CN107807534B - Self-adaptive cooperative control algorithm and control system for multi-wheeled robot - Google Patents
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Abstract
The invention discloses a self-adaptive cooperative control algorithm and a control system of a multi-wheel robot, wherein the control algorithm comprises the following steps: step 1: establishing a multi-wheeled robot system containing N wheeled robots and a nonlinear dynamic model of a single wheeled robot; step 2: converting a nonlinear dynamic model of the wheeled robot into a second-order linear system through linear feedback transformation, and designing a self-adaptive cooperative controller; and step 3: after the self-adaptive cooperative controller is designed, the evolution law of the acceleration and the angular acceleration is obtained through inverse transformation, the acceleration and the angular acceleration are further obtained, the corresponding control force and control moment are further obtained, and the self-adaptive cooperative control of the plurality of wheeled robots is completed. The invention can effectively overcome the nonlinear items of uncertain system structures and parameters, automatically update the communication coupling coefficients of different robots, adapt to the dynamically changing environment and the change of communication topological structures, and efficiently finish the consistent formation action.
Description
Technical Field
The invention relates to the field of multi-robot control, in particular to a multi-wheel robot self-adaptive cooperative control algorithm and a control system.
Background
The working environment and task complexity of the robot gradually rise, and a single robot is more and more difficult to meet the requirements; the multi-robot system shows great superiority in the aspects of task applicability, economy, optimality, robustness, expandability and the like, and is one of the most popular research subjects in the field of robots at present; the robot cooperative detection and control is beneficial to realizing the comprehensive perception of the environment and finishing the efficiency which can not be finished by a single robot, and the working efficiency of the robot is greatly improved. The coordination and cooperation of multiple robots as a brand-new robot application form is receiving increasing attention at home and abroad. With the application of multi-robot systems in the fields of industry, military, medical treatment, etc., the development of robot platforms has become one of the hot spots for multi-robot research. The system is widely applied to multiple civil and military dual-purpose fields such as logistics, storage, intelligent transportation, detection and investigation. Currently, various research institutes at home and abroad are dedicated to developing their own multi-robot platforms to verify applications related to multiple robots.
Among various mobile robots, a wheeled robot has the remarkable characteristics of simple system structure, flexible movement, convenience in operation and low cost. Usually, two driving wheels are used to drive a driven wheel. Although the cooperative controller has a wide application prospect in civil fields such as logistics storage and the like, when the cooperative controller is used for completing a given task, various challenges exist, such as the realization of distributed control, automatic obstacle avoidance and the adaptation to the dynamic change among a plurality of robots, the design of the cooperative controller is favorable for the realization of engineering, and various performances of a control system can be improved and the working performance of the control system can be improved. In the related researches of the structure and design of the existing mobile robot system, a formation control method and intelligent embodiment, the error influence of the actual robot motion is mostly not considered and the coupling weight is automatically adjusted, and the robot has more uncertainty, for example, the mileometer technology has larger error accumulation due to the integral characteristic; the inertial navigation technology can drift along with the increase of time, so that errors increase along with the increase of time; GPS accuracy is problematic and is not suitable for indoor use, etc. For robot motion errors in a real environment, it is often difficult to accurately represent the robot motion errors in a certain error model, which causes manual remote adjustment to continue the task in the task process.
In a logistics storage scene, when multi-robot cooperative control is carried out, various shielding, failure, communication topology switching and other characteristics exist in the environment, therefore, in order to effectively adapt to various uncertainties, a self-adaptive coupling coefficient adjustment strategy is necessary to be adopted, the strategy can change the coupling coefficient among different robots in a self-adaptive manner by establishing a dynamic evolution equation of the coupling coefficient, so that the strategy is suitable for various tasks of a distributed system, better accords with an engineering implementation scene, is expected to improve various performances of a control system, and improves the operational performance of the control system.
Disclosure of Invention
The invention aims to provide a self-adaptive cooperative control algorithm and a control system of a multi-wheeled robot, so as to effectively overcome the nonlinear items of uncertain system structures and parameters, save the field with limited working scenes through efficient cooperation and greatly improve the efficiency of tasks under the condition of not increasing the field area.
