In quasistatic motions the robot contacts objects in the environment at ... requiring a solution of the path-planning problem while maintaining stable equilibrium during the ... when limited general external forces (forces or torques) are applied.
Spider Robot for Motion with Quasistatic Force Constraints Shraga Shoval, Elon Rimon and Amir Shapira Technion - Israel Institute of Technology - Haifa, Israel 32000. Abstract In quasistatic motions the robot contacts objects in the environment at several points, and moves by pushing itself against these objects. This motion type leads to the design of a spider-like mechanism consisting of four limbs, each with four links (total of 16 links). The robot operates by embracing itself against objects in the environment and changing its internal configuration to move the central body toward the target. A control system maintains controllable contact forces required for static equilibrium. The robot is equipped with special footpads which enable motion regardless of friction between the robot and the environment. The robot can be used for travel through complicated and unstructured environments such as disaster areas, nuclear reactors, oil refineries, etc. The robot can also be used for traveling in non-gravitational environments such as congested space stations. A micro version of the robot can be utilized for minimally invasive medical procedures inside a human body
1.
Introduction
Classical motion planning problems deal with navigating a robot towards a goal configuration while avoiding collisions with obstacles. However, some motion planning problems permit or even require some type of interaction of the robot with objects in the environment. For example, surveillance of an earthquake area, dangerous exploration such as in the crater of a live volcano, and inspection of nuclear reactors, all require motion in congested, unstructured and complex environments In these type of problems, motion is performed under force/torque constraints, requiring a solution of the path-planning problem while maintaining stable equilibrium during the motion. In quasistatic motion, inertial effects due to moving parts are small relative to the
forces/torques of interaction between the robot and the environment. Motion is generated by reaction forces between the robot and objects in the environment. Motion of spider-like [Boissonnat et. al., 1992] and snake-like [Shan and Koren, 1993] mechanisms are examples of mobile robots that can operate with quasistatic motion planning.
Mobile legged mechanisms are usually designed to operate on limited variety types of terrains such as flat terrain [Hirose and Kunieda, 1991; Furusho and Sano, 1990], pipe-like terrain [Neubauer, 1994], or between ladder rungs [Madhani and Dubowski, 1992]. In contrast, our goal is to design a multi-legged mechanism that can move over a general piecewise rigid terrains. We limit ourselves to quasistatic motion as one of the important properties of this type of locomotion is the continuous equilibrium under which the robot can operate. Furthermore, when the environment is rich enough (e.g. the environment contains large amount of possible footholds within the reachability of the robot), it is also possible to plan the motion such that the mechanism is immobilized. In such a case locomotion is performed similar to a rock climber which continuously holds several artificial or natural hinges, pegs or steps, and moves while maintaining contact with these objects. Immobilization of a mobile robot means that the mechanism can maintain its configuration even when limited general external forces (forces or torques) are applied. In such a case, motion of the robot’s main body is performed by changing its internal configuration, and stability is not affected by external forces (including gravity). This property enables the robot to reliably operate in general and complex terrains even when un-predicted forces are applied.
Applications of quasistatic motion of legged mechanisms include inspection of complicated structures such as nuclear reactors or refinery plants, which typically have a large number of pipes, tubes, tunnels, steps etc. Similarly, a collapsed structure after an earthquake or other disaster requires immediate inspection for survivors before any clearing procedure can take place. Moreover, in such tasks the robot cannot always rely on friction, as surfaces may be wet, oily or icy. Space structures is another type of environment which requires quasistatic motion, as motion
relies entirely on contact with objects rather than on gravitational forces. Finally, minimally invasive medical diagnostics and surgery could be performed by small autonomous “mini-robots”. This application requires motion through small and complex shaped organs in many directions, often against gravity, with little or no friction forces between the robot and the environment. These mini-robots may often need to operate against external forces (i.e. the drag forces generated by the blood pressure), and therefore must immobilize themselves during operation.
2.
The Robot Motion
Motion consists of three phases in which the central body advances toward the target configuration while maintaining stable equilibrium: Phase I: At this phase all but one limb contact the environment to maintain immobilization, while the free limb (the fourth) is moving forward toward the next foothold. When the limb reaches its position, controlled contact between the limb’s foot pad and the surface is generated, in which the required contact force is maintained. The dynamic forces generated by the slow motion of the free limb are negligible compared with the contact forces between the other limbs and the objects. Phase II: All four limbs now are in contact with stationary surfaces. The central body can now move forward in an internal motion (due to the redundancy of the 16 DOF of the four limbs) such that the contacts between the limbs and the environment are maintained. As with the previous stage, motion is relatively slow, and dynamic forces are negligible compared with the interaction forces between the robot and the environment. Phase III: One limb starts motion towards its next position. Motion is performed such that the limb maintains contact with surfaces in the environment to provide sufficient conditions for immobilization. The final position of this limb is determined to achieve a new stability point (A point where the contact forces of three limbs intersect). Again, no dynamic effects are generated due to the slow motion of the limb. Once this limb reaches its final position, the next limb can detach itself from contact with the environment and moves towards its next foot hold (back to phase I).
Forces Intersection point
Phase 1: One limb motion
Initial Configuration
Phase 2: Central body motion
End of motion in Phase 1
New Forces Intersecting Point
Phase 3: Controlled motion of one limb
Back to Phase 1: One limb motion
Figure 1. The three motion phases of the spider 3.
