Introduction

We describe a framework and control algorithms for coordinating multiple mobile robots with manipulators focussing on tasks that require grasping, manipulation and transporting of large and possibly flexible objects without special purpose fixtures and minimal human intervention. Because each robot has an independent controller and is autonomous, the coordination and synergy is realized through a suitable communication protocol. The robots can cooperatively transport objects and march in a tightly controlled formation, while also having the capability to navigate autonomously. In what follows, we describe the key aspects of the overall control hierarchy and the basic algorithms, with specific applications to our experimental testbed consisting of two TRC Labmate robots and one Nomad robot.
 
 
 

Figure 1 Multiple cooperating robots allow a fixtureless approach to material handling.

The Robots in Our Experimental System

Our experimental system consists of three mobile manipulators. Each manipulator is described briefly below.

1. The Nomad XR 4000 platform is equipped with a stiff forklift arm that has one prismatic joint along a vertical axis.
2. The second robot is a TRC Labmate platform equipped with an actively controlled, compliant arm.
3. The third robot is a TRC Labmate platform equipped with a passive, articulated rigid arm with one revolute joint.

(a)	(b)

Figure 2 (a) The Nomad XR 4000 platform with a forklift (right) and the TRC Labmate (the follower in this formation) with the actively controlled arm transporting a large object; (b) The TRC Labmate with a rigid, passive arm leading a formation of three robots (the other two are the same as those shown in (a)), carrying a long flexible board.

Controller

The task for the follower robot is to maintain the required grasp forces while trailing behind the lead robot. We decompose the planning and arm control into three subsystems.

1. Planner: The planner "listens" to the information broadcast from the lead robot, gets information from its sensors, and plans an appropriate reference trajectory that avoids obstacles. It provides set points for the platform controller, (a reference trajectory). Currently, for two robots, the follower trails behind like a rear wheel of a bicycle and for three platforms, the analogy of a tricycle can be used.
2. Platform Controller: The platform controller insures that the robot will follow the specified reference trajectory. A look-ahead controller adds an error signal to the specified trajectory to compensate for errors due to arm movements and to ensure that the arm does not extend past its workspace boundary. For the nonholonomic platforms, a nonlinear controller based on feedback linearization is used while the omnidirectional robot uses three separate linear controllers.
3. Arm Controller: The arm senses and controls the grasp forces, according to specifications transmitted from the lead robot. In this process, the arm controller compensates for platform positioning errors. The controller is independent from the platforms and the arm acts to control the "internal forces".

Arm

The three degree-of-freedom, in-parallel, actively controlled arm has three "limbs" each consisting of a linear actuator with a spring in series. The actuator position is controlled in order to maintain a desired Cartesian impedance. While the stiffness of the springs cannot be changed, the equilibrium position of the spring can be changed quickly in order to adjust the effective stiffness of the individual limb. The arm is naturally compliant because of the springs and gives it the ability to control the grasp forces and counteract disturbances.
 

Figure 3 The three degree-of-freedom, in-parallel, actively controlled arm allows forces to be applied in the X and Y direction as well as a moment in the Z direction.	Figure 4 Each limb has a spring attached in series to a linear actuator driven by a DC motor attached to a ball screw transmission.
Figure 5 Design concept.

Communication

Communicating between computers and between platforms is accomplished by sending and receiving packets of data using Ethernet technology. Between computers on each platform, a wired network is installed using the UDP/IP protocol. Between platforms, a wireless peer to peer network is installed using the IPX/IP protocol. We chose IPX for the Wireless Ethernet protocol because it has the ability to send small packets quickly. It is important to note that we imposed a timing sequence on the transmission of the packets because of the critical importance in sharing information between robots which must work in a tightly coupled fashion.

Experimental Results

The three platforms work cooperatively to transport the flexible board as shown in Figure 2. The rear platform follows the lead platform like the rear wheel of a bicycle and the planner's desired trajectories for the two TRC Labmates are shown in Figure 6a. The forces applied by the active arm during an experiment are shown in Figure 6b. The desired longitudinal force is 1 lb. during the experiment. The platform's controller maintains the arm in the home position and the relative movement is very small.
 
 

Figure 6 Typical experimental results. (a) The platform trajectories for the lead robot and a follower robot while executing a turn, and (b) The forces in the longitudinal (y) and transverse (x) direction exerted by the follower platform on the grasped object.

Extensions

We briefly discuss the scalability of the proposed framework, the control algorithms, and the communication protocol to other multirobot teams and to teams with more than three robots. The first set of issues pertains to communication and control. In our experimental system, we have one leader robot that transmits information on the order of 10 Kb/s, which corresponds to a communication rate of roughly 20 Hz sending 56 bytes per packet. Without changing the hardware, we can easily scale our system up to four "leader robots" without compromising the transmission rate, and to as many as 16 leaders with a communication rate of approximately 5 Hz. The overall framework lends itself to the coordination of large teams of robots. As discussed by Desai et al, 1998, the control and coordination can be mathematically described in terms of the motion planning and control of the lead robot(s), the design of controllers for the follower robot(s), and the discrete changes in the robot controllers. Thus, as shown in Figure 7.

Figure 7 Control of robot formation. A team of five robots with one leader can effectively change from a triangular to a rectangular formation using our framework. See [Desai et al, 1998] for details.

References

1. "Design and Control of a Compliant Parallel Manipulator for a Mobile Platform", by T. Sugar and V. Kumar, In the Proceedings of the 1998 ASME Design Engineering and Technical Conferences, Atlanta, Georgia, September 1998

 

 
 
 

variable truss paper.

2. "Decentralized Control of Cooperating Manipulators", by T. Sugar and V. Kumar, In the Proceedings of the IEEE International Conference on Robotics and Automation, Leuven, Belgium, May 1998

 

 
 
 

compliant paper.

3. "Control of changes in formation for a team of mobile robots," by J. Desai, V. Kumar, and J. Ostrowski, submitted to Proceedings of 1999 International Conference on Robotics and Automation, (Detroit), 1999.

 
4. A mpeg movie 7Meg of a demonstration of two robots is available.
5. A mpeg movie 6 Meg of a demonstration of three robots is available.