Vector Field Histogram (VFH)

VFH reduces massive sensor datasets into a one-dimensional polar histogram around the robot's momentary location. The active window is divided into discrete angular sectors, and an obstacle density value is calculated for each sector by summing the magnitude vectors of occupied cells. This statistical representation abstracts the exact geometric shape of obstacles, focusing purely on the navigability of specific directions.

The primary histogram is thresholded to create a binary polar histogram, where sectors exceeding a safety threshold are marked as blocked (1) and free sectors are marked as open (0). To account for the robot's physical width, a masked polar histogram is generated by convolving the binary histogram with the robot's turning radius, effectively widening blocked sectors to prevent the robot from cutting corners too closely.

The algorithm identifies all contiguous gaps of free sectors in the masked histogram. A cost function evaluates candidate directions based on three criteria:

• Goal alignment: Preference for directions pointing toward the target
• Wheel orientation: Alignment with the current direction of travel
• Previous command: Hysteresis to prevent oscillation This ensures smooth, goal-oriented motion without jitter.

Unlike static path planners, VFH dynamically adjusts its binary threshold based on the density of the environment. In cluttered spaces, the threshold rises to identify only the most promising openings; in open areas, it lowers to maintain high sensitivity to distant obstacles. This adaptive mechanism prevents the robot from getting trapped in dense obstacle fields while maintaining smooth navigation in sparse environments.

VFH operates on a certainty grid—a probabilistic occupancy map—rather than raw sensor data. This abstraction layer makes the algorithm sensor-agnostic, functioning identically with ultrasonic sonar, LiDAR, stereo cameras, or fused multi-modal inputs. The only requirement is that the sensor data can be converted into a 2D Cartesian grid of obstacle probabilities.

The enhanced VFH+ variant introduces forward-projected trajectory smoothing by modeling the robot's kinematic constraints. Instead of selecting a raw angle, VFH+ evaluates candidate arcs that the robot can physically execute, considering its minimum turning radius. It also incorporates a cost-bounded look-ahead mechanism that verifies sufficient clearance exists along the chosen trajectory before committing to a steering command.

VFH is a local reactive planner, meaning it makes immediate, sensor-driven decisions to avoid obstacles. It relies on a global planner (like A* or RRT) to provide a high-level route to the goal. The local planner handles dynamic changes the global map doesn't know about.

• Global Planner: Computes the optimal route from start to goal using a static map.
• Local Planner: Generates velocity commands to follow the global path while reacting to sensor data in real-time.

VFH operates on a local costmap, a rolling grid centered on the robot. Sensor readings (LiDAR, sonar) are fused into this grid, where cells are marked as occupied, free, or unknown. An inflation radius is applied around obstacles to account for the robot's physical footprint.

• VFH uses the costmap to build its polar histogram.
• The inflation layer ensures the robot maintains a safe distance, not just a collision-free one.

A competing local planner that searches the robot's velocity space directly. DWA samples achievable linear and angular velocities, simulates short trajectories, and scores them based on progress toward the goal, obstacle clearance, and speed.

• VFH: Searches in heading space, then commands a velocity.
• DWA: Searches in velocity space, inherently considering dynamics.
• Both are reactive, but DWA explicitly models acceleration limits.

A more advanced alternative to VFH that solves a constrained optimization problem over a finite time horizon. MPC uses an explicit model of the robot's dynamics to predict future states and minimize a cost function.

• VFