Neural-Network-Based Path Planning for a Multirobot System With ...
410
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 39, NO. 4, JULY 2009
Neural-Network-Based Path Planning for a Multirobot System With Moving Obstacles Howard Li, Senior Member, IEEE, Simon X. Yang, Senior Member, IEEE, and Mae L. Seto, Member, IEEE
Abstract—Recently, a coordinated hybrid agent (CHA) framework was proposed for the control of multiagent systems (MASs). It was demonstrated that an intelligent planner can be designed for the CHA framework to automatically generate desired actions for multiple robots in an MAS. However, in previous studies, only static obstacles in the workspace were considered. In this paper, a neural-network-based approach is proposed for a multirobot system with moving obstacles. A biologically inspired neural-networkbased intelligent planner is designed for the coordination of MASs. A landscape of the neural activities for all neurons of a CHA agent contains information about the agent’s local goal and moving obstacles. The proposed approach is able to plan the paths for multiple robots while avoiding moving obstacles. The proposed approach is simulated using both MATLAB and Vortex. The Vortex module executes control commands from the control system module, and provides the outputs describing the vehicle state and terrain information, which are, in turn, used in the control module to produce the control commands. Simulation results show that the developed intelligent planner of the CHA framework can control a large complex system so that coordination among agents can be achieved. Index Terms—Framework, hybrid systems, multiagent systems (MASs), neural networks, path planning. Fig. 1.
Internal structure of a CHA agent.
I. INTRODUCTION ULTIAGENT systems (MASs) represent a group of agents that cooperatively work to solve common tasks in a dynamic environment. Multiagent control systems have been widely studied in the past few years. The control of MASs relates to synthesizing control schemes for systems that are inherently distributed and composed of multiple interacting entities. Because of the wide applications of multiagent theory in large and complex control systems, it is necessary to develop a framework to simplify the process of developing control schemes for MASs. A framework is proposed in [1] and [2] for the distributed control and coordination of MASs. In this framework, the control of MASs is considered as a decentralized control scheme involving coordination of agents. Each agent is modeled as a coordinated hybrid agent (CHA), which is composed of an intelligent coordination control layer (ICCL) and a hybrid
M
Manuscript received March 19, 2008; revised September 1, 2008. First published May 15, 2009; current version published June 17, 2009. This work is supported in parts by Natural Sciences and Engineering Research Council (NSERC) of Canada. This paper was recommended by Associate Editor E. Trucco. H. Li is with the Department of Electrical and Computer Engineering, University of New Brunswick, Fredericton, NB E3B 5A3, Canada (e-mail: [email protected]). S. X. Yang is with the Advanced Robotics and Intelligent Systems (ARIS) Laboratory, School of Engineering, University of Guelph, Guelph, ON N1G 2W1, Canada (e-mail: [email protected]). M. L. Seto is with the Mine and Harbour Defence, Defence Research and Development, Ottawa, ON, K1A 024, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSMCC.2009.2020789
control layer, as shown in Fig. 1. The ICCL takes the coordination input, plant input, and workspace input. After processing the coordination primitives, the ICCL outputs the desired action to the hybrid layer. The ICCL deals with the planning, coordination, decision making, and computation of the agent. The hybrid control layer of the proposed framework then takes the output of the ICCL, and generates discrete control signals and continuous control signals to control the controlled plant in the hybrid control layer, as shown in Fig. 1. It has been demonstrated that an intelligent planner can be designed for the CHA framework to automatically generate desired actions for multiple robots in MASs [3]. The intelligent planner is based on the construction of a biologically inspired neural network. In 1952, Hodgkin and Huxley [4] proposed a computational model for a patch of membrane in a biological neural system using electrical circuit elements. This model provided the foundation of the shunting model and led to a number of model variations and applications [5]. The shunting model is used in [6]–[11]. To build a neural network to solve path-planning problems. However, these applications only deal with one single robot. The neural-networkbased intelligent planner is developed in [3] and [12], for multiple robots. However, only static obstacles are included in the workspace. It is uncertain if we are able to plan paths for multiple robots in a dynamic workspace with moving obstacles. In this study, a topologically organized neural network is designed as the intelligent planner for a CHA system. Moving obstacles are
1094-6977/$25.00 © 2009 IEEE Authorized licensed use limited to: CZECH TECHNICAL UNIVERSITY. Downloaded on September 22, 2009 at 03:45 from IEEE Xplore. Restrictions apply.
