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Short Papers Connection Mechanism for Autonomous Self-Assembly in Mobile Robots Mehdi Delrobaei, Student Member, IEEE, and Kenneth A. McIsaac, Member, IEEE Abstract—This paper presents a connection mechanism for autonomous self-assembly in mobile robots. Using this connection mechanism, mobile robots can be autonomously connected and disconnected. The purpose of self-assembly in mobile robotics is to add a new capability to mobile robots, thus, improving their performance to best fit the terrain conditions. Construction of a reconnectable joint is of primary concern in such systems. In this paper, first the geometric conditions and force equations of a general docking mechanism are studied. Then, we discuss the design details of our connection mechanism and present some experimental results that show that the proposed mechanism overcomes significant alignment errors and is considerably power efficient. Index Terms—Mobile robot, self-assembly.
I. INTRODUCTION Self-assembly is a concept that offers a new approach in robotics, in which robot modules are able to assemble and form a connected structure, or a rigid body can disassemble into a group of unconnected units. In robotics, autonomous robot docking is generally divided into two classes [1]: intrarobot docking (e.g., ATRON [2]) and interrobot docking. A situation where a self-reconfigurable robot is disassembled into a set of autonomous mobile units and later reassembled back into a single robot can be an example of interrobot docking [3]. Mobile self-reconfiguring robots have been explored less in the literature because of reconfiguration difficulties [4]. To build such robots, some technical challenges must be overcome. Of primary concern is the need to build a docking interface that autonomously and easily connects and disconnects the modules and allows the transfer of mechanical forces and moments without degrading the performance. For this purpose, the design must overcome the following challenges to 1) build the connector as lightweight and compact as possible, 2) form a secure and reliable connection, 3) overcome unavoidable alignment errors, and 4) design the locking/unlocking mechanism to be considerably power efficient. Despite its importance, focusing on connection mechanism design and performance has been rarely addressed in the literature. The purpose of this paper is to investigate the possibility to construct a functional connection mechanism for mobile robots, thereby satisfying the four key requirements mentioned earlier. The final goal is to develop an autonomous multirover robot, in which a number of self-sustained mobile robots can self-assemble into a single serial-chain modular robot. This multirover robot will demonstrate new features, such as snakeManuscript received March 18, 2009; revised May 28, 2009. First published September 15, 2009; current version published December 8, 2009. This paper was recommended for publication by Associate Editor H. R. Choi and Editor W. K. Chung upon evaluation of the reviewers’ comments. This work was supported in part by the Ontario Center of Excellence. This paper was presented in part at the IEEE Canadian Conference on Electrical and Computer Engineering, Niagara Falls, ON, Canada, May 2008. The authors are with the Department of Electrical and Computer Engineering, The University of Western Ontario, London, ON N6A 5B9, Canada (e-mail:
[email protected];
[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/TRO.2009.2030227
like [5] and eel-like locomotion [6], to respond to different terrain conditions. This paper is organized as follows. Section II surveys related work. In Section III, the geometric conditions of a general docking mechanism are analyzed, the limitations on allowed errors are investigated, and the insertion force equations using a simplified model are derived. Section IV contains a description of the mechanism design. In Section V, we report on experiments in which we study the performance of the connection mechanism. In Section VI, we discuss the results. Section VII gives a brief summary of our future work and concludes the paper. II. RELATED WORK Taking the basic concept of the connection mechanism and applying it to the whole robot was first introduced with cellular robotic system (CEBOT) in the late 1980s [7]–[9]. Fukuda and Nakagawa studied a docking system for a cell-structured robot using a hook-type coupling mechanism [10] in which the connection mechanism requires a very precise alignment. PolyBot is a modular chain robot that was first presented by Yim et al. [11]. A shape-memory-alloy actuator integrated in each connection plate can rotate a latch to catch lateral grooves in the pins from the mating connection plate. Hirose et al. [12] proposed Gunryu, which is a distributed robotic concept, in which each robot is capable of fully autonomous locomotion. The manipulator could be used to set up a physical link with another robot. This configuration does not necessarily make a rigid connection. In 2000, the CONRO self-reconfigurable robots were presented [13]. Each CONRO module is equipped with four docking connectors to connect with other modules. Khoshnevis et al. [14], [15] presented a design of CONRO connectors. In both CONRO and PolyBot, no alignment error is acceptable. Brown et al. [16] developed Millibot in 2002. Similar to CONRO and PolyBot, the connection mechanism of a Millibot module is based on a set of pins and holes, but the modules are initially docked manually, and the system is controlled off-board with a joystick. In a similar work, Zhang et al. [17] presented a reconfigurable robot. The utilized connection mechanism consists of a cone-shaped connector and a matching couple and seems too bulky and heavy for a small robot module. Shen et al. [18] developed Super-Bot in 2005. The docking is initially carried out manually, and then, the robot can autonomously change shape. The most recent work in this area is carried out by Gross et al. [19], which is called Swarm-Bots (S-Bots). The system comprises autonomous modules, each equipped with a gripper and a surrounding ring that matches the shape of the gripper. The design of the connection mechanism allows for some misalignment. Bererton and Khosla [3] have used a docking connector that has forklift pins to dock between separate mobile robots with repair capabilities. The docking connector does not make a rigid connection. Docking is also essential for security robots to get automatically recharged [20]. A docking strategy has been proposed by Luo et al. [21]. As mentioned in Section I, a connection mechanism for mobile selfreconfiguring robots should satisfy four key requirements. None of the mentioned mechanisms seem to include all four specifications, due to the following constraints.
