High Mobility Platform
Report of the Academic Project
Department of Mechanical Engineering,
Mr. Jose Mathew
John Francis K.
Sreejith K. Kurup
We express our deepest gratitude to Mr Krishna Warrier for his plentiful advices and guidance. We are deeply indebted to him.
A new concept for a High Mobility Platform (HMP) design using Universal Wheels is presented. A universal wheel is an assembly, which provides a combination of constrained and unconstrained motion when turning. The concept of building highly mobile and easily manoeuvrable vehicles using universal wheels is presented and their design and control are discussed. The kinematics and characteristics of the HMP design are analyzed and compared with conventional mobile vehicle designs.
Mobility is of primary importance in robotic implementations, automated workshop arrangements and flexible manufacturing systems. A high mobility is essential to perform tasks in environments congested with static and/or dynamic obstacles and narrow aisles, such as those commonly found in nuclear plants, offices, factory workshops and warehouses, eldercare facilities and hospitals. The transport of equipments and materials through cluttered and narrow passages is a commonly faced problem in factories. Also the control strategies for manoeuvring of mobile platforms are generally extremely complicated, needing complex electronics. Such designs besides being expensive prove unreliable and short-lived especially in hostile environments such as in nuclear reactors. Vehicles with a high mobility, easy manoeuvrings and simple controls would be very desirable for such applications. Mobile robotic vehicles built on High Mobility Platforms (HMPs) have invaluable advantages in congested environments such as factories, eldercare facilities, and hospitals.
Many wheeled mobile designs steer the wheels by twisting them around an axis perpendicular to the floor. The drawback of these actively-steered conventional wheel designs is that as the wheel is actively twisted around a vertical axis, it experiences high friction and scrubbing forces. This reduces positioning accuracy and increases power consumption and tire wear especially for heavy vehicles. The fundamental cause of the scrubbing problem is that a wheel generates larger frictional forces when steered actively around a vertical axis than when it is rolling.
Current wheeled mobile vehicle designs based on concepts like skid steering have limited mobility due to the non-holonomic constraints of their wheels. While they can generally reach any position and orientation in a plane, they may need very complex manoeuvres, complicated path planning and control strategies in a constrained environment.
Concepts for omni-directionally mobile vehicles need to maintain accurate wheel velocity ratios which are generally difficult to hold. Vehicles like the Mobo-2 needed sophisticated mathematical equations of motion in plane and wheel velocities as an essential step leading to efficient control of this mobile robot. Hence the control, navigation and manoeuvring of such designs is inherently complicated.
The Universal Wheel
The Universal Wheel is an assembly, which provides a combination of constrained and unconstrained motion when turning (see Fig. 1). When two or more of these wheels are mounted on a platform, their constrained and unconstrained motions can be combined to provide omni-directionality. The universal wheel is a special wheel design, based on a concept of achieving traction in one direction while allowing passive motion in another.
The universal wheel is so designed as to accommodate a number of small passive rollers mounted on the periphery of a normal wheel. The axes of the rollers are perpendicular to that of the wheel. The wheel is driven in a normal fashion, while the rollers allow for a free motion in the perpendicular direction. Thus, the universal wheel involves a large wheel with many small rollers mounted on the periphery of the main wheel orientation. As the drive shaft turns, the wheel is driven in a normal fashion in a direction perpendicular to the axis of the drive shaft i.e., in the constrained direction of motion. At the same time, the small rollers allow the wheel to freely move parallel to the drive shaft, providing the unconstrained direction of motion. In principle, the roller axis can be mounted at any non-zero angle with respect to the wheel orientation.
Fig. 1, Universal Wheel
Each universal wheel has three Degrees of Freedom (DOFs). One DOF is in the direction of wheel orientation. The second DOF is in the direction of roller rotation. The third DOF is rotational slip about the point of contact between the wheel and the floor.
The High Mobility Platform
A combination of a swivelling and a translational motion enables a vehicle to reach any position and orientation in a plane. The High Mobility Platform (HMP) has a capability to swivel about a vertical axis through its centroid. When steering and traction are realised through a single wheel, the design becomes inherently complicated and the positioning accuracy degrades. The HMP design uses independent drives for steering and traction. Ideally, the HMP is of a circular cross-section. This lends credibility to the argument that the capability to swivel about a vertical axis lends a vehicle superior mobility. The HMP therefore, essentially has a length to width ratio close to unity. The four wheels of the HMP are so arranged that, the four wheel-to-floor contact points define four quadrants of a circle.
The HMP has two universal wheels mounted in such a way that that their orientations are mutually perpendicular; one radial and the other tangential to the HMP (see Fig. 2). The former is called is the Traction Wheel, T and the later, the Rudder Wheel, R. The traction wheel supplies the traction, and the rudder wheel steers the HMP. The two universal wheels are driven independently by two separate motors. This arrangement effectively decouples the traction and steering drives. The two universal wheels do not interfere with each other’s constrained rolling motions, owing to the passive rolling of the rollers. The constrained rolling of the traction wheel induces a passive rolling of the rudder wheel rollers. This lends the rudder wheel a velocity in a direction perpendicular to its orientation. Similarly the constrained motion of rudder wheel imparts a passive rolling on rollers of the traction wheel, thus providing the traction wheel with a velocity component perpendicular to its orientation.