LI et al.: NEURAL-NETWORK-BASED PATH PLANNING FOR A MULTIROBOT SYSTEM WITH MOVING OBSTACLES
included in the workspace. Multiple robots have to coordinate in the workspace while avoiding moving obstacles. In the proposed approach, the dynamics of each neuron in the topologically organized neural network is characterized by a shunting neural equation. A landscape of the neural activities for all neurons of a CHA agent contains information about the agent’s local goal, permanent obstacles, and moving obstacles. The goal for the intelligent planner is to plan actions for multiple mobile robots to coordinate with others and achieve the global goal while each agent achieves its local goal. The proposed approach is simulated using both MATLAB and Vortex. Vortex is a software tool that can be used to simulate physics of the real world. The virtual physical world can be used to test and develop navigation strategies for robot platforms. The Vortex module executes control commands from the control system module, and provides the outputs describing the vehicle state and terrain information, which are, in turn, used in the control module to produce the control commands. Simulation results show that an intelligent planner can be designed for the CHA framework for the coordination among agents. Related work is presented in Section II. The proposed intelligent planner for a multiple robot environment with moving obstacles is proposed in Section III. Simulation results for the control of the multirobot system with the application of the proposed intelligent planner are given in Section IV. A discussion is given in Section V. Conclusion and future work are given in Section VI. II. RELATED WORK The CHA framework for coordination control of MASs is introduced. Neural-network-based path-planning methods are discussed.
411
much an agent has completed a series of hybrid actions in order to complete a desired task. 3) Coordination rule base: In order to coordinate the agents while planning, the concept of coordination rule base (CRB) is introduced, which is inspired by social laws defined in [13]. The CRB provides a skeleton for the agents to coordinate with others. 4) Intelligent planner: Without violating the CRB, the ICCL can have built-in intelligent planners to generate actions as the input to the action executor. Following the next coordination state R, the selected action is determined by T : R × A × C → P(R)
(1)
where A is the set of actions, C is the coordination rule set, and P(·) is the power set. Based on the objectives of the agent, the intelligent planner plans the desired coordination state trajectory that fulfills these objectives. The desired trajectory is checked against the CRB to make sure that the trajectory is not violating the rules. After the desired trajectory has been planned, the action a ∈ A for each step along the trajectory can be selected and given as output to the action executor. For a given present state in R, denoted by rp , the next state rn is obtained by rn ⇐ xr n = max{xi , i = 1, 2, . . . , k}
(2)
where x is the degree of fitness of the coordination state and i is the number of the neighboring coordination states including itself, i.e., all possible next states. 5) Implicit communication: This is a mechanism that provides continuous communication among agents for some special tasks. The application of this module can be found in [1].