In order to achieve the above object, the present invention provides a multi-wheeled robot adaptive cooperative control algorithm, which comprises the following steps:
step 1: establishing a multi-wheeled robot system containing N wheeled robots and a nonlinear dynamic model of a single wheeled robot;
step 2: converting a nonlinear dynamic model of the wheeled robot into a second-order linear system through linear feedback transformation, and designing a self-adaptive cooperative controller;
and step 3: after the self-adaptive cooperative controller is designed, the evolution law of the acceleration and the angular acceleration is obtained through inverse transformation, the acceleration and the angular acceleration are further obtained, the corresponding control force and control moment are further obtained, and the self-adaptive cooperative control of the plurality of wheeled robots is completed.
The adaptive cooperative control algorithm for the multi-wheeled robot is characterized in that the nonlinear dynamical model is as follows:
wherein,
the speeds of the ith wheeled robot in the x and y coordinate directions at the moment t are respectively; v. ofi(t) is the speed of the ith wheeled robot at time t; thetai(t) is the angle of the ith wheeled robot at the time t;
is the angular velocity of the ith wheeled robot at time t, an
The multi-wheeled robot self-adaptive cooperative control algorithm comprises the following steps in step 2:
step 2.1: order to
Wherein u isi(t) is the control input of the ith wheeled robot at the moment t; u. ofi1(t) and ui2(t) are each ui(t) the 1 st component and the 2 nd component;
and
acceleration of the ith wheeled robot in the x and y coordinate directions at the moment t,
the acceleration of the ith wheeled robot at the moment t;
the angular acceleration of the ith wheeled robot at the moment t;
equation (1) then translates into a second order linear system:
wherein,
in the state of the i-th wheeled robot,
uia control input for an ith wheeled robot;
step 2.2: calculating a proximity matrix A in an undirected graph of a multi-wheeled robot system according to a communication topology of the multi-wheeled robot system0；
Step 2.3: and designing an adaptive cooperative controller and an adaptive cooperative control law of the multi-wheeled robot system.
The adaptive cooperative control algorithm for the multi-wheeled robot includes that step 2.2 specifically includes the following steps:
assume that a network between cooperative communications of multiple wheeled robots employs an undirected graph G ═ (V)0,,A0) Is shown in which V0＝{v1,v2,…vNDenotes a set of multi-wheeled robotic system nodes,
an unordered set of nodes, called a boundary set; two nodes v are calledi,vjIs a neighbor set, if { v }i,vjIs the boundary of graph G, in which the slave node viTo node vjHas a path of { vik,vjk+1A set of boundaries in the form of 1, …, l-1, which is called a connected graph if there is a path reachable for each pair of nodes in the graph, adjacent to the matrix a0＝[aij]∈RN×NWhich is a compound with a non-negative element aijAnd the diagonals are all 0 matrixes; if the boundary { vi,vj∈, then node vjReferred to as node viIs close to the node, and
node viIs denoted as Ni＝{j∈I|{vi,vj}∈}。
In the adaptive cooperative control algorithm for the multi-wheeled robot, the adaptive cooperative controller and the adaptive cooperative control law respectively include:
wherein, aijIs a proximity matrix A0The corresponding element of (1); c. CijTo adapt the coupling coefficients in the cooperative control law,
and c isij(0)＝cji(0)；
And
the states of the ith and j robots after being transformed into a second-order linear system are respectively; k is a radical ofijIs a constant; feedback matrix F ═ BTP-1，Ω＝P-1BBTP-1And P is a positive definite matrix, and the value of the positive definite matrix satisfies the following conditions:
(6) and I is an identity matrix.
The adaptive cooperative control algorithm for the multi-wheeled robot includes the following specific steps in step 3:
step 3.1: and (2) obtaining an evolution rule of the acceleration and the angular acceleration according to the inverse transformation relation:
step 3.2: the value of P can be obtained by optimizing and solving the formula (6), and then the feedback matrix F is obtained, and u is obtained according to the formula (4)iTaking the value of (A);
step 3.3: obtaining acceleration by equation (7)
And angular acceleration
Step 3.4: according to
Wherein M isg,JgThe mass and the moment of inertia of the wheeled robot are respectively; respectively obtaining the control force and the control moment of the ith wheeled robot at the moment t as Fi(t)，τi(t); and completing the self-adaptive cooperative control of the plurality of wheeled robots.
