Land locomotion can be broadly characterized as quasi-static or dynamic. Quasi-static equilibrium implies that inertial (acceleration-related) effects are small enough to ignore. That is, motions are slow enough that static equilibrium can be assumed. Stability of quasi-static systems depends on keeping the gravity vector through the center of mass within the vehicle's polygon of support determined by the ground-contact points of its wheels or feet. Energy input is utilized predominantly in reacting against static forces. Such systems typically have relatively rigid members, and can be simply, kinematically controlled. In dynamic locomotion, inertial forces are significant with respect to gravitional forces. Dynamic effects gain relative importance when speed is high, gravity is weak and dynamic disturbances (e.g. rough terrain) are high. Significant energy input is required in controlling system momentum, and in some cases, in controlling elastic energy storage in the system. As performance limits of mobile robots are pushed, dynamic effects will increasingly come into play. Further, robotic systems that behave dynamically may be able to exploit momentum to enhance mobility, as is clearly demonstrated by numerous human- controlled systems: gymnasts, dancers and other athletes; stunt bicycles and motorcycles; motorcycles on rough terrain; cars that vault obstacles from ramps; etc.
It is paradoxical that those factors which produce static stability may be contradict dynamic stability. For example, a four-wheel vehicle that is very low and wide has a broad polygon of support, is very stable statically, and can tolerate large slopes without roll-over. However, when this vehicle passes over bumps, dynamic disturbances at the wheels generate large torques, tending to upset the vehicle about the roll, pitch and yaw axes. In effect, the large, rigid polygon of support required for static stability provides a leverage mechanism for the generation of dynamic torque disturbances. Further, the support points must comply with the surface, statically as well as dynamically, by control of support points (e.g. active suspension) and/or by vehicle attitude changes. Sophisticated vehicle suspensions have been developed to minimize dynamic disturbances, yet the introduction of passive-spring suspensions decreases static stability by allowing the center of mass to move toward the outside of the support polygon. Active suspensions may overcome this problem, but require additional complexity and energy requirements.
Consider a bicycle or motorcycle which has two wheels in the fore-aft (tandem) configuration. Such a vehicle is statically unstable in the roll direction, but achieves dynamic stability at moderate speed through appropriate steering geometry and gyroscopic action of the steered front wheel. Steering stability generally increases with speed, due gyroscopic effects. Dynamic forces at the wheel-ground contact point act on or near the vehicle centerline, and thus produce minimal roll disturbances. Additionally, the bicycle can remain upright when traveling on side slopes. Thus, sacrificing static roll stability enhances the dynamic roll stability and permits the vehicle to automatically adjust to side slopes.
As a logical extension of this argument, consider a single wheel rolling down an incline. Under the influence of gravity, gyroscopic action causes the wheel to precess (the axis of wheel rotation turns) about the vertical axis--rather than simply falling sideways as it does when not rolling--and the wheel steers in the direction it is leaning. The resulting curved path of motion of the wheel on the ground produces radial ("centrifugal") forces at the wheel-ground contact point, tending to right the wheel. Dynamic disturbances due to surface irregularities act through or near the wheel's center of mass, producing minimal torques in roll, pitch and yaw. The angular momentum of the wheel, in addition to providing the natural gyroscopic steering mechanism, tends to stabilize the wheel with respect to roll and yaw. In terms of attitude control, the wheel is practically insensitive to fore/aft and side slopes. The result is a highly stable rolling motion with minimal attitude disturbances and tolerance to fore/aft and vertical disturbances. One can readily observe this behavior by rolling an automobile tire down a bumpy hillside.
"Gyrover" is a novel, single-wheel, gyroscopically stabilized robot concept. The behavior of Gyrover is based on the principle of gyroscopic precession, as exhibited in the stability of a rolling wheel. Gyrover supplements this basic concept with the addition of an internal gyroscope nominally aligned with the wheel and spinning in the direction of forward motion. The gyro's angular momentum produces lateral stability when the wheel is stopped or moving slowly. A tilt mechanism enables tilting the gyro's axis about the fore/aft (roll) axis with respect to the wheel. Because the gyro acts as an inertial reference in attitude, the principal effect of the tilt action is to cause the wheel to lean left or right, which in turn causes the wheel to steer (precess) in the direction of leaning. Torques generated by a drive motor--reacting against the internal mechanism which hangs as a pendulum from the wheel's axle--produce thrust for acceleration and braking.
In addition to those advantages cited above for a single-wheel vehicle, there are potentially a number of additional advantages to this concept over multi-wheeled vehicles:
Potential applications for Gyrover are numerous. Because it can travel on both land and water, it may find amphibious use on beaches or swampy areas, for general transportation, exploration, rescue or recreation. Similarly, with appropriate tread,it should travel well over soft snow with good traction and minimal rolling resistance. As a surveillance robot, Gyrover could use its slim profile to pass through doorways and narrow passages, and its ability to turn in place to maneuver in tight quarters. Another potential application is as a high-speed lunar vehicle, where the absence of aerodynamic disturbances and low gravity would permit efficient, high-speed mobility. As the development progresses, we anticipate that other, more specific uses will become evident.
During a year of preliminary work, Gyrover has grown from an improbable yet intriguing concept for mobility, to the reality of working vehicles. We have studied the feasibility through basic analysis and simple experiments, and designed and built two, radio- controlled (RC) working models. These have proven the concept workable, and have verified many of the expected advantages.
Experimental work to date includes several simple experiments to verify the stability and steering principle, and two working vehicles. The first vehicle, Gyrover I was assembled from available RC model airplane/car components, and quickly confirmed the concept. The vehicle has a diameter of 29 cm and mass of 2.0 kg. It can be easily driven and steered by remote control; has good high-speed stability on smooth or rough terrain; and can be kept standing in place. This vehicle has traveled at over 10 kph, negotiated relatively rough terrain (a small gravel pile), and traversed a 45-degree ramp 75% its height. Recovery from falls (resting on the round side of the wheel) has been achieved with a strategy using both the wheel forward drive and gyro-tilt control. The main drawbacks to this robot are its lack of resilience and vulnerability to wheel damage; excessive battery drain due to drag on the gyro (bearing and aerodynamic); inadequate torque in the tilt servo; and incomplete enclosure of the wheel.
Gyrover I
A second vehicle, Gyrover II was designed to address these drawbacks. It is slightly larger than Gyrover I (34 cm diameter, 2.0 kg), and also utilizes many RC model parts. Tilt-servo torque and travel were both approximately doubled. Gyrover II uses a gyro housed in a vacuum chamber to cut power consumption by 80%, which increases battery life from about 10 minutes to 60 minutes. The entire robot is housed inside a specially designed pneumatic tire which protects the mechanism from mechanical and environmental abuse, and provides an enclosure that is resilient, although less rugged than hoped. The robot contains a variety of sensors to monitor motor currents, positions and speeds, tire and vacuum pressure, wheel/body orientation, and gyro temperature. Gyrover II has been assembled and driven by manual remote control on a smooth floor, and has shown the ability to float and be controllable on water.
Gyrover II
For more information, please contact Yangsheng Xu (xu+@cs.cmu.edu), or Ben Brown (hbb@cs.cmu.edu)