A. Short Introduction to the Framework for Coordinated Control
B. Neural-Network-Based Path Planning
Many control problems involve processes that are inherently distributed, hybrid, and complex, and that may operate in multiple modes. Agent-based control is an emerging paradigm within the subdiscipline of distributed intelligent control. The CHA framework is proposed in [2] for the distributed control and coordination of MASs. In the proposed framework, the control of MASs focuses on decentralized control and coordination of agents. Each agent is modeled as a CHA that is composed of an intelligent coordination control layer and a hybrid control layer, as shown in Fig. 1. In CHA, the ICCL is built upon the action executor. In this framework, the ICCL plans the sequence of control primitives and selects appropriate hybrid actions without violating the coordination rules. It also communicates with the supervisor and neighboring agents, whenever necessary, to enhance the cooperation and coordination. In the ICCL, we have the following components. 1) Communication mechanism: The ICCL interacts with other agents through the communication mechanism. 2) Coordination states: The ICCL treats the system as a discrete event system. The coordination states represent how
When we apply the CHA framework for large complex systems, it would be ideal if we can plan the coordination among agents dynamically. An agent’s ability to sense and map the environment has always been a limiting factor to autonomous navigation. There are various ways for planning agents motion. Models have been developed in [14]–[16] for the environment in order to carry out the planning tasks. However, the traditional ways of path planning employ recursive algorithms in which unwanted or nonpaths are eliminated in a recursive manner. These algorithms can be computationally expensive. We need an approach that can plan the coordination dynamically without building models for the environment. Neural networks with their parallel and distributed nature of processing seem to provide a natural solution to this problem. A biologically inspired solution is proposed in [17] to use a two-level hierarchical neural network for the mapping of a maze and also the generation of the path, if it exists. In [18], a novel neural network approach is proposed for complete coverage path planning with obstacle avoidance of cleaning robots in nonstationary environments. The dynamics of each neuron in the topologically organized neural network is characterized by a shunting equation derived
Authorized licensed use limited to: CZECH TECHNICAL UNIVERSITY. Downloaded on September 22, 2009 at 03:45 from IEEE Xplore. Restrictions apply.
412
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 39, NO. 4, JULY 2009
from the membrane equation. In [19], this work is extended to real-time concurrent map building and complete coverage of cleaning robots in unknown environments. In [20], it is demonstrated that dynamical neural networks based on the neural field formalism can be used for the control of a mobile robot. The robot navigates in an open environment and is able to plan a path for reaching a particular goal. III. INTELLIGENT PLANNER FOR A MULTIROBOT SYSTEM WITH MOVING OBSTACLES In [5], a biologically inspired neural network approach to collision-free motion planning of mobile robots or robot manipulators is proposed. Each neuron in the topologically organized neural network has only local connections, whose neural dynamics are characterized by a shunting equation. The robot motion is planned through the dynamic activity landscape of neural networks without any prior knowledge of the dynamic workspace. The proposed planning algorithm employs a shunting equation model to establish a neural-network-based optimal pathplanning approach in a 2-D grid cell workspace. Therefore, the planning problem can be transformed into an artificial neuron propagation problem in a 2-D grid cell neuron net. In a grid cell workspace, the actual path of a mobile robot is considered as a sequence of cells that a mobile robot traverses from the initial position to the target position. Each step that the mobile robot takes in the workspace is similar to a neuron that propagates in the neuron net. Therefore, the problem of planning a path is transformed into finding a sequence of cells passed by the activated neuron. With this approach, we can set the target position as a global variable with the highest positive landscape value, which is considered as the peak of the landscape. We set the obstacles as local variables with negative landscape values. They can be thought of as valleys. In the structured landscape workspace, robots with zero value seek for the peak as the global target. The landscape values of the robots will increase gradually when they move closer to the targets. On the other hand, robots will be repelled from valleys of the landscape workspace. The shunting equation is employed to update the landscape activities. There is no training required for this approach. The neural network can learn from the dynamics of the landscape activities automatically. A. Intelligent Planner Inspired by [5], a neural-network-based intelligent planner is proposed for a CHA system that is composed of multiple mobile robots in [3] and a moving obstacle. The fundamental concept of the model proposed in [5] is to develop a neural network architecture, whose dynamic neural activity landscape represents the dynamically varying workspace. The dynamics of the ith neuron is characterized by a shunting equation dxi = −Axi + (B − xi )([Ii ]+ + Σkj=1 wij [xj ]+ ) dt − (D + xi )[Ii ]− .
(3)
By properly defining the external inputs from the workspace and internal neural connections, the target and obstacles are guaranteed to stay at the peak and the valley of the activity landscape of the neural network, respectively. The target can globally attract the robot in the whole workspace through the neural activity propagation, while the obstacles have only local effect to avoid conflicts. The motion planning is realized through the dynamic activity landscape of the neural network. Inspired by this approach, we propose an intelligent planner for the multirobot coordination scenario. We implement a topologically organized neural network that is expressed in a state space S. The location of the jth neuron of the ith agent at the grid in S, denoted by a vector qij ∈ RF , where F represents the dimension of the space, uniquely represents a state of an agent in S. Each neuron has local lateral connections to its neighboring neurons that constitute a subset in S, which is called the receptive field of the jth neuron of the ith agent in neurophysiology. The dynamics of the jth neuron of the ith agent are characterized by a modified shunting equation dxij = −Axij + (B − xij ) dt + m + ([Iij + βIcoold ij ] + Σk =1 wij k [xik ] )
− (D + xij )([Iij + Icoij ]− ).
(4)
1) Parameters A, B, and D represent the passive decay rate, and the upper and lower bounds of the neural activity, respectively. 2) Variable xij is the neural activity of the jth neuron of the ith agent, which has a bounded continuous value xij ∈ [−D, B]. 3) t is a virtual time index that only depends on the occurrence of events. + m 4) The excitatory input, [Iij + βIcoold ij ] + Σk =1 wij k + [xik ] , results from the target, the coordination factors determined by the states of other agents, and the lateral connections among neurons. 5) The external input Iij to the jth neuron of the ith agent is defined as Iij = E if there is a target; Iij = −E if there is an obstacle; Iij = 0 otherwise, where E is a positive constant. 6) β is a coordination recovery rate to adjust the recovery speed of the neural network to the inhibitory stimulus of the conflict states caused by other agents. 7) Icoold ij is the stimulus of the previous conflict state. 8) The inhibitory input [Iij + Icoij ]− results from the obstacles and the conflict states caused by other agents while Icoij is a coordination term determined by a coordination coefficient α. 9) Icoij is defined as Icoij = −αE if there is another agent at that state; Icoij = 0 otherwise. 10) The connection weight wij k from the kth neuron to the jth neuron of the ith agent is defined as wij k = f (|dij k |), where dij k = |qij − qik | represents the Euclidean distance between qij and qik in S. 11) Function f (a) is a monotonically decreasing function, e.g., a function defined as f (a) = µ/a, if 0 < a
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 39, NO. 4, JULY 2009
Neural-Network-Based Path Planning for a Multirobot System With Moving Obstacles Howard Li, Senior Member, IEEE, Simon X. Yang, Senior Member, IEEE, and Mae L. Seto, Member, IEEE
Abstract—Recently, a coordinated hybrid agent (CHA) framework was proposed for the control of multiagent systems (MASs). It was demonstrated that an intelligent planner can be designed for the CHA framework to automatically generate desired actions for multiple robots in an MAS. However, in previous studies, only static obstacles in the workspace were considered. In this paper, a neural-network-based approach is proposed for a multirobot system with moving obstacles. A biologically inspired neural-networkbased intelligent planner is designed for the coordination of MASs. A landscape of the neural activities for all neurons of a CHA agent contains information about the agent’s local goal and moving obstacles. The proposed approach is able to plan the paths for multiple robots while avoiding moving obstacles. The proposed approach is simulated using both MATLAB and Vortex. The Vortex module executes control commands from the control system module, and provides the outputs describing the vehicle state and terrain information, which are, in turn, used in the control module to produce the control commands. Simulation results show that the developed intelligent planner of the CHA framework can control a large complex system so that coordination among agents can be achieved. Index Terms—Framework, hybrid systems, multiagent systems (MASs), neural networks, path planning. Fig. 1.
Internal structure of a CHA agent.
