JL-2: A Mobile Multi-robot System with Docking and Manipulating Capabilities

3.1. System overview and design ideas

The new design of the JL-2 prototype is based on the following ideas:

Combining the manipulation and a part of the docking and posture-adjusting functions to form a docking manipulator. One robot can take advantage of its manipulator to grasp and operate objects independently, as well as to connect with another robot in the system. Moreover, the joints of the manipulator also provide the DOF for the posture-adjusting and docking procedures.

Based on the above ideas, the JL-2 prototype is designed, as shown in Fig. 1. As same as JL-1, JL-2 is also composed of three independent robots with full navigation abilities in the field. They are called the back robot, the middle robot and the front robot respectively. If the robots connect, they will form a chain structure in which one robot is able to actively adjust the posture of the adjacent one in three dimensions by virtue of the two spherical joints between them.

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Fig. 1.

Three robots in the JL-2 system

One robot in JL-2 may consist of three units: two track units, one rotation unit and a docking manipulator. In fact, for economical reasons only the middle robot contains all of these units. Though it is ideal to construct all of the robots with a uniform structure, currently a simplified version is sufficient for testing the basic functions of JL-2.

The functions of the docking manipulator include: 1) Grasping and manipulating objects; 2) Holding the docking disk of the rotation unit on the other robot; 3) Adjusting the pitching and yawing postures between two connected robots.

Fig. 2 shows the kinematic structure of the docking manipulator, which is composed of a two-DOF parallel mechanism and an end gripper. The parallel mechanism consists of two parallel ball screws AC and BD, the gripper base ABO, and the supporting pole GO fixed with the robot platform. There are two ball bearings at points C and D, and three hooker joints at points A, B and O respectively. Along with the changes of the two screws' lengths, namely L₁ and L₂, the gripper base will turn around the axes X and Y. Equations (1) and (2) show the relations between L₁, L₂ and the yawing and pitching angles θ_x, θ_y.

L 1 = ( L 2 + 4 K 2 + 2 K L s θ y + 2 K 2 c θ x − 2 K 2 c θ y + 2 K L s θ x c θ y + 2 K 2 s θ x s θ y ) 1 / 2

(1)

L 2 = ( L 2 + 4 K 2 + 2 K L s θ y − 2 K 2 c θ x − 2 K 2 c θ y − 2 K L s θ x c θ y − 2 K 2 s θ x s θ y ) 1 / 2

(2)

Where,

L is the distance between the main hooker joint and the center of the ball bearing along the Z axis;

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Fig. 2.

Kinematic diagram of the docking manipulator

The gripper fixed on the gripper base consists of a screw-nut mechanism and two fingers which can rotate around two shafts respectively. Two pins are fixed with the nut (Docking base) and pass through the grooves of the fingers called the cam grooves. When the docking screw is turning, the pins will move forward or backward and drive the gripper to close or open by virtue of the special shape of the cam groove. To arrange the mass center of the docking manipulator close to the center of the robot, all of the driving motors are assembled at the opposite side of the gripper. A mechanism with two synchronal belts, two pairs of gears and a slide key mechanism are applied to transfer the output torques of the motors to the two parallel screws and the docking screw respectively.

Fig. 3 shows the realization of the docking manipulator, which can be assembled with the track units by a connecting board. The outline of the fingers and the structure of the Docking base are specially designed to realize two grasping modes, as shown in Fig. 3, as well as the grasping-locking and gradual-alignment docking procedure, which will be explained in sub-section 3.4. The tip of the finger is designed in a half-circle and hook shape to grip the shaft behind the docking disk on the other robot. At the center of the docking base, there is a large cone-shaped hole called main-docking hole; four small cone-shaped holes called sub-docking holes are at the four corners of the docking base. All of these holes will be coupled with the cones on the docking disk of the rotation unit to realize self-alignment and self-constrain.

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Fig. 3.

