Why is my robot slower when strafing than driving forward?

A robot with a mecanum drivetrain will drive slightly faster forwards/backwards than in any other direction due to friction . Combining translation and rotation will also result in slower movement .

For an X-Drive, the ratio of strafe speed to forward speed is exactly 1, meaning they are equivalent . However, X-Drive robots are slower when strafing at 45 degrees, at approximately frac√(2)2 of their forward speed .

The provided documentation does not state why an H-Drive robot might be slower when strafing than driving forward.

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Kinematics > Mecanum Drive > Forward Kinematics

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The forward kinematics of a mecanum drive relate the velocity of the wheels to the forward, strafe, and rotational velocities of the robot, relative to itself. These are as follows:

vf = frac{v_fr + v_fl + v_br + v_bl}{4}

vs = frac{v_bl + v_fr - v_fl - v_br}{4}

ω = frac{v_br + v_fr - v_fl - v_bl}{4*2r_b}

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Holonomic Drivetrains > H-Drive

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H-Drive (also known as U-drive, depending on the configuration) is a holonomic type drive that uses all omni wheels. H-Drive relies on a set of "strafer wheels" that are perpendicular to the forward/backward wheels to achieve strafing. H-Drive is similar to a fusion of a tank drivetrain while retaining the maneuverability and strafing of holonomic drivetrains.

H-Drive is theoretically very easy to code, but most teams employ some sort of gyro correction to strafe straight, although it is not necessary with proper weight distribution.

H-Drive has a number of possible motor configurations - 1 or 2 motors can be put on each forward drive pod, and one or two motors can be put on the strafe wheels. In the configuration with one motor on each forward drive pod, H-Drive has slightly reduced acceleration compared to mecanum drive.

For the highest possible reliability, many FRC® teams will suspend their strafe wheels on a rocker system to ensure that all wheels are in contact with the ground while the robot is not strafing.

By far the biggest advantage of H-drive is its ability to accommodate multiple motor distributions. For instance, if you want to dedicate only 3 motors to your mechanisms and you have a motor left over, using a 1 strafe motor, 4 drive motor configuration is absolutely viable. Or if you dedicate 5 motors for your mechanisms, H-drive with 2 drive motors and 1 strafe motor is definitely optimal.

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Holonomic Drivetrains > X-Drive

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X-Drive is a holonomic omni-wheel based drivetrain. This type of drive involves mounting 4 omni wheels at the corner of the robot at a 45 degree angle.

One notable difference between X-Drive and mecanum is strafe speed. While, as mentioned in the mecanum section, the ratio of strafe speed to forward speed is noticeably less than 1, the ratio on an X-Drive is exactly 1 due to the rotational symmetry of the wheel placement. This means that an X-Drive bot's strafe speed and forward speed are equivalent. The drivetrains are slower, however, when strafing at 45° (approximately frac{sqrt{2}}{2} of its forward speed).

Even though X-drive has good turning and acceleration, the main downside to the drive is packaging/form factor. Packaging refers to how easy/convenient the drivetrain fits into the overall design of the robot.

Ideally, the drivetrain should take up as little space as possible to make it easier to design mechanisms around. Because the omni wheels are offset, packaging a X-Drive is more difficult than other types of holonomic drive like mecanum or H-Drive. Also because of the strange packaging, it is relatively difficult to cleanly transfer power from the motors to wheels, meaning that most X-Drives end up being direct-driven, which is bad for the lifespan of the motor gearbox.

Note: When using X-Drive, the robot moves forwards/backwards/straight side-to-side sqrt{2} times faster than a drivetrain with wheels in the normal orientation (with the same gear ratio and wheel size).

For an explanation of why exactly this is, see this analysis (https://www.chiefdelphi.com/t/paper-mecanum-and-omni-kinematic-and-force-analysis/106153).

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Kinematics > Tank (Differential Drive) > Forward Kinematics

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The forward kinematics of a tank drive relate the velocity of the wheels to the forward and rotational velocities of the robot, relative to itself. The forward velocity vf and the rotational velocity v_theta} is:

vf = (vr + vl)/(2)

ω = (vr - vl)/(2 rb)

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Mecanum TeleOp

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Note: Some common COTS mecanum drivetrain kits are the goBILDA Strafer Chassis Kit (https://www.gobilda.com/strafer-chassis-kit-v5/) and the REV Mecanum Drivetrain Kit (https://www.revrobotics.com/rev-45-2470/).

A standard mecanum drive configuration possesses 4 mecanum wheels oriented in an "X" shape. This means that the rollers are angled towards the center when looking at it from above. This configuration allows one to add up the force vectors generated by the offset rollers and derive movement in any direction. It is important to note that because of friction, perfect movement isn't possible in every direction, so a mecanum drivetrain will be able to drive slightly faster forwards/backwards than any other directions. Combining translation and rotation will also result in slower movement.

In the image above, vectors 1, 2, 3, and 4 are the force vectors created by the mecanum wheels when the chassis is instructed to drive towards the top of the image. All motors are driving forward. The blue and red lines are their X and Y components, respectively. Here are a few examples of how the wheels must be driven to achieve different movements:

Attention: It is strongly advised to not hardcode these movements in; there is a much better way described below that allows for true holonomic movement and is much more elegant.

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Kinematics > Tank (Differential Drive) > Inverse Kinematics

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The inverse kinematics of a tank drive relate the desired velocity of the robot to the velocity required of the wheels. These velocities are as follows:

vr = vf + rd · ω

vl = vf - rd · ω

Mecanum kinematics uses the same variables as differential drive, except with four wheel velocity variables and an additional robot velocity vector for the left to right velocity.

vmathrm{fr} denotes the linear velocity of the front (leading) right wheel
vmathrm{br} denotes the linear velocity of the back (trailing) right wheel
vmathrm{fl} denotes the linear velocity of the front (leading) left wheel(s)
vmathrm{bl} denotes the linear velocity of the back (trailing) left wheel(s)
vf denotes the forward velocity of the robot, relative to itself.
vs denotes the strafe (sideways) velocity of the robot, relative to itself.
omega denotes the rotational velocity of the robot in radians/second
rb represents the base track radius, or the distance between the wheel and center of the robot (half of the distance between wheels)

Warning: These variables, with the exception of omega, represent linear velocities NOT rotational velocities. Wheel rotational velocity in radians/second can be converted to linear velocity by multiplying by the wheel's radius.

Positive rotational velocity (omega) will spin the robot COUNTERCLOCKWISE when viewed from above.

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