I. INTRODUCTION ULTIAGENT systems (MASs) represent a group of agents that cooperatively work to solve common tasks in a dynamic environment. Multiagent control systems have been widely studied in the past few years. The control of MASs relates to synthesizing control schemes for systems that are inherently distributed and composed of multiple interacting entities. Because of the wide applications of multiagent theory in large and complex control systems, it is necessary to develop a framework to simplify the process of developing control schemes for MASs. A framework is proposed in [1] and [2] for the distributed control and coordination of MASs. In this framework, the control of MASs is considered as a decentralized control scheme involving coordination of agents. Each agent is modeled as a coordinated hybrid agent (CHA), which is composed of an intelligent coordination control layer (ICCL) and a hybrid
M
Manuscript received March 19, 2008; revised September 1, 2008. First published May 15, 2009; current version published June 17, 2009. This work is supported in parts by Natural Sciences and Engineering Research Council (NSERC) of Canada. This paper was recommended by Associate Editor E. Trucco. H. Li is with the Department of Electrical and Computer Engineering, University of New Brunswick, Fredericton, NB E3B 5A3, Canada (e-mail: [email protected]). S. X. Yang is with the Advanced Robotics and Intelligent Systems (ARIS) Laboratory, School of Engineering, University of Guelph, Guelph, ON N1G 2W1, Canada (e-mail: [email protected]). M. L. Seto is with the Mine and Harbour Defence, Defence Research and Development, Ottawa, ON, K1A 024, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSMCC.2009.2020789
control layer, as shown in Fig. 1. The ICCL takes the coordination input, plant input, and workspace input. After processing the coordination primitives, the ICCL outputs the desired action to the hybrid layer. The ICCL deals with the planning, coordination, decision making, and computation of the agent. The hybrid control layer of the proposed framework then takes the output of the ICCL, and generates discrete control signals and continuous control signals to control the controlled plant in the hybrid control layer, as shown in Fig. 1. It has been demonstrated that an intelligent planner can be designed for the CHA framework to automatically generate desired actions for multiple robots in MASs [3]. The intelligent planner is based on the construction of a biologically inspired neural network. In 1952, Hodgkin and Huxley [4] proposed a computational model for a patch of membrane in a biological neural system using electrical circuit elements. This model provided the foundation of the shunting model and led to a number of model variations and applications [5]. The shunting model is used in [6]–[11]. To build a neural network to solve path-planning problems. However, these applications only deal with one single robot. The neural-networkbased intelligent planner is developed in [3] and [12], for multiple robots. However, only static obstacles are included in the workspace. It is uncertain if we are able to plan paths for multiple robots in a dynamic workspace with moving obstacles. In this study, a topologically organized neural network is designed as the intelligent planner for a CHA system. Moving obstacles are
1094-6977/$25.00 © 2009 IEEE Authorized licensed use limited to: CZECH TECHNICAL UNIVERSITY. Downloaded on September 22, 2009 at 03:45 from IEEE Xplore. Restrictions apply.
LI et al.: NEURAL-NETWORK-BASED PATH PLANNING FOR A MULTIROBOT SYSTEM WITH MOVING OBSTACLES
included in the workspace. Multiple robots have to coordinate in the workspace while avoiding moving obstacles. In the proposed approach, the dynamics of each neuron in the topologically organized neural network is characterized by a shunting neural equation. A landscape of the neural activities for all neurons of a CHA agent contains information about the agent’s local goal, permanent obstacles, and moving obstacles. The goal for the intelligent planner is to plan actions for multiple mobile robots to coordinate with others and achieve the global goal while each agent achieves its local goal. The proposed approach is simulated using both MATLAB and Vortex. Vortex is a software tool that can be used to simulate physics of the real world. The virtual physical world can be used to test and develop navigation strategies for robot platforms. The Vortex module executes control commands from the control system module, and provides the outputs describing the vehicle state and terrain information, which are, in turn, used in the control module to produce the control commands. Simulation results show that an intelligent planner can be designed for the CHA framework for the coordination among agents. Related work is presented in Section II. The proposed intelligent planner for a multiple robot environment with moving obstacles is proposed in Section III. Simulation results for the control of the multirobot system with the application of the proposed intelligent planner are given in Section IV. A discussion is given in Section V. Conclusion and future work are given in Section VI. II. RELATED WORK The CHA framework for coordination control of MASs is introduced. Neural-network-based path-planning methods are discussed.
