Traditional magnetic guide sensors only provide one-dimensional position information, indicating how much the robot deviates from the center of the path. The common method for steering correction in robotics is proportional control, where the steering adjustment is proportional to the error detected between the robot's measured positionand the desired position. This article highlights the inherent challenges and limitations of relying solely on position information and explains how the addition of angle measurement overcomes these limitations, leading to more precise and effective steering control.

#### Proportional Steering Control: The Basics

The fundamental principle of proportional control can be summarized by the equation:

*Steering = Error * Pgain*

In this context, "Error" represents the difference between the robot's current (measured) position and the desired position, while "Pgain" (proportional gain) is a coefficient that determines the magnitude of the correction applied based on the error. For effective steering correction to occur, an error must be present. This means that the robot constantly needs to detect a deviation from the desired path to make the necessary adjustments.

#### Challenges with Position-Only Proportional Control

A fundamental requirement for steering correction is that an error must exist. Without an error, no corrective action will be taken. This means that the robot is always in a state of slight deviation from the desired path.

To keep the error small, the proportional gain (Pgain) must be high. However, increasing Pgain makes the system harder to tune and can lead to inherent instability.

High Pgain values can cause the robot to overreact to small errors, leading to oscillations and reduced stability. Properly tuning the Pgain is a delicate process. An incorrectly tuned system can either be too sluggish, failing to correct errors promptly, or too aggressive, causing instability and erratic movements.

A position-only system cannot distinguish between different types of path deviations, such as drifting off-track or entering a curve. Both scenarios produce an error, but the corrective action needed differs considerably. Small deviations along a straight path only require minor corrections, which means a smaller gain in the proportional control system is sufficient. This small gain ensures stability and prevents overcorrection for slight deviations. However, when navigating curves, the corrections need to be larger and sustained to keep the robot on track. This scenario demands a higher gain to provide the necessary steering adjustments.

Finding a gain that works well in both situations requires compromise. A gain set too low will struggle to maintain the correct path in curves, leading to poor tracking performance. Conversely, a gain set too high will cause instability and overcorrection on straight paths, resulting in erratic movements and reduced overall efficiency. This compromise often results in suboptimal performance in either straight paths or curves, highlighting the limitations of relying solely on position information for steering control. Higher speeds can exacerbate the errors and make the system even harder to control, necessitating a reduction in operational speed to maintain stability.

Integrating angle measurement addresses these challenges by providing additional data that helps differentiate between straight path deviations and curves, allowing for more tailored and effective corrections.

#### Calculated Steering Using Angle, Position, and Robot Geometry

Naviq's magnetic guide sensor features a unique and patented angle measurement capability that significantly enhances steering performance over traditional sensors that can only measure position and are reactive in nature. By knowing both the robot's geometry and the angle relative to the track, Naviq's approach allows for preemptive and precise steering adjustments. This combination of angle, position, and robot geometry data provides more accurate and stable navigation, setting a new standard in robotic steering systems.

The control system uses a calculated steering approach that factors in the angle (Ta) between the robot's current path and the desired track. By incorporating both the angle and position (Tp), alongside the robot's geometric parameters such as the distance between traction wheels (Dw), wheels radius (Wr), and the distance to the sensor (Ds), the system can estimate the radius of the curve and make informed steering adjustments.

The angle information is therefore used as a feedforward term in the control loop for predictive adjustments. This proactive approach reduces the reliance on reactive corrections, enhancing the system's stability and responsiveness.

In this particular robot chassis geometry, the formula for adjusting the left and right wheel RPMs is:

$\omega_R = \frac{V \cos(\theta)}{r} - \frac{w V \sin(\theta)}{2dr} - \frac{K_p w y}{2dr}$

Where:

- $\omega_L, \omega_R$ : Angular velocities of left and right wheels (rad/s)
- $V_x$ : Forward velocity of the robot (m/s)
- $\theta$ : Angle between robot's current path and desired track (rad)
- $r$ : Wheel radius (m)
- $w$ : Distance between traction wheels (m)
- $d$ : Distance from wheel axis to sensor (m)
- $K_p$ : Position gain coefficient
- $y$ : Lateral position error (m)

#### Visualizing Predictive Steering

In this side-by-side animated comparison, we observe two robotic sensors navigating the same track—one using position-only information and the other utilizing both position and angle measurements.

On the left, the position-only sensor performs relatively well on straight segments of the track. However, as the robot enters a curve, its reactive nature and relatively low proportional gain cause it to deviate from the center of the track. This deviation results in oscillations as the robot works to stabilize and center itself once the curve ends. The position-only sensor fails to anticipate the curve, leading to noticeable lag and instability.

On the right, the sensor equipped with both position and angle measurements detects the sudden angle change characteristic of a curve, as opposed to the gradual linear deviations of a straight path. This additional angle information enables the navigation computer to evaluate the precise steering adjustments needed to remain centered on the track throughout the curve. By applying the correct amount of steering in advance, only small proportional corrections are necessary to keep it centered, allowing the robot to smoothly navigate the curve and maintain its position with minimal deviation.

This video dramatization clearly demonstrates the superior performance of the dual-measurement sensor, highlighting its ability to provide more stable and accurate navigation, especially in challenging curved sections of the track.