The invention also provides a self-adaptive cooperative control system of the multi-wheel robot, which comprises the following components:
the system comprises a group planning layer, a system decision layer in wireless connection with the group planning layer and an entity control layer in wireless connection with the system decision layer;
the group planning layer is used for forming and sending group planning information for determining respective roles of the plurality of wheeled robots and which formation is adopted to complete tasks;
the system decision layer is used for receiving group planning information sent by the group planning layer and environment information around each wheeled robot and pose information among the wheeled robots sent by the entity control layer, generating corresponding control information of the acceleration and the angular acceleration of each wheeled robot by utilizing the multi-wheeled robot self-adaptive cooperative control algorithm according to the received information, and further sending the control information to the entity control layer;
the entity control layer comprises a plurality of wheeled robots, and the entity control layer is used for collecting environmental information around each wheeled robot and pose information among the wheeled robots and executing corresponding actions according to received control information so as to achieve consistent formation and control of the wheeled robots.
In the adaptive cooperative control system for the multi-wheeled robot, the roles are divided into a piloting wheeled robot and a following wheeled robot.
The adaptive cooperative control system for a multi-wheeled robot is described above, wherein the wheeled robot includes a vehicle body; two driving wheels and a driven wheel connected with the vehicle body; the control mechanism is arranged on the vehicle body and used for controlling the wheeled robot to execute actions; the communication mechanism is connected with the control mechanism and is used for receiving and sending information; the system comprises an execution mechanism connected with the control mechanism and used for executing tasks, and a detection system connected with the control mechanism and used for acquiring environmental information around each wheeled robot and pose information between the wheeled robots.
The multi-wheeled robot self-adaptive cooperative control system comprises a binocular vision sensor and a laser sensor, and the binocular vision sensor and the laser sensor are used for collecting environmental information around each wheeled robot and pose information between the wheeled robots.
Compared with the prior art, the invention has the following beneficial effects:
the self-adaptive cooperative control algorithm for the multi-wheel robot can effectively overcome the non-linear items with uncertain system structures and parameters, automatically update communication coupling coefficients of different robots, adapt to the dynamically changing environment and the change of communication topological structures, and efficiently finish consistent formation actions. The invention also combines the characteristics of the working scene of the wheeled robot, such as the task characteristics of the warehouse logistics robot and the intelligent logistics platform, and adopts a three-level step-by-step hierarchical control structure to carry out formation control on the mobile robot. The advantages brought are that (1) the whole wheeled robot team is controlled in a centralized way; (2) each robot is controlled in a distributed manner; (3) the layered formation may reduce the complexity of the system. Through efficient cooperation, the wheeled robot system can save the limited site of the logistics storage working scene, greatly improves the utilization rate of the logistics system under the condition of not increasing the site area, has important economic benefits, can be popularized in a plurality of scenes, and has remarkable economic and social benefits.
Drawings
FIG. 1 is a graph of a single wheeled robot according to the present invention;
fig. 2 is a schematic diagram of the adaptive cooperative control system of the multi-wheeled robot according to the present invention.
Detailed Description
The invention will be further described by the following specific examples in conjunction with the drawings, which are provided for illustration only and are not intended to limit the scope of the invention.