411
much an agent has completed a series of hybrid actions in order to complete a desired task. 3) Coordination rule base: In order to coordinate the agents while planning, the concept of coordination rule base (CRB) is introduced, which is inspired by social laws defined in [13]. The CRB provides a skeleton for the agents to coordinate with others. 4) Intelligent planner: Without violating the CRB, the ICCL can have built-in intelligent planners to generate actions as the input to the action executor. Following the next coordination state R, the selected action is determined by T : R × A × C → P(R)
(1)
where A is the set of actions, C is the coordination rule set, and P(·) is the power set. Based on the objectives of the agent, the intelligent planner plans the desired coordination state trajectory that fulfills these objectives. The desired trajectory is checked against the CRB to make sure that the trajectory is not violating the rules. After the desired trajectory has been planned, the action a ∈ A for each step along the trajectory can be selected and given as output to the action executor. For a given present state in R, denoted by rp , the next state rn is obtained by rn ⇐ xr n = max{xi , i = 1, 2, . . . , k}
(2)
where x is the degree of fitness of the coordination state and i is the number of the neighboring coordination states including itself, i.e., all possible next states. 5) Implicit communication: This is a mechanism that provides continuous communication among agents for some special tasks. The application of this module can be found in [1].
A. Short Introduction to the Framework for Coordinated Control
B. Neural-Network-Based Path Planning
Many control problems involve processes that are inherently distributed, hybrid, and complex, and that may operate in multiple modes. Agent-based control is an emerging paradigm within the subdiscipline of distributed intelligent control. The CHA framework is proposed in [2] for the distributed control and coordination of MASs. In the proposed framework, the control of MASs focuses on decentralized control and coordination of agents. Each agent is modeled as a CHA that is composed of an intelligent coordination control layer and a hybrid control layer, as shown in Fig. 1. In CHA, the ICCL is built upon the action executor. In this framework, the ICCL plans the sequence of control primitives and selects appropriate hybrid actions without violating the coordination rules. It also communicates with the supervisor and neighboring agents, whenever necessary, to enhance the cooperation and coordination. In the ICCL, we have the following components. 1) Communication mechanism: The ICCL interacts with other agents through the communication mechanism. 2) Coordination states: The ICCL treats the system as a discrete event system. The coordination states represent how
When we apply the CHA framework for large complex systems, it would be ideal if we can plan the coordination among agents dynamically. An agent’s ability to sense and map the environment has always been a limiting factor to autonomous navigation. There are various ways for planning agents motion. Models have been developed in [14]–[16] for the environment in order to carry out the planning tasks. However, the traditional ways of path planning employ recursive algorithms in which unwanted or nonpaths are eliminated in a recursive manner. These algorithms can be computationally expensive. We need an approach that can plan the coordination dynamically without building models for the environment. Neural networks with their parallel and distributed nature of processing seem to provide a natural solution to this problem. A biologically inspired solution is proposed in [17] to use a two-level hierarchical neural network for the mapping of a maze and also the generation of the path, if it exists. In [18], a novel neural network approach is proposed for complete coverage path planning with obstacle avoidance of cleaning robots in nonstationary environments. The dynamics of each neuron in the topologically organized neural network is characterized by a shunting equation derived
Authorized licensed use limited to: CZECH TECHNICAL UNIVERSITY. Downloaded on September 22, 2009 at 03:45 from IEEE Xplore. Restrictions apply.