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Fig. 2.
Fig. 1. Geometry of docking connectors with a misaligned chamfered pin approaching a cylindrical hole.
1) Some of the mentioned joints do not include locking mechanisms (e.g., security robots and robots with repair capabilities). For autonomous self-assembly in mobile robots, it is necessary to lock the joint to secure a reliable connection. 2) Some mechanisms are not power efficient. For instance, S-Bots have rigid and flexible grippers actuated by dc motors, which are continuously activated while the S-Bots are connected. In our study, we look for a mechanism, which is in passive mode most of the time. 3) In most of the mentioned mechanisms, the modules need to be exactly aligned to get connected (e.g., CONRO, PolyBot, and Super-Bot). For our application, we try to permit considerable misalignment. 4) Those that satisfy the requirements are too heavy and bulky for a small-sized robot [17].
Projection of the pin’s edges on the hole plane.
We begin by developing an equation describing the distance from the hole’s center to an arbitrary point on the projected nose disk (the → → − − → − ellipse shown in Fig. 2). According to Fig. 2, d = − ρ +→ r , where d is jt → − the distance from the hole’s center to the point | r |e on the projected → nose disk, and − ρ is the distance between the hole and projected nose centers. It is noted that the position of the center of the ellipse denotes horizontal and vertical offsets, and the following derivations can be simply generalized to consider additional horizontal and vertical offsets misalignments. For successful docking, the nose of the pin should be located inside → − the rim of the hole. Therefore, as shown in Fig. 2, Rm in = | d |m a x is an essential condition for a successful docking (Rm in is the minimum necessary hole’s radius). In other words, the furthest point on the ellipse determines the minimum necessary hole’s radius. → − Distance | d | can be expressed by
→ − | d | = ((lc sinθ + r1 cos t)2 + (lc sinφ + r1 sin t)2 ). → − Calculating the derivative of | d | versus t yields r dr · + r(sin φ cos t − sin θ sin t) l dt dr (sin φ cos t + sin φ sin t) = 0 + dt
III. ALIGNMENT ANALYSIS Parts geometry, the stiffness of grippers supporting the parts, and friction between the connectors are the major factors in rigid-part mating [22]. In this section, two general analyses are performed to describe geometric conditions and force requirements of a common connection mechanism.
where r=
A. Kinematic Contact Analysis Before discussing contact forces, we first derive the kinematic conditions for successful assembly. For this purpose, a chamfered pin approaching a cylindrical hole is considered, and the effects of angular misalignments and the center of compliance length are investigated. A general geometry of docking connectors is shown in Fig. 1. In this figure, R, r1 , and r2 denote the hole, the nose, and the pin radii, respectively. We define yaw and pitch angular misalignments (with respect to the center axis of the hole) by θ and ϕ, respectively. Consequently, it is deviated by the horizontal and vertical offset values lc sinθ and lc sinφ, respectively, where lc is the center of compliance length. We set up a coordinate system O–XY to the front plane of the hole. The pin’s nose edge is projected on the hole’s front plane, and a coordinate system O –X Y is assigned to the projected surface, where O and O are the centers of the hole and the projected nose disk, respectively (see Fig. 2).
(1)
(2)
a2 b2 a2 sin2 t + b2 cos2 t
a = r1 cos θ, and b = r1 cos φ. → − Calculating t from (2) and substituting it into (1), we obtain | d |m a x . For this analysis, given a geometry (r1 , lc , R), we can find a kinematic upper bound on yaw and pitch errors, assuming the center of compliance is on the hole’s center line. However, since larger yaw angles can be accommodated by moving the center of compliance, the kinematic result is not sufficient.
B. Force Analysis In a docking maneuver, due to practical constraints and technical limitations, it is not always possible to eliminate all the errors in advance. Therefore, the connectors may be misaligned at the moment of docking. The following analysis describes the forces appearing during an imperfect docking process.
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Fig. 5. (a) For θ = α, two-point contact changes into a line contact, and wedging happens. (b) Any yaw angle greater than α eventually results in wedging.
applied by the approaching robot, and the friction force between robot wheels and floor are expressed in terms of Ft r and Ff r at this point. In this case, the force balance yields
Fig. 3. small.
Forces acting during a two-point contact while the yaw angle is very
fx = 0 ⇒ f1 + f2 (µ sin α − cos α) − Ff r = 0
(3)
fy = 0 ⇒ Ft r − µf1 − f2 (µ cos α + sin α) = 0
(4)
d 2
τ = 0 ⇒ µf1
− lc Ff r − lf2 sin γ − µlf2 cos γ = 0 (5)
where γ = α − θ − sin−1
d sin θ 2l
(6)
2
and l=
d 2
+ D 2 − dD cos θ.
(7)
Combining (3) through (5) yields Fig. 4. Forces acting during a two-point contact while the contacts both happen on the rim of the hole.
Docking can be analyzed to be a geometric problem. Our analysis is worked out on a cylindrical chamfered pin and a chamferless hole as docking connectors, which are fixed on mobile robots, and the robots, as supports, would have some compliance. The analyses that follow assume that the forces are in approximate static equilibrium. This means, in practice, that accelerations are negligible. It is noted that the force balance represents a stuck condition. Any greater traction force can complete the docking maneuver. Following Whitney [23], consideration of a typical dockingconnector geometry shows that a docking event has five stages: approach, chamfer crossing, one-point contact, two-point contact, and line contact. In general, the approaching (and/or the goal) robot (support) rotates and translates during docking, as alignment errors are corrected. The compliant support must, therefore, provide both lateral and angular compliances for at least one of the docking parts. As wedging and jamming conditions occur during two-point contact, hence, we focus on two-point contact analysis. Considering the yaw angle to be very small, the forces acting during a two-point contact are shown in Fig. 3. A force balance can be written for this geometry, but since wedging does not occur in this phase, we focus on the analysis of the next phase. Depending on the geometry of the connectors and the trajectory of the robot motion, for larger yaw angles, both two-point contacts may happen on the rim of the hole. The forces acting during this phase are shown in Fig. 4. It is assumed that the pin is attached to the support at a point called center of compliance (which is marked as ), and lc is the distance from this point to the rim of the hole. The traction force
Ft r =
lc + C1 µ(lsin γ + µl cos γ) + (µd/2)(C2 µ − 1) · Ff r (8) (C2 µd/2) + C1 (lsin γ + µl cos γ)
where γ and l are defined using (6) and (7), respectively, and C1 =
1 (µ2 − 1)sinα − 2µcosα
C2 =
µsin α − cos α . (µ2 − 1)sin α − 2µcos α
(9) (10)
It is interesting to note that the traction force is linear to the friction force. Hence, reducing the friction force (or making one robot free to turn) will always reduce the traction force. If the yaw angle increases, a situation occurs in which two-point contact changes into a line contact, and this happens if θ = α [see Fig. 5(a)]. In this case, wedging happens and docking fails. Any yaw angle greater than α [see Fig. 5(b)] will finally result in wedging. Using (8), docking can be analyzed, and the relation between θ and Ft r can be investigated. For example, we set D = 0.022 m, d = 0.02 m, α = 30◦ , lc = 0.15 m, µ = 0.5, and Ff r = 0.5 N. Fig. 6 shows the plot of traction force that is needed to complete the docking as the yaw angle changes. As discussed earlier, the values for very small yaw angles are not exact, since this model is based on a two-point contact with both contacts on the rim of the hole. As can be seen, the docking force increases and becomes very large as the yaw angle increases and approaches α. IV. CONNECTION MECHANISM DESIGN AND CONSTRUCTION In this section, we discuss the design details of the proposed mechanism.