Docking manipulator and grasping modes

The cam groove in each finger is divided into two segments: a nipping segment and a holding segment. When the pins are in the nipping segments, they will drive the gripper to open or close as long as the docking base moves backward or forward. In this phase, the gripper may perform a grasping mode called nipping. The fingers revolving around the gripper shafts from 0° – 24° will result in a fluctuating distance between two tips from 2mm – 43mm, which are also the width limits of the object being nipped. The nipping force F_N is introduced by the pushing force of the docking base F_D. When the pins enter the holding segments, a holding mode will be performed by the gripper. The available thickness of the objects that can be held is between 1mm to 22mm in theory. The holding force equals F_D. The value of F_D and F_N can be calculated by according to the physical parameters of the docking motor, the gear ratio, the docking screw, and the dimensions of the fingers. The continuous stall value of F_D is 28.3 KN; and the possible maximum value of F_N changes from 4.8 KN to 17.3 KN, when the object width changes from 43mm to 2mm.

When grasping, the robots in JL-2 will perform a nipping action for an object with flat surfaces and a holding action for a round object. It seems that the contact forces between the gripper and objects are too large, but those are necessary to ensure a reliable self-alignment and solid connection when docking. Actually, during the grasping and docking phases, the contacting forces will be limited by monitoring the current in the docking motor to protect the object and fingers from being damaged.

The rotation unit is simply composed of a motor and a docking disk mounted on the output shaft of the motor, as shown in Fig. 4. Two functions will be performed by the rotation units. The first one is to coordinate with the docking manipulator to complete the gradual aligning procedure, which is guaranteed by the shape of the docking disk. The other one is to turn the robot about the Z axis when docked. Therefore, the axis of the rotation unit should pass through point O (as shown in Fig. 2) in the connected state. As mentioned above, the main-docking cone and the sub-docking cones on the docking disk will be coupled with the holes in the docking base to guarantee the self-aligning function and to overcome the rotation load around the Z axis when docked. Two edges of the docking disk are designed in a curve to permit the gripper to encompass the disk easily. The diameter of the shaft behind the disk is less than that of the circle of the finger tip of the docking gripper. As a result, when the gripper catches the shaft, the misalignments between two robots are acceptable to a certain degree. The connection between the gripper and the docking disk should be powerful enough to overcome the loads arising from the weight of the robot. The rotation unit will be supported by a connecting board when assembled on the robot.

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Fig. 4.

Realization of the rotation unit

By virtue of the special designs of the docking gripper and the docking disk, the docking procedure is divided into three phases: the approaching phase, grasping phase and locking phase.

When docking, one robot is called the “active robot”, if it makes use of its docking manipulator to actively connect another one. On the contrary, the robot waiting to be connected is called the “passive robot”. During the approaching phase, the “passive robot” stops moving, but rotates its docking disk to align with the gripper of the “active robot”. The “active robot” opens the gripper completely, and then it keeps moving forward and adjusting the postures of the gripper simultaneously, until the gripper encompasses the docking disk belonging to the “passive robot”.

Then the grasping phase begins, during which the gripper closes to diminish the errors in the horizontal plane, namely d_y and ɛ_x, as shown in Fig. 5. This function is ensured by the contacting forces between the fingers and the docking disk. Although the contacting forces are changing during this procedure, they are powerful enough to overcome the friction force between the tracks and the ground, and will align two robots in the horizontal plane. At the end of the grasping phase, the completely closed gripper not only decreases the d_y and ɛ_x distinctively, but also grasps the docking disk and prevents it from escaping.

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Fig. 5.

Two phases in docking procedure

After the grasping phase, the locking phase will be triggered. Here the docking base will be stretched out while the main-docking cone will be embedded in the main-docking hole. This procedure is ensured by their respective dimensions. As soon as the main-docking cone and the main-docking hole make contact, the contacting forces will diminish the aligning errors in the vertical plane, namely d_x and ɛ_y, as well as the rudimental errors d_y and ɛ_x in the horizontal plane. At the end of this period, the sub-docking cones will fit the sub-docking holes, eliminating all of the five errors in the end.