412
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 39, NO. 4, JULY 2009
from the membrane equation. In [19], this work is extended to real-time concurrent map building and complete coverage of cleaning robots in unknown environments. In [20], it is demonstrated that dynamical neural networks based on the neural field formalism can be used for the control of a mobile robot. The robot navigates in an open environment and is able to plan a path for reaching a particular goal. III. INTELLIGENT PLANNER FOR A MULTIROBOT SYSTEM WITH MOVING OBSTACLES In [5], a biologically inspired neural network approach to collision-free motion planning of mobile robots or robot manipulators is proposed. Each neuron in the topologically organized neural network has only local connections, whose neural dynamics are characterized by a shunting equation. The robot motion is planned through the dynamic activity landscape of neural networks without any prior knowledge of the dynamic workspace. The proposed planning algorithm employs a shunting equation model to establish a neural-network-based optimal pathplanning approach in a 2-D grid cell workspace. Therefore, the planning problem can be transformed into an artificial neuron propagation problem in a 2-D grid cell neuron net. In a grid cell workspace, the actual path of a mobile robot is considered as a sequence of cells that a mobile robot traverses from the initial position to the target position. Each step that the mobile robot takes in the workspace is similar to a neuron that propagates in the neuron net. Therefore, the problem of planning a path is transformed into finding a sequence of cells passed by the activated neuron. With this approach, we can set the target position as a global variable with the highest positive landscape value, which is considered as the peak of the landscape. We set the obstacles as local variables with negative landscape values. They can be thought of as valleys. In the structured landscape workspace, robots with zero value seek for the peak as the global target. The landscape values of the robots will increase gradually when they move closer to the targets. On the other hand, robots will be repelled from valleys of the landscape workspace. The shunting equation is employed to update the landscape activities. There is no training required for this approach. The neural network can learn from the dynamics of the landscape activities automatically. A. Intelligent Planner Inspired by [5], a neural-network-based intelligent planner is proposed for a CHA system that is composed of multiple mobile robots in [3] and a moving obstacle. The fundamental concept of the model proposed in [5] is to develop a neural network architecture, whose dynamic neural activity landscape represents the dynamically varying workspace. The dynamics of the ith neuron is characterized by a shunting equation dxi = −Axi + (B − xi )([Ii ]+ + Σkj=1 wij [xj ]+ ) dt − (D + xi )[Ii ]− .
(3)
By properly defining the external inputs from the workspace and internal neural connections, the target and obstacles are guaranteed to stay at the peak and the valley of the activity landscape of the neural network, respectively. The target can globally attract the robot in the whole workspace through the neural activity propagation, while the obstacles have only local effect to avoid conflicts. The motion planning is realized through the dynamic activity landscape of the neural network. Inspired by this approach, we propose an intelligent planner for the multirobot coordination scenario. We implement a topologically organized neural network that is expressed in a state space S. The location of the jth neuron of the ith agent at the grid in S, denoted by a vector qij ∈ RF , where F represents the dimension of the space, uniquely represents a state of an agent in S. Each neuron has local lateral connections to its neighboring neurons that constitute a subset in S, which is called the receptive field of the jth neuron of the ith agent in neurophysiology. The dynamics of the jth neuron of the ith agent are characterized by a modified shunting equation dxij = −Axij + (B − xij ) dt + m + ([Iij + βIcoold ij ] + Σk =1 wij k [xik ] )
− (D + xij )([Iij + Icoij ]− ).
(4)
1) Parameters A, B, and D represent the passive decay rate, and the upper and lower bounds of the neural activity, respectively. 2) Variable xij is the neural activity of the jth neuron of the ith agent, which has a bounded continuous value xij ∈ [−D, B]. 3) t is a virtual time index that only depends on the occurrence of events. + m 4) The excitatory input, [Iij + βIcoold ij ] + Σk =1 wij k + [xik ] , results from the target, the coordination factors determined by the states of other agents, and the lateral connections among neurons. 5) The external input Iij to the jth neuron of the ith agent is defined as Iij = E if there is a target; Iij = −E if there is an obstacle; Iij = 0 otherwise, where E is a positive constant. 6) β is a coordination recovery rate to adjust the recovery speed of the neural network to the inhibitory stimulus of the conflict states caused by other agents. 7) Icoold ij is the stimulus of the previous conflict state. 8) The inhibitory input [Iij + Icoij ]− results from the obstacles and the conflict states caused by other agents while Icoij is a coordination term determined by a coordination coefficient α. 9) Icoij is defined as Icoij = −αE if there is another agent at that state; Icoij = 0 otherwise. 10) The connection weight wij k from the kth neuron to the jth neuron of the ith agent is defined as wij k = f (|dij k |), where dij k = |qij − qik | represents the Euclidean distance between qij and qik in S. 11) Function f (a) is a monotonically decreasing function, e.g., a function defined as f (a) = µ/a, if 0 < a
