated convolution 27 is shown in Table I In order to increase the network depth while maintaining the dilated convolution network structure each node is set to 3 layer residual convolutions 28 Except for the 9th layer the nodes inputs are the cascade of the two feature maps of the previous layer and then passes through 3 residual convolutions see Fig 5 The output channel of each node is consistent with the input where represents the input channels TABLE I THE STEP OF DILATED CONVOLUTION Layer 9 8 7 6 5 4 3 2 1 Step 1 2 4 8 16 32 64 128 256 2 4 8 16 32 64 128 256 512 Fig 5 The structure of the nodes in the neural network C Training Loss The final output of the causal network is then processed through three convolutions to generate the that needs to be predicted The training loss function is where represents the ground truth The network processes the control signal as two channels parallel to the motion signal and abandoned the Gated Activation Unit 26 in the original text The training sample is a trajectory denoted as where represents the total number of points in trajectory and indicating the 256 input nodes in 9th layer and the 4 loosed position in bottom convolution Since the causal convolution belongs to the autoregressive network the currently output parameter is the input of the next moment the training follows the same mechanism and the in utilize the output of the previous moment The total loss is Manually controlling the vehicle to travel randomly can generate raw trajectory samples and the distribution of should be made uniform The training sample is formed by randomly intercepting sub trajectory Since the positioning signal is 25Hz and the control signal is 30 Hz based on the corresponding values of the control signals are calculated linearly by time The trained network can simulate the motion model of CFFR on the indoor floor providing support for subsequent self modeling tracking IV SELF MODELING TRACKING Using the motion model network in the virtual environment the trajectory under different command can be simulated and the evaluation function can search optimal control strategy But for tracking it is more efficient to derive the control command based on a path that is going to travel rather than a target point In turn using the neural network to learn the strategy based on future trajectories can avoid repeated simulations and searches and increase real time performance A Control Strategy The trajectory and control commands during are known and the vehicle needs to follow the trajectory during According to the trained simulator and the vehicle state at random values are taken in the space based on and then after a period of simulation compared with the target trajectory the highest evaluation control commands can be obtained Fig 6 The measure of similarity between trajectories a is the actual trajectory and the mapping of the simulated trajectory b shows the details of the simulated trajectory processing The method for evaluating the similarity of two trajectories is shown in Fig 6 For each control command the trajectory in the future steps are simulated and the points beyond the border range are discarded and the intersection with the frame is defined as the last point A fixed number of points are sampled in equal steps from the starting point to the ending point The smaller the distance between the corresponding points in the two trajectories the more similar 3914 the two trajectories are For the convenience of calculation the sampling points are equally spaced on the fold line Specifically the length of the fold line is calculated first and the points are s

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