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Fig. 9. Latch consisting of two linear actuators and a key attached to the ends of the actuators.
Fig. 6. Traction force that is needed to complete the docking as the yaw angle changes. Note the approach to singularity as yaw angle approaches α.
Fig. 7. Pin’s head design can prevent wedging by curving the end of the cone with a curvature equal to the pin’s diameter. Fig. 10.
Fig. 8. Docking joint. (a) Male connector, whose head curvature allows a smooth docking. (b) Female connector, whose slot enables a key to lock the joint. (c) Merging of the connectors.
A. Connectors The traditional approach to prevent wedging due to line contact is to curve the end of the cone with a curvature equal to the pin’s diameter [23] (see Fig. 7). Therefore, we profiled the conical head of our original design [25] to allow misalignments larger than α. According to the following figures, the designed joint consists of a male piece [see Fig. 8(a)] and a female opponent [see Fig. 8(b)] that join together and a locking mechanism that locks the joint. The slots on both male and female connectors enable a key to lock the joint. Fig. 8(c) shows the way in which these two parts fit together. B. Latching Mechanism For physically docking and undocking, the female part also houses a latch (see Fig. 9), which consists of two linear actuators that are located on the sides of the pipe (the female part), and a key attached to the ends of the actuators. The key is placed on the slot of the pipe. When the pin (the male part) enters the pipe and reaches the end of it, a contact switch is closed that activates the linear actuators. The attached key moves down into the slot of the pin and locks the joint. To unlock the joint, the linear actuators are activated to move back so that the key is disengaged, and the pin is released. This mechanism is advantageous, as it is compact and easy to use, which makes it reliable. Moreover, the mechanism is quite power ef-
Physical implementation of the docking mechanism.
ficient, because activation of the actuators is needed only during the opening and closing phase. The latch consists of two linear actuators, each driven by a small dc motor linked to a gear train and, finally, a lead screw. This configuration is normally locked unless the actuators are powered. The latch mechanism is activated only during the docking/undocking operation, which takes a few seconds. It should be noted that both actuators are actuated simultaneously and with great precision. The actuators positions along their strokes are accurately controlled based on feedback from built-in 2-kΩ precision linear potentiometers [24].
C. Joint Construction Fig. 10 shows the physical implementation of the docking mechanism built from aluminum 6061-T6. The total height is 8 cm, and the whole mechanism weighs 185 g. As can be seen, a contact switch is used to sense the pin once it reaches the end of the pipe. The high-force (24 N each) linear actuators are PQ-12f from Firgelli Technologies, Inc.
V. EXPERIMENTAL RESULTS In this section, experimental studies are carried out to evaluate the performance of the connection mechanism. The experiments are designed to include possible misalignment errors (yaw, roll, and offset) in order to determine the capabilities of the proposed mechanism. Considering pitch angular misalignment is not quite relevant for this research because the robots are expected to dock with one another while they are on the same level, however, it is noted that due to the spherical head of the male piece, the mechanism should have the same pitch angular tolerance as its yaw angular misalignment tolerance. The following sections discuss the experimental setup and results.
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Fig. 11.
Experimental setup.
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Fig. 12. Relationship between the docking force and the yaw misalignment angle while the goal robot is immoveable. In this, and all figures, a trend line has been added to make the graph easier to read.
A. Experimental Setup Fig. 11 shows the experimental setup, which is utilized to evaluate the performance of the proposed docking joint, and it includes two mobile robots. The connection mechanism base is fixed on the back of the goal robot, and the pin is located in front of the approaching robot. The pin is connected to a force meter, which, in turn, is attached to the body of the approaching robot. This configuration allows us to directly measure the docking force. In this paper, docking force is defined as the maximum traction force applied by the approaching robot to complete the docking maneuver. The goal robot is stationary, and the other robot is free to approach from different directions. While the robot is running, docking force and robot motor current are monitored. It is noted that these robots are used only to identify the mechanism capabilities and are not those that will be utilized in the final system. The experiments are performed while a fixed digital camera records the docking maneuver of the robots. Basic image processing is performed to measure the connectors’ misalignment (offset or angular). During the experiments, the voltage supplied to the robot has to be kept constant to make sure that the experiments are done under the same conditions. Therefore, we power the robot through an external power supply instead of using the onboard batteries. The coefficient of friction between the robot wheels and the surface is 0.53, and the approaching robot weighs 44 N. No lubricant is used for this test.
it is observed that once the robot reaches the docking base, the goal robot turns to get aligned. This experiment shows that if the goal robot is free to turn, this configuration allows a maximum ±37◦ yaw angular misalignment. As the docking station can easily turn around, the docking force can be neglected (roughly 3 N).
