Design, Modeling, and Control of a Differential Drive Rimless Wheel That Can Move Straight and Turn

A rimless wheel or a wheel without a rim, is the simplest example of a legged robot and is an ideal testbed to understand the mechanics of locomotion. This paper presents the design, modeling, and control of a differential drive rimless wheel robot that achieves straight-line movement and turning. The robot design comprises a central axis with two 10-spoked springy rimless wheels on either side and a central body that houses the electronics, motors, transmission, computers, and batteries. To move straight, both motors are commanded to constant pitch control of the central body. To turn while maintaining constant pitch, a differential current is added and subtracted from currents on either motor. In separate tests, the robot achieved the maximum speed of 4.3 m per sec (9.66 miles per hour), the lowest total cost of transport (power per unit weight per unit velocity) of 0.13, and a smallest turning radius of 0.5 m. A kinematics-based model for steering and a dynamics-based sagittal (fore-aft) plane model for forward movement is presented. Finally, parameters studies that influence the speed, torque, power, and energetics of locomotion are performed. A rimless wheel that can move straight and turn can potentially be used to navigate in constrained spaces such as homes and offices.

The Split-Belt Rimless Wheel

Split-belt treadmill training, common in stroke rehabilitation and motor learning experiments, reveals a mechanism through which energy can be extracted from the environment. People can extract net positive work from a split-belt treadmill by lengthening their step onto the fast belt. To understand how leg angles and belt speed differences affect energy transfer between the treadmill and the person during split-belt walking, we simulated a split-belt rimless wheel that alternates rotating on fast and slow treadmill belts. We found that the split-belt rimless wheel can passively walk steadily forward under a range of conditions, extracting enough energy from the treadmill to overcome losses during collisions. The simulated wheel can tolerate both speed disturbances and ground height variability, and it can even capture enough energy to walk uphill. We also built a physical split-belt rimless wheel robot, demonstrating the feasibility of energy extraction during split-belt treadmill walking. In comparing the wheel solutions to human split-belt gait, we found that humans do not maximize positive work performed by the treadmill; costs associated with balance and free vertical moments likely limit adaptation. This study characterizes the mechanics and energetics of split-belt walking, demonstrating that energy capture through intermittent contacts with the two belts is possible when the belt speed difference is paired with an asymmetry in leg angles at step-to-step transitions. This study demonstrates a novel way of harnessing energy through individual rotations rather than continuous contact and offers a simple model framework for understanding human choices during split-belt walking.