After the locking phase, all of the six DOF between two robots are constrained, and the docking disk is held forcefully between the docking base and the gripper by the resident pressure with a maximum value of 28.3KN. Since the driving chain from the docking motor to the gripper and the docking disk is self-locked, there is no possibility to open the gripper and disconnect the two robots, unless the docking motor is controlled to do it.

When the robots connect, JL-2 is able to perform particular motions by virtue of the two motorized spherical joints between them, such as self-recovery, crossing wide trenches, climbing stairs, passing through narrow fences, lateral motion, and etc. These locomotion capabilities will enhance the adaptability of JL-2 to rugged terrains and have been validated by JL-1 (Wang, W.; et al., 2008).

In Fig. 6, two Cartesian coordinates OXYZ and O'X'Y'Z', whose original points are both located at the center of the spherical joint, coincide with the middle robot and the front robot respectively. Therefore, the posture changing of the robot can be represented by the relative rotation between these two coordinates, which is denoted by a vector θ in equation (3). The outputs of the three motors of the spherical joints are denoted by a vector q in equation (4).

θ = [ θ x , θ y , θ z ] T

(3)

q = [ θ m 1 , θ m 2 , θ R ] T

(4)

Where,

θ_m1 and θ_m2 are the output angles of two motors driving the parallel mechanism respectively;

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Fig. 6.

Spherial joints of JL-2

The relationship between θ and q can be denoted by the following equations (5) ~ (7).

θ m 1 = 2 π ( A − L ) / l b

(5)

θ m 2 = 2 π ( B − L ) / l b

(6)

θ R = θ z

(7)

Where,

A = [ ( K ( c θ y c θ z + s θ x s θ y s θ z ) − K ( − s θ z c θ y + s θ x s θ y c θ z ) + L c θ x s θ y − K c θ z − K s θ z ) 2 + ( K ( c θ x s θ z ) − K ( c θ x c θ z ) − L s θ x − K s θ z + K c θ z ) 2 + ( K ( − s θ y c θ z + s θ x c θ y s θ z ) − K ( s θ y s θ z + s θ x c θ y c θ z ) + L c θ x c θ y ) 2 ] 1 / 2 ;

According to equations (5) ~ (7), the controllers can calculate the output angles of the motors to realize the desired posture-adjustment actions.

When the robots connect, JL-2 is able to perform particular motions by virtue of the two motorized spherical joints between them, such as self-recovery, crossing wide trenches, climbing stairs, passing through narrow fences, lateral motion, and etc. These locomotion capabilities will enhance the adaptability of JL-2 to rugged terrains and have been validated by JL-1. According to equations (5) ~ (7) and the structure constraints between two robots, we can acquire the available kinematics workspace of one spherical joint, as shown in Fig. 7. If special joint paths are selected inside this workspace and followed by the joint, JL-2 will perform the above locomotion actions.

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Fig. 7.

Available kinematics workspace of the spherical joint

To ensure that every point in the kinematics workspace is reachable, the layout of the three motors should follow equations (8) and (9).

[ θ m 1 ∙ θ m 2 ∙ θ R ∙ ] T = J [ θ x ∙ θ y ∙ θ z ∙ ] T

(8)

[ M 1 M 2 M R ] T = ( J T ) − 1 [ M x M y M z ] T

(9)

Where,

J is the Jacobian matrix, which is acquired from the differentiation of the equations (5) ~ (7);

The loads on the spherical joints arise from the weight of the robots G and the supporting forces of the ground N _G , and change when JL-2 adjusts the robots' postures, as shown in Fig. 8. To estimate the continuous stall torque of the spherical joint motors, three typical postures where the M _x , M _y and M _z reach their maximum values respectively are illustrated by Fig. 8.

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Fig. 8.

Three typical postures

In Fig. 8(a), JL-2 is lifting the middle robot by turning the joints about the Y axes. According to the structure of the robots, M _y will reach its maximum value when θ _y equals 12°. If the weight of one robot is supposed to be 10 kg in the design period, the maximum value of M _y will equal 23.8Nm in this situation. In Fig. 8(b), JL-2 is turning the joints about the X axes to lift the middle robot to self-right from the side-over state. When θ _x equals 2.5°, M _x will reach the maximum value 19.6Nm. In Fig. 8(c), the front robot is supported by the other two robots and is turned about the Z axis. When θ _x and θ _z equal 45° and 0° respectively, M _z will reach the maximum value 4.2Nm.