Mechanical Design
3.1 General structure The robot consists of a central body to carry power supplies, control devices and additional sensors and equipment (figure 2). Four articulated limbs each with four degrees of freedom are attached to the central body. Motion of the spider refers to movements of the central body while the limbs provide contact with the environment and generate the forces to move the central body.
Central Body
Articulated Limbs
Figure 2 General Structure of the spider robot 3.2 The footpad Although we assume no friction forces between the footpad and the contact surface, practically it is impossible to select materials (both for the robot and the environment) that create no friction. In general, friction forces improve the stability of legged mechanisms, and materials and geometry are selected to increase friction (e.g. shape and materials of automobile wheels and walking shoes). However, the introduction of friction forces in Quasistatic motion affects motion planning, as it is difficult to predict the magnitude of these forces. Furthermore, friction forces vary upon temperature, moisture, dust, surface quality and other environmental effects which cannot be accurately predicted in advance. To eliminate the effect of friction forces, a semi passive footpad mechanism, shown in Fig. 3, is attached to the last link of each limb. This mechanism consists of rotating triangular shaped flange, with two bearings at each edge, and an electronic brake. When the foot pad reaches a surface, the mechanism is switched to passive mode, enabling one of the edges to fully contact the surface with the two bearings, by freely rotating around its pivot. Next, the electronic clutch is activated, “locking” the mechanism from rotating. This locked configuration enables only perpendicular forces to be transferred from the contact surface to the robot, similar to a non friction surface.
Ball bearings Last link
Electrical brake Figure 3 The foot pad 3.3 Interaction between limbs
The four limbs are attached to the central body which is a rigid square. This configuration obviously requires careful motion planning and synchronization in the motion of each limb as working volume of the limbs overlap each other. To minimize interference between adjacent limbs two types of limbs were developed: an upper and a lower limb. In the upper limb all motors, gears and other peripherals are positioned above the links, while in the lower limb all driving mechanisms are underneath. This way each limb can utilize nearly all its working volume, regardless of the configuration of the other limbs. The only overlap is between any two diagonal limbs, reducing significantly the total overlapping areas, while enabling effective utilization of each limb. Figure 4 shows a schematic description of the upper limb while figure 5 shows the lower limb. It should be noted that the upper limb is equipped with a balancing pad attached to the last link, and the lower limb is equipped with a roller ball. These mechanisms increase the stability of the robot. In certain configurations the robot may be subjected to a gravitational torque generated by the weight of the motors and the links, which can tip over the robot. The balancing mechanisms are aim to prevent such an occurrence. The balancing pad of the upper limb can be lifted up when this limb is required to move above the lower limb, again to reduce interference between limbs.
LINEAR ACTUATOR ENCODER
MOTOR
LINK III BALANCING PAD
LINK II LINK I CENTRAL BODY
Figure 4 Schematic description of the upper limb
CENTRAL BODY
LINK I LINK II LINK III
MOTOR ENCODER
ROLLER BALL
Figure 5 Schematic description of the lower limb 4. Summary The design of a spider like mobile robot was presented. The robot consists of a central body and four limbs, each with four degrees of freedom. Motion consists of three major phases in which the robot embraces itself against objects in the environment and changes its internal configuration toward the target. This motion requires continuous contacts with objects in the environment for maintaining a stable equilibrium during all motion phases. This motion planning also guarantees that the mechanism is immobilized such that equilibrium is maintained even if external forces are applied on the robot. Each limb is equipped with a special foot pad to enable the robot to move regardless of the friction at contact points.
This type of robot is suitable for operation is cluttered and unstructured environments where conventional mechanisms are not efficient. Possible applications include nuclear reactors, refineries plants or collapsed structures which typically consists of a large number of pipes, tubes, tunnels etc. The robot is also suitable for missions in space stations where due to lack of gravity motion must rely on pushing or pulling of objects. Finally, a micro version of the robot can be utilized for minimally invasive medical procedures inside a human body.
References
1. Boissonnat J-D., Devillers, O., Donati L., Preparata F. P., “Motion Planning for Spider Robots”, Proceedings of the IEEE 1992 conference on Robotics and Automation, Nice France, May, 1992, pp. 2321-2326 2. Furusho J., and Sano A., “Sensor Based Control of a Nine-Link Biped”, The International Journal of Robotics Research, Vol. 9, No. 2, April 1990, pp. 83-98. 3. Hirose S., and Kunieda O., “Generalized Standard Foot Trajectory for a Quadruped Walking Vehicle”, The International Journal of Robotics Research, Vol. 10, No. 1, February 1991, pp. 312. 4. Madhani A., and Dubowsky S., “Motion Planning of Mobile Multi-Limb Robotic Systems Subject to Force and Friction Constraints”, Proceedings IEEE Robotics and Automation, pp. 133-139, Nice France, May 1992. 5. Neubuer W., “Spider-like robot that climbs vertically in ducts or pipes”, Proceedings of the IEEE conference on Intelligent Robots and Systems, Munich Germany, Vol., 2, pp. 1178-1185, 1994. 6. Shan Y., Koren Y., “Design and Motion Planning of a Mechanical Snake”, IEEE Transactions on Systems Man and Cybernetics, 23(4), pp. 1091-1100, July-August 1993.