The invention provides a self-adaptive cooperative control algorithm of a multi-wheel robot, which comprises the following steps:
step 1: establishing a multi-wheeled robot system containing N wheeled robots and a nonlinear dynamic model of a single wheeled robot; FIG. 1 is a schematic view of a single wheeled robotic system of the present invention;
the nonlinear dynamical model is as follows:
wherein,
the speeds of the ith wheeled robot in the x and y coordinate directions at the moment t are respectively; v. ofi(t) is the speed of the ith wheeled robot at time t; thetai(t) is the angle of the ith wheeled robot at the time t;
and ωi(t) is an angular velocity of the ith wheeled robot at time t, and
step 2: converting a nonlinear dynamic model of the wheeled robot into a second-order linear system through linear feedback transformation, and designing a self-adaptive cooperative controller;
the step 2 specifically comprises the following steps:
step 2.1: order to
Wherein u isi(t) is the control input of the ith wheeled robot at the moment t; u. ofi1(t) and ui2(t) are each ui(t) the 1 st component and the 2 nd component;
and
acceleration of the ith wheeled robot in the x and y coordinate directions at the moment t,
the acceleration of the ith wheeled robot at the moment t;
the angular acceleration of the ith wheeled robot at the moment t;
equation (1) then translates into a second order linear system:
wherein,
in the state of the i-th wheeled robot,
uia control input for an ith wheeled robot;
step 2.2: calculating a proximity matrix A in an undirected graph of a multi-wheeled robot system according to a communication topology of the multi-wheeled robot system0；
The step 2.2 specifically comprises the following steps:
assume that a network between cooperative communications of multiple wheeled robots employs an undirected graph G ═ (V)0,,A0) Is shown in which V0＝{v1,v2,…vNDenotes a set of multi-wheeled robotic system nodes,
an unordered set of nodes, called a boundary set; two nodes v are calledi,vjIs a neighbor set, if { v }i,vjIs the boundary of graph G, in which the slave node viTo node vjHas a path of { vik,vjk+1A set of boundaries in the form of 1, …, l-1, which is called a connected graph if there is a path reachable for each pair of nodes in the graph, adjacent to the matrix a0＝[aij]∈RN×NWhich is a compound with a non-negative element aijAnd the diagonals are all 0 matrixes; if the boundary { vi,vj∈, then node vjReferred to as node viIs close to the node, and
node viIs denoted as Ni＝{j∈I|{vi,vj}∈}。
Step 2.3: and designing an adaptive cooperative controller and an adaptive cooperative control law of the multi-wheeled robot system.
The self-adaptive cooperative controller and the self-adaptive cooperative control law are respectively as follows:
wherein, aijIs a proximity matrix A0The corresponding element of (1); c. CijTo adapt the coupling coefficients in the cooperative control law,
and c isij(0)＝cji(0)；
And
the states of the ith and j robots after being transformed into a second-order linear system are respectively; k is a radical ofijIs a constant; feedback matrix F ═ BTP-1，Ω＝P-1BBTP-1And P is a positive definite matrix, and the value of the positive definite matrix satisfies the following conditions:
(6) and I is an identity matrix.
It can be proved that the L yapunov function only needs to satisfy the condition of formula (6)
First derivative of
Wherein
α is constant, α lambdai≥1,i＝2,...,N；λiIs L aplarian matrix corresponding to the graph G, under the action of the self-adaptive cooperative controller formula (2), the multi-wheel robot can achieve global consistency,
the physical significance of the method is that the multi-wheel robot formation can finally reach the same posture and speed, so that the stable formation effect is achieved, and a foundation is laid for executing various tasks.
And step 3: after the self-adaptive cooperative controller is designed, the evolution law of the acceleration and the angular acceleration is obtained through inverse transformation, the acceleration and the angular acceleration are further obtained, the corresponding control force and control moment are further obtained, and the self-adaptive cooperative control of the plurality of wheeled robots is completed.
The step 3 specifically comprises the following steps:
step 3.1: and (2) obtaining an evolution rule of the acceleration and the angular acceleration according to the inverse transformation relation:
step 3.2: the value of P can be obtained by optimizing and solving the formula (6), and then the feedback matrix F is obtained, and u is obtained according to the formula (4)iTaking the value of (A);
step 3.3: obtaining acceleration by equation (7)
And angular acceleration
Step 3.4: according to
Wherein M isg,JgThe mass and the moment of inertia of the wheeled robot are respectively; respectively obtaining the control force and the control moment of the ith wheeled robot at the moment t as Fi(t)，τi(t); and completing the self-adaptive cooperative control of the plurality of wheeled robots.
As shown in fig. 2, the present invention also provides an adaptive cooperative control system for a multi-wheeled robot, comprising:
a group planning layer 10, a system decision layer 20 wirelessly connected with the group planning layer 10, and an entity control layer 30 wirelessly connected with the system decision layer 20;
the group planning layer 10 is used for forming and sending group planning information for determining respective roles of the plurality of wheeled robots and which formation is adopted to complete tasks; the roles are divided into a piloting wheeled robot and a following wheeled robot.