Fig. 2, High Mobility Platform
Two conventional wheels complete the support to the vehicle. The conventional wheels are passive; they are not driven. Their sole intend is to support the vehicle. This design of the HMP enables it to achieve a high degree of mobility at easiest and simplest control. The ability of the HMP to swivel about a vertical axis through its centroid along with a translational tractability permits it to be manoeuvred to any point and orientation in a plane. The HMP thus achieves a level of mobility equivalent to omni-directional mobility. The motion of the HMP is wholly controlled via the inputs to the universal wheels. The HMP may be therefore manoeuvred along any desired trajectory by controlling the inputs to the two universal wheels. A very simple control strategy is there by achieved by limiting the control variables to two; the inputs to either wheels. Also, consequently it is possible to effectively immobilise the HMP by locking solely the two universal wheels. The passive wheels need not be locked, since, if the universal wheels are braked, the HMP if completely restricted and does not have any degree of freedom.
Two practical assumptions make the kinematic modelling of the High Mobility Platform tractable. First, the motion of the suspension and compliance of rollers are negligible. The assumption permits us to model the kinematics of the robot independently of the dynamics of these flexible components. Second, the HMP moves on a planar surface. We thus neglect irregularities in the floor surface. Even though this assumption restricts the range of practical applications, environments which do not satisfy this assumption (bumpy rocky surface) do not lend themselves to energy efficient wheeled-vehicle travel.
The HMP may be manoeuvred through any desired path on a plane by controlling the inputs to the universal wheels. We examine a circular trajectory of radius R. Since both the universal wheels are driven simultaneously, each induces a velocity on the other perpendicular to the constrained velocity of the later due to the passive rolling of the rollers of the universal wheels. Thus either universal wheels have two velocity components; one due to its own constrained motion, and the other due to passive rolling of its rollers induced by the constrained rolling of the other wheel.
The linear velocity of the universal wheels (tangential to the vehicle’s trajectory) may be therefore resolved as follows;
The constrained rolling due to positive drive of the traction wheel at ωT rad-s-1 imparts a linear velocity component of
(ωT x D/2) m-s-1
in the direction of the traction wheel orientation. Here D is the diameter of the universal wheel.
The passive rolling of the traction wheel rollers owing to the constrained rolling of the rudder wheel at ωR rad-s-1 lends it a linear velocity component of
(ωR x D/2) m-s-1
in the direction perpendicular to the traction wheel orientation.
Similarly, the rudder wheel has linear velocity components
(ωR x D/2) m-s-1
(ωT x D/2) m-s-1
The former due to the positive drive of the rudder wheel and the later due the passive roller motions of the rudder wheel on account of the positive rolling of the traction wheel.
Fig. 3, HMP Kinematics
Hence, the resultant linear velocity of the vehicle,
S = [(ωT2 + ωR2)½ x D/2] m-s-1
Referring to Fig. 3,
ωR /( ωR2+ ωT2)½
Thus, any turning radius maybe achieved by controlling the input to the two universal wheels. Thereby, the HMP can be manoeuvred along any trajectory on a plane by controlling the two control variables namely, ωR & ωT.
When traction is null,
ωT = 0
And the equation (ii) simplifies to
L = R
i.e., the turn radius is equal to half of wheel-base. This is the limiting condition, when the vehicle takes a point turn. The vehicle swivels about a vertical axis.
Also, the case of a null ωR, is of a straight line trajectory i.e., a turning radius of
R = ∞
The equation (ii) thus provides a, comprehensive control strategy for the HMP.
Development of the Prototype
To prove the feasibility of the HMP concept, a prototype of the basic mechanical features was made. Intended only as a demonstration model, the prototype was made from off-the-shelf components, from a limited budget and was not designed for any particular load or terrain.
Two separate independent DC motors, powered by an onboard battery and controlled independently by two off-board switch buttons, provided the independent drives for traction and steering. Each universal wheel in the prototype HMP consisted of eight rollers; two pairs of four, mounted on two spiders, set at an angular offset of 45o. The rollers were machined from soft-wood and cup and cone rollers were used in them for their axles. Rubber grips were glued on the rollers to improve traction and reduce noise.
Fig. 4, The Prototype HMP
To demonstrate and evaluate the effectiveness of the HMP, a series of experiments were performed using different paths which included circular, rectangular, and combined translational and rotational motions. The prototype HMP demonstrated high levels of mobility. The desired ease of control was proven possible. The platform demonstrated smooth motion and achieved good tracking performance. Experiments with the HMP confirmed it superior manoeuvrability in cluttered and constricted pathways.
HMP Discussion Forum
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