Omni Wheels & Holonomic Drive Systems

Traction wheel
- Also called a “regular” or “normal” wheel.
- Continuous rubber (or tread) surface around rim.
- High traction (friction) in every direction that lies in the plane of the wheel; no intentional slip.
Omni wheel
- Rim is ringed with free-spinning rollers (casters).
- Each roller’s axle is tangent to the circle of the wheel and points “through the screen” (i.e.
  perpendicular to the drawing of the wheel).
- Generates high traction in the direction perpendicular to the axle (the wheel’s driving direction) but almost no traction parallel to the axle (sideways direction).
- Lets the wheel drive forward/backward while freely sliding sideways.
- Became the “new fancy” wheel of choice in VEX robotics kits.

Roller layout encircles the wheel so that at any ground-contact point a roller can spin freely.
Resulting force properties
- Red (drive) direction = along the circumference; rollers do not rotate ⇒ full traction.
- Blue (slip) direction = parallel to shaft; rollers rotate ⇒ minimal resistance (denoted ‘s’ for slip).
Practical interpretation:
- Apply motor torque → force only in drive direction.
- Any external lateral force → wheel slides instead of resisting.

Draw a wheel with radial red arrows (drive force) and tangential blue arrows (slip vectors).
Motor power couples only to red axis; blue axis is “decoupled.”

Problem: Six-wheel (or four-wheel) traction drive
- Outer wheels describe larger arcs when robot pivots about center.
- Those wheels cannot naturally follow that curved path ⇒ scrub, skip, or stutter.
- Automotive solution: differential, but adds complexity.
Remedy: Keep traction wheels inside, replace outer wheels with omni wheels
- Omni wheels’ sideways slip absorbs the lateral component of the turning vector.
- Result: robot pivots far more smoothly while retaining longitudinal traction/pushing force.
- Benefits: wide wheelbase, stability, even weight distribution, and easier driver control.

Holonomic drive = omnidirectional drivetrain capable of pure translation in any planar direction without first re-orienting.
Enables “strafing” on a competition field: faster alignment, simpler strategy.

Two omni wheels placed orthogonally (one produces X-axis force, the other Y-axis).
If weight were perfectly balanced and friction neglected, any 2-D vector of motion could be produced by combining the two one-dimensional wheel forces.
Demonstrates vector addition foundation for holonomic control.

Four omni wheels, wheel axles aligned with robot X & Y axes (look like a plus sign from above).
Directional behaviour
- Wheels on Y-axis create/accept force in ±Y, slip in ±X.
- Wheels on X-axis create/accept force in ±X, slip in ±Y.
Translational control
- To move +Y: power the two Y-aligned wheels forward.
- To move +X: power the two X-aligned wheels forward.
- To move at 45°: power both pairs simultaneously with equal magnitude. Vector diagram: two unit forces at right angle → resultant $\sqrt{1^2+1^2}=\sqrt{2}\approx1.41$ .
Speed anomaly
- Straight motions (axes): speed proportional to 1 (unit input).
- Diagonals: speed increases by $41\%$ (factor $\sqrt{2}$ ) but torque drops because only component forces push.
Rotation
- Spin all four wheels the same direction → highly efficient rotation; every wheel is tangent to rotation center.

Same four-wheel layout rotated $45^\circ$ .
Wheel axles now lie on diagonals; drive directions align with robot’s forward/back/left/right axes.
Consequences
- Forward/back/left/right vectors gain the $\sqrt{2}$ speed boost; diagonals are slower.
- Robot is fastest and strongest in the directions drivers use most (forward/back/strafe).
Building notes
- Draw wheels at corners forming an “X.”
- Inner sides of wheels still slip; outer tread still supplies propulsion.

Any desired planar velocity $\vec{v}=(vx,vy)$ decomposes into wheel unit vectors.
For + drive: wheels form orthogonal basis (X, Y).
For X drive: wheels form basis rotated $45^\circ$ .
Resultant magnitude when commanding equal orthogonal powers: $|\vec{v}|=\sqrt{vx^2+vy^2}$ .
Example shown: $vx=1,\ vy=1\Rightarrow |\vec{v}|=\sqrt{2}\approx1.41$ .

$\sqrt{2}$ gain is a speed advantage but steals available torque (force per motor) in boosted directions.
Real-world gearing should factor the $1.41$ scalar so top speed on boosted axis matches design goal.
In straight axes of + drive (or diagonal axes of X drive) torque is lower because only two motors supply propulsion.

Because every wheel applies force tangentially to the center, rotational acceleration is very high.
Drivers often find default rotation “too twitchy.”
- Software fixes: scale rotational joystick input (e.g.
  halve or quarter), or apply logarithmic mapping for finer low-speed control.

Requires coordinate transform from joystick X/Y/Rotation into per-wheel speeds.
Will be covered in a separate tutorial; mention that mathematics is straightforward once vector bases are defined.

VEX now sells omni wheels sized to pair cleanly with their gear ratios for holonomic designs.
Common industrial parallels: mecanum-equipped scissor lifts, warehouse AGVs.
Omni designs unsuitable for road vehicles due to poor longitudinal grip on uneven surfaces.

Encourages students to explore non-traditional drivetrains, fostering creativity and deeper kinematic understanding.
Demonstrates interplay of physics, math, and programming in real-world engineering.
Highlights importance of transparent driver controls to avoid unexpected speed jumps (safety & usability).

Omni wheel = traction in drive axis, slip in lateral axis.
Replacing outer traction wheels with omni wheels solves turning scrub in multi-wheel bases.
Holonomic drives (+ or X) enable true 2-D translation using vector addition of wheel forces.
$\sqrt{2}$ speed boost occurs when commanding equal orthogonal motor powers; plan gearing accordingly.
X drive places boosted speed on the directions teams use most, making it many builders’ preferred holonomic setup.
Rotation is naturally powerful; software damping is recommended.