The system decision layer 20 is configured to receive group planning information sent from the group planning layer 10, environment information around each wheeled robot and pose information between the wheeled robots sent from the entity control layer 30, generate corresponding control information of acceleration and angular acceleration of each wheeled robot by using the multi-wheeled robot adaptive cooperative control algorithm according to the received information, and send the control information to the entity control layer 30;
the entity control layer 30 includes a plurality of wheeled robots, and is configured to collect environmental information around each wheeled robot and pose information between the wheeled robots, and perform corresponding actions according to received control information, so as to implement consistent formation and control of the plurality of wheeled robots.
The wheeled robot includes a vehicle body; two driving wheels and a driven wheel connected with the vehicle body; the control mechanism is arranged on the vehicle body and used for controlling the wheeled robot to execute actions; the communication mechanism is connected with the control mechanism and is used for receiving and sending information; the system comprises an execution mechanism connected with the control mechanism and used for executing tasks, and a detection system connected with the control mechanism and used for acquiring environmental information around each wheeled robot and pose information between the wheeled robots. The detection system comprises a binocular vision sensor and a laser sensor, and is used for collecting environmental information around each wheeled robot and pose information between the wheeled robots.
In conclusion, the self-adaptive cooperative control algorithm for the multi-wheeled robot provided by the invention can effectively overcome the non-linear items with uncertain system structures and parameters, automatically update communication coupling coefficients of different robots, adapt to the dynamically changing environment and the change of communication topological structures, and efficiently finish consistent formation actions. The invention also combines the characteristics of the working scene of the wheeled robot, such as the task characteristics of the warehouse logistics robot and the intelligent logistics platform, and adopts a three-level step-by-step hierarchical control structure to carry out formation control on the mobile robot. The advantages brought are that (1) the whole wheeled robot team is controlled in a centralized way; (2) each robot is controlled in a distributed manner; (3) the layered formation may reduce the complexity of the system. Through efficient cooperation, the wheeled robot system can save the limited site of the logistics storage working scene, greatly improves the utilization rate of the logistics system under the condition of not increasing the site area, has important economic benefits, can be popularized in a plurality of scenes, and has remarkable economic and social benefits.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (9)
1. A multi-wheeled robot self-adaptive cooperative control algorithm is characterized by comprising the following steps:
step 1: establishing a multi-wheeled robot system containing N wheeled robots and a nonlinear dynamic model of a single wheeled robot;
step 2: converting a nonlinear dynamic model of the wheeled robot into a second-order linear system through linear feedback transformation, and designing a self-adaptive cooperative controller;
the self-adaptive cooperative controller and the self-adaptive cooperative control law are respectively as follows:
wherein u isiA control input for an ith wheeled robot; a isijIs a proximity matrix A0Of the corresponding element, the proximity matrix
It is a non-negative element aijAnd the diagonals are all 0 matrixes; c. CijTo adapt the coupling coefficients in the cooperative control law,
and c isij(0)＝cji(0)；
And
the states of the ith and j robots after being transformed into a second-order linear system are respectively; k is a radical ofijIs a constant; feedback matrix F ═ BTP-1，Ω＝P-1BBTP-1And P is a positive definite matrix, and the value of the positive definite matrix satisfies the following conditions:
i is an identity matrix and is a matrix of the identity,
and step 3: after the self-adaptive cooperative controller is designed, the evolution law of the acceleration and the angular acceleration is obtained through inverse transformation, the acceleration and the angular acceleration are further obtained, the corresponding control force and control moment are further obtained, and the self-adaptive cooperative control of the plurality of wheeled robots is completed.
2. The multi-wheeled robot adaptive cooperative control algorithm of claim 1, wherein the nonlinear dynamical model is:
wherein,
the speeds of the ith wheeled robot in the x and y coordinate directions at the moment t are respectively; v. ofi(t) is the speed of the ith wheeled robot at time t; thetai(t) is the angle of the ith wheeled robot at the time t;
is the angular velocity of the ith wheeled robot at time t, an
3. The multi-wheeled robot adaptive cooperative control algorithm according to claim 2, wherein the step 2 comprises the following steps:
step 2.1: order to
Wherein u isi(t) is the control input of the ith wheeled robot at the moment t; u. ofi1(t) and ui2(t) are each ui(t) the 1 st component and the 2 nd component;
and
acceleration of the ith wheeled robot in the x and y coordinate directions at the moment t,
the acceleration of the ith wheeled robot at the moment t;
the angular acceleration of the ith wheeled robot at the moment t;
equation (1) then translates into a second order linear system:
wherein,
in the state of the i-th wheeled robot,
uia control input for an ith wheeled robot;
step 2.2: calculating a proximity matrix A in an undirected graph of a multi-wheeled robot system according to a communication topology of the multi-wheeled robot system0；
Step 2.3: and designing an adaptive cooperative controller and an adaptive cooperative control law of the multi-wheeled robot system.