By inserting the above maximum values of M _x , M _y and M _z into equation (9), we can acquire the necessary output torques of the motors for the spherical joint, by which the layout of these motors can be completed.

4.1. Hardware and sensors for automatic docking

Different cooperation modes are available for JL-2, such as parallel movement or manipulation and physically related reconfiguration. To meet the requirements of the changing cooperation mode, JL-2 adopts a distributed control system as shown in Fig. 9, so that every robot can process the information and performs the motion independently. In this distributed system, a PC with joystick and three robots communicate with each other through a wireless LAN.

Every robot in the JL-2 prototype adopts the same control hardware, which is also shown in Fig. 9. This control hardware is based on the master-slave structure and meets the requirements of functionality, extensibility, and easy handling.

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Fig. 9.

Hardware of the control system

A global and local positioning sensor system is intergrated in JL-2 to realize the automatic docking. Each robot of JL-2 is equipped with a GPS and an electric compass which are responsible for the global positioning in a large area. However, the positioning accuracy of GPS is normally no better than 0.2m, and does not meet the requirement of the docking action. Therefore, a sonar based inter-robot docking guidance system is designed to guide the robots to diminish the position and orientation errors among them, as shown in Fig. 10.

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Fig. 10.

Sonar sensors for automatic docking

This sonar guidance system is composed of one transmitter which is centrally installed on one robot, and four receivers symmetrically installed on the other robot. When docking, two robots firstly approach each other by following the position and oritation data of the GPS and compasse sensors. As soon as the distance between the robots is less than 0.5m, which is the maximum detectable distance of the sonar system, the two robots will start the sonar system and rotate in different speeds to ensure that the receivers capture the altrasonic signal sent by the transmitter. In theory, the intensity of the received signal is linear to the distance between the transmitter and the receiver. By comparing the signal intensities of the two horizontally arranged receivers and the two vertically arranged recerviers respectively, we will acquire the horizontal and vertical aligning errors between two robots. The oritation of the robots will be adjusted to diminish the signal differences between the receivers. Then, two robots will approach each other and adjust their oritation repeatedly according to the sensor data, until the docking disk is surrounded by the docking gripper. At last, the controller triggers the final grasping action described in 3.4.

The detailed discussion of this sonar guidance system can be found in our previous paper (Li, D.Z.; et al., 2008).

To cope with the distributed hardware and the changing cooperation modes, the software architecture of JL-2 is based on a multi-agent behavior-based structure and a multi-threaded programming methodology. The architecture shown in Fig. 11 includes a master serving as a global path planner and several slaves executing the commands from the master. Depending on the requirements of the tasks, each robot could be a master or a slave.

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Fig. 11.

Software architecture

To handle different hardware requests simultaneously and compute in real-time, the multi-task software is built in the SBC-X255 and the S3C2410 based on the Embeded Linux Operation System. The ExDataCon thread provides the data communication between robots and user interface; the InDataCon thread takes charge of receiving data or sending commands to the inner-devices; the SenFuse and PathPlaning threads process the sensor data, construct a local map and generate a feasible path, and the CompMotion thread deals with the composite behaviors composed of several primitive motions such as “Forward” and “Turning around”, which are controlled by the PrimMotion thread. The communication threads, ExDataCon and InDataCon, maintain the Robot Status Database which records all of the information. As a result, the reconfigurating action can be implemented efficiently and harmoniously according to the global information saved in the system status database. Actually, every robot and the interface have one copy of the Robot Status Database in their memory. Therefore, the Robot Status Database is a common “Blackboard” being accessable for every node in the JL-2 control system.