B. Yaw Angular Misalignment
C. Roll Angular Misalignment
In this part, two experiments are planned to investigate the effect of yaw misalignment on the docking force. Yaw angular misalignment occurs when the pin (male connector) is set at a yaw angle to the pipe (female connector). The angle can be to the left or the right. In the first test, the goal robot is considered to be fixed. This case could happen when a single robot tries to dock to a set of connected modules. Therefore, in order to carry out the docking maneuver, the approaching robot has to slip in order to get aligned. As a result, the docking force changes as the angle increases. In this paper, docking force is defined as the maximum force that is needed to complete the docking maneuver. It is observed during the experiment that if the goal robot is fixed, this configuration allows a maximum ±10◦ yaw angular misalignment. Fig. 12 shows how the docking force changes as the yaw angular misalignment increases. In the second test, the goal robot is free to turn, which is likely to happen when two single robots are connecting together. In this test,
The purpose of this experiment is to determine the relationship between the actuators maximum current and the roll-misalignment angle of the connectors and to identify the maximum allowable rollmisalignment angle. In roll misalignment, the male connector rotates around its centerline, whereas the female connector is fixed (see Fig. 13). Therefore, some force is applied to the key when it is moving downward to lock the joint. Fig. 14 shows the experimental setup, which is utilized for this part. The setup includes a load with the same moment of inertia as that of one robot module (≈1 g·m2 ), which is attached to the male connector. The connector is set to different roll angles, and the actuator’s motor current is monitored while the key is moving downward. Fig. 15 shows the relationship between the actuators maximum current and the roll-misalignment angle of the connectors. The experiment reveals that the mechanism overcomes maximum ±75◦ roll misalignment, while the mentioned load is attached to the joint.
Fig. 13.
Roll misalignment.
Fig. 14.
Experimental setup utilized to test-roll-misalignment tolerance.
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Fig. 15. Relationship between the actuators maximum current and the rollmisalignment angle of the connectors.
Fig. 18. Energy needed to lock the joint for different loads. External forces are applied as exerted loads.
TABLE I MAXIMUM MISALIGNMENT TOLERANCE
Fig. 16.
Fig. 17.
Offset misalignment.
Relationship between the docking force and the offset displacement.
D. Offset Misalignment Offset misalignment occurs when the pin and pipe centerlines are parallel but not in the same line; therefore, they are offset horizontally (see Fig. 16). It is observed during the experiments that this configuration allows a maximum ±10-mm offset displacement. Fig. 17 shows the relationship between the docking force and the connectors’ offset displacement. E. Energy Consumption As the power on a mobile robot is limited, energy consumption is a key consideration when designing an electromechanical mechanism for mobile robots. Fig. 18 shows the energy needed to lock the joint for different loads. VI. DISCUSSION The misalignment tolerance analysis for the proposed configuration is summarized in Table I, and the results are compared with some related work. It is seen from the table that the performance of the docking mechanism is highly dependent on the joint head design. Profiling
the conical head design allows significantly more yaw misalignment, which is the most likely constraint on the docking system. The proposed configuration seems to be the first of its kind in robotic applications that allows such misalignment tolerance, since in most of the proposed systems with a passive joint, no misalignment is acceptable [10], [11], [14], [16], [18]. The experiments only cover the docking maneuver of the robots. It is clear that compared with docking, undocking is a relatively simple process, since no realignment is needed. Overall, it is observed that this docking mechanism is reliable, easy to construct, and lightweight yet sturdy. The locking mechanism is quite power efficient in that it is in a passive mode most of the time.
VII. CONCLUSION AND FUTURE WORK This paper presented the design and implementation of a reconnectable joint that autonomously connects and disconnects two robot modules. The proposed mechanism is lightweight, compact, and powerful enough to secure a reliable connection. It overcomes significant alignment errors, and it is considerably power efficient. The proposed mechanism can be extended to fit the needs of different types of self-reconfiguring, mainly for intrarobot docking applications, in which robot modules may connect with one another at different roll angles. If grooves are engraved on four sides of the pin, the latching mechanism can lock the pin at multiple roll angles. Once the modules are connected, it would be quite useful if they could exchange data. Since there will be point-to-point connections between the docking plates of the modules, therefore, infrared transceivers (aimed in the same direction) can be embedded on the docking plates, thereby allowing data to be shared between the modules without any physical connection.