4. The adaptive multi-wheeled robot cooperative control algorithm according to claim 3, wherein the step 2.2 comprises the steps of:
assume that a network between cooperative communications of multiple wheeled robots employs an undirected graph G ═ (V)0,,A0) Is shown in which V0＝{v1,v2,…vNDenotes a set of multi-wheeled robotic system nodes,
an unordered set of nodes, called a boundary set; two nodes v are calledi,vjIs a neighbor set, if { v }i,vjIs the boundary of the graph G, in which the subordinate nodesPoint viTo node vjHas a path of { vik,vjk+1A set of boundaries in the form of 1, …, l-1, which is called a connected graph if there is a path reachable for each pair of nodes in the graph, adjacent to the matrix a0＝[aij]∈RN×NWhich is a compound with a non-negative element aijAnd the diagonals are all 0 matrixes; if the boundary { vi,vj∈, then node vjReferred to as node viIs close to the node, andnode viIs denoted as Ni＝{j∈I|{vi,vj}∈}。
5. The adaptive multi-wheeled robot cooperative control algorithm according to claim 4, wherein the step 3 comprises the following steps:
step 3.1: and (2) obtaining an evolution rule of the acceleration and the angular acceleration according to the inverse transformation relation:
step 3.2: the value of P can be obtained by optimizing and solving the formula (6), and then the feedback matrix F is obtained, and u is obtained according to the formula (4)iTaking the value of (A);
step 3.3: obtaining acceleration by equation (7)
And angular acceleration
Step 3.4: according to
Wherein M isg,JgRespectively wheel-type machinesHuman mass and moment of inertia; respectively obtaining the control force and the control moment of the ith wheeled robot at the moment t as Fi(t)，τi(t); and completing the self-adaptive cooperative control of the plurality of wheeled robots.
6. A multi-wheeled robot adaptive cooperative control system is characterized by comprising:
the system comprises a group planning layer, a system decision layer in wireless connection with the group planning layer and an entity control layer in wireless connection with the system decision layer;
the group planning layer is used for forming and sending group planning information for determining respective roles of the plurality of wheeled robots and which formation is adopted to complete tasks;
the system decision layer is used for receiving group planning information sent by the group planning layer and environment information around each wheeled robot and pose information among the wheeled robots sent by the entity control layer, generating corresponding control information of acceleration and angular acceleration of each wheeled robot by using the multi-wheeled robot self-adaptive cooperative control algorithm according to any one of claims 1 to 5 according to the received information, and further sending the control information to the entity control layer;
the entity control layer comprises a plurality of wheeled robots, and the entity control layer is used for collecting environmental information around each wheeled robot and pose information among the wheeled robots and executing corresponding actions according to received control information so as to achieve consistent formation and control of the wheeled robots.
7. The adaptive multi-wheeled robot cooperative control system according to claim 6, wherein the roles are classified into a leading wheeled robot and a following wheeled robot.
8. The multi-wheeled robot adaptive cooperative control system according to claim 6, wherein the wheeled robot includes a vehicle body; two driving wheels and a driven wheel connected with the vehicle body; the control mechanism is arranged on the vehicle body and used for controlling the wheeled robot to execute actions; the communication mechanism is connected with the control mechanism and is used for receiving and sending information; the system comprises an execution mechanism connected with the control mechanism and used for executing tasks, and a detection system connected with the control mechanism and used for acquiring environmental information around each wheeled robot and pose information between the wheeled robots.
9. The adaptive multi-wheeled robot cooperative control system of claim 8, wherein the detection system comprises binocular vision sensors and laser sensors, collectively configured to collect environmental information around each wheeled robot and pose information between the wheeled robots.
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| CN201711269804.1A CN107807534B (en) | 2017-12-05 | 2017-12-05 | Self-adaptive cooperative control algorithm and control system for multi-wheeled robot |
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