Once the global tasks, such as “Docking”, “Undocking”, “90° recovery”, “Whole turning left”, etc., are sent by the user through the interface on the PC, one robot is chosen to be a master according to its role in the task, and then the master generates a set of composite motions based on the task and the status of all robots. For example, when the “90° recovery” task is sent out, the middle robot is chosen to be the master, since it will control the two spherical joints simultaneously. Afterwards, every composite motion is transmitted to the appropriate robot by the ExDataCon thread. At last, the composite motions are decomposed and sent to the PrimMotion thread to achieve the desirable motions.

5.1. Grasping

Fig. 12 shows the grasping tests. Two grasping modes have been tested on the middle robot and the back robot. In the experiments, the gripper successfully nipped several wood blocks. To grasp a round object, the holding mode was applied. If being operated carefully, the robot can even grasp a pingpong.

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Fig. 12.

Grasping experiments

To test the self-aligning abilities of the docking mechanism, the five posture errors, d_x, d_y, ɛ_x, ɛ_y, and ɛ_z, were preset individually in several experiments. Fig. 13 shows the four docking experiments, in which the photos above the arrows present the states before docking, and the others below the arrows show the docked states. Since the posture error ɛ_z between two robots can be diminished by the rotation motor, the docking procedure to overcome ɛ_z is relatively simple and not shown at here. According to these experiments, we can find that when horizontal errors ɛ_x and d_y are involved, the docking mechanism only needs to overcome the friction force between the tracks and the ground, but with vertical errors ɛ_y and d_x, the weight of the robot has to be overcome. As a result, the docking ability of JL-2 in the horizontal plane is better than that in the vertical plane.

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Fig. 13.

Docking experiments

The self-aligning ability around the Z axis is the poorest one, because the multi sub-cones can cause over-constraint, although they will help to realize a solid connection. It is not a serious problem in actual docking actions, as the rotation angle of the docking disk can be accurately adjusted by the rotation motor.

When docked, a very solid connection is ensured by the high pressure and the multi-point mating structure between the docking base and disk. Such a connection without any gap between connected parts enables the posture-adjusting experiments.

However, the multi-point mating structure introduces the over-constraint phenomena between the docking base and disk, and limits the further improvement of the self-aligning capability.

Besides the above experiments testing the docking limits, the automatic docking actions are also performed. According to our experiments, the robots in JL-2 are able to finish the docking actions successfully if the distance between them is less than the detectable distance (0.5m) of the sonar guidance system.

JL-2 performed similar posture-adjusting experiments to JL-1, such as self recovery, lateral motion, passing through a narrow fence, and so on. Because JL-2 shares the same principle with JL-1 when performing the posture-adjusting actions, only the 90° self recovery experiment is shown in Fig. 14 as en example. The detailed discussion can be found in our previous paper (Wang, W.; et al., 2008).

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Fig. 14.

90° self recovery

The results of our experiments are listed in Table 1.

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Table 1.

Basic performance specifications

Item		Values
Physical parameters of single robot
Weight	Front robot	7.2kg
	Middle robot	9.1kg
	Back robot	8.5kg
Dimensions	Front robot	370*252*172mm3
	Middle robot	569*252*172mm3
	Back robot	569*252*172mm3
Maximum moving velocity		200 mm/s
Maximum endurance time		2 hour
Grasping ability
Pitching angle		−45°~+45°
Yawing angle		−42°~+42°
Object width in nipping mode		5–30mm
Object diameter in holding mode		5–20mm
Rating nipping force		0.65–0.88kN
Rating holding force		10.1kN
Docking ability (Maximum permitted errors)
Horizontal position error dy		−30−+30mm
Horizontal orientation error ɛx		−35−+35°
Vertical position error dx		−15−+15mm
Vertical orientation error ɛy		−20−+20°
Rotation error ɛz		−8−+8°
Posture adjusting ability
Turning angle around X-axis θ x		−45~+45°
Turning angle around Y-axis θ y		−42~+42°
Turning angle around Y-axis θ z		−180~+180°
Maximum torque around X-axis M x		20.5Nm
Maximum torque around Y-axis M y		24.5Nm
Maximum torque around Z-axis M z		4.5Nm