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Our future work includes integrating the proposed connection mechanism with an exact yet wide-ranging relative pose system for detection and localization of the robots. The overall objective is to develop an autonomous multirover robot, in which a team of autonomous mobile robots can assemble into a single serial-chain modular robot.
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[24] Firgelli. (2008, May). Miniature linear motion PQ-12f [Online]. Available: http://www.firgelli.com/pdf/PQ12_datasheet.pdf [25] M. Delrobaei and K. McIsaac, “Docking joint for autonomous selfassembly,” in Proc. IEEE Can. Conf. Electr. Comput. Eng., May 2008, pp. 1025–1029.
Drive Train Optimization for Industrial Robots
[1] M. Rubenstein, K. Payne, P. Will, and W. Shen, “Docking among independent and autonomous CONRO self-reconfigurable robots,” in Proc. IEEE ICRA, Apr. 2004, vol. 3, pp. 2877–2882. [2] M. W. Jorgensen, E. H. Ostergaard, and H. H. Lund, “Modular ATRON: Modules for a self-reconfigurable robot,” in Proc. Int. Conf. Intell. Robots Syst., Sep. 2004, vol. 2, pp. 2068–2073. [3] C. Bererton and P. K. Khosla, “Towards a team of robots with reconfiguration and repair capabilities,” in Proc. IEEE ICRA, 2001, vol. 3, pp. 2923–2928. [4] M. Yim, Y. Zhang, and D. Duff, “Modular Robots,” IEEE Spectr., vol. 39, no. 2, pp. 30–34, Feb. 2002. [5] S. Hirose and M. Mori, “Biologically inspired snake-like robots,” in Proc. IEEE Int. Conf. Robot. Biomimetics, Aug. 2004, pp. 1–7. [6] K. A. McIsaac and J. P. Ostrowski, “Motion planning for anguilliform locomotion,” IEEE Trans. Robot. Autom., vol. 19, no. 4, pp. 637–652, Aug. 2003. [7] M. Yim, W. Shen, B. Salemi, and D. Rus, “Modular self-reconfigurable robot systems; challenges and opportunities for the future,” IEEE Robot. Autom. Mag., vol. 14, no. 1, pp. 43–52, Mar. 2007. [8] T. Fukuda and S. Nakagawa, “A dynamically reconfigurable robotic system (concept of a system and optimal configurations),” in Proc. IEEE Int. Conf. Ind. Electron., Control, Instrum., Los Alamitos, CA, 1987, pp. 588– 595. [9] T. Fukuda and S. Nakagawa, “Approach to the dynamically reconfigurable robotic system,” J. Intell. Robot. Syst., vol. 1, no. 1, pp. 55–72, 1988. [10] T. Fukuda and S. Nakagawa, “Method of autonomous approach, docking and detaching between cells for dynamically reconfigurable robotic system cebot,” JSME Int. J., vol. 33, no. 2, pp. 263–268, 1990. [11] M. Yim, D. G. Duff, and K. D. Roufas, “PolyBot: A modular reconfigurable robot,” in Proc. IEEE ICRA, Apr. 2000, vol. 1, pp. 514–520. [12] S. Hirose, T. Shirasu, and E. F. Fukushima, “Proposal for cooperative robot Gunryu composed of autonomous segments,” Robot. Auton. Syst., vol. 17, pp. 107–118, 1996. [13] W. Shen and P. Will, “Docking in self-reconfigurable robots,” in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst., Oct. 2001, vol. 2, pp. 1049–1054. [14] B. Khoshnevis, R. Kovac, W. Shen, and P. Will, “Reconnectable joints for self-reconfigurable robots,” in Proc. IEEE Int. Conf. Intell. Robots Syst., Oct. 2001, vol. 1, pp. 584–589. [15] B. Khoshnevis, P. Will, and W. Shen, “Highly compliant and selftightening docking modules for precise and fast connection of selfreconfigurable robots,” in Proc. IEEE Int. Conf. Robot. Autom., Sep. 2003, vol. 2, pp. 2311–2316. [16] H. B. Brown, Jr., J. M. V. Weghe, C. A. Bererton, and P. K. Khosla, “Millibot trains for enhanced mobility,” IEEE/ASME Trans. Mechatron., vol. 7, no. 4, pp. 452–461, Jul. 2002. [17] H. Zhang, W. Wang, Z. Deng, and G. Zong, “A novel reconfigurable robot for urban search and rescue,” Int. J. Adv. Robot. Syst., vol. 3, no. 4, pp. 359–366, 2006. [18] W. Shen, M. Krivokon, H. Chiu, J. Everist, M. Rubenstein, and J. Venkatesh, “Multimode locomotion via SuperBot reconfigurable robots,” Auton. Robots, vol. 20, no. 2, pp. 165–177, Mar. 2006. [19] R. Gross, M. Bonani, F. Mondada, and M. Dorigo, “Autonomous selfassembly in swarm-bots,” IEEE Trans. Robot., vol. 22, no. 6, pp. 1115– 1130, Dec. 2006. [20] M. C. Silverman, D. Nies, B. Jung, and G. S. Sukhatme, “Staying alive: A docking station for autonomous robot recharging,” in Proc. IEEE Int. Conf. Robot. Autom., 2002, vol. 1, pp. 1050–1055. [21] R. C. Luo, C. T. Liao, K. L. Su, and K. C. Lin, “Automatic docking and recharging system for autonomous security robot,” in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst., Aug. 2005, pp. 2953–2958. [22] D. E. Whitney, “Quasi-static assembly of compliantly supported rigid parts,” ASME J. Dyn. Syst. Meas. Control, vol. 104, pp. 65–77, 1982. [23] D. E. Whitney, Mechanical Assemblies: Their Design, Manufacture, and Role in Product Development. London, U.K.: Oxford Univ. Press, 2004.
¨ Marcus Pettersson and Johan Olvander Abstract—This paper presents an optimization strategy for finding the trade-offs between cost, lifetime, and performance when designing the drive train, i.e., gearboxes and electric motors, for new robot concepts. The method is illustrated with an example in which the drive trains of two principal axes on a six-axis serial manipulator are designed. Drive train design for industrial robots is a complex task that requires a concurrent design approach. For instance, the mass properties of one motor affect the torque requirements for another, and the method needs to consider several drive trains simultaneously. Since the trajectory has a large impact on the load on the actuators when running a robot, the method also includes the trajectory generation itself in the design loop. It is shown how the design problem can be formalized as an optimization problem. A non-gradientbased optimization algorithm that can handle mixed variable problems is used to solve the highly nonlinear problem. The outcome from an industrial point of view is minimization of cost and the simulataneous balancing of the trade-off between lifetime and performance. Index Terms—Design automation, drive train optimization, industrial robots.
I. INTRODUCTION Reducing cycle time is an important objective for many manufacturers in order to remain competitive in the marketplace. In many areas where cutting cycle time is desirable, industrial robots are used, and the robot itself is often the bottleneck. Meeting the demand for better performance and still make profitable robots is in turn a considerable challenge for robot manufacturers. In the case of industrial robots, there is also a conflict between performance in terms of cycle time for a specific application and the range of possible applications. Pushing the design toward high performance for a typical area of application often means shrinking the total size of the range of applications. For example, designing an articulated robot dedicated for high-speed material handling leads to a design that is not applicable to (or at least far from optimal for) high-precision laser cutting. When designing a robot for a large spectrum of user scenarios, where many are even unknown, the designers are often forced to think in terms of worst-case scenarios. However, stricter requirements increase the cost and a key factor for
Manuscript received February 5, 2009; revised May 26, 2009. First published September 1, 2009; current version published December 8, 2009. This paper was recommended for publication by Associate Editor I.-M. Chen and Editor K. Lynch upon evaluation of the reviewers’ comments. This work was supported in part by the Swedish Governmental Agency for Innovation Systems under Grant 2004-02314. M. Pettersson was with the Department of Management and Engineering, Link¨oping University, SE 58183 Link¨oping, Sweden. He is now with ABB, Corporate Research, SE-721 78 V¨aster˚as, Sweden (e-mail: marcus.pettersson@ se.abb.com). ¨ J. Olvander is with the Department of Management and Engineering, Link¨oping University, SE 58183 Link¨oping, Sweden (e-mail: johan.olvander@ liu.se). 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/TRO.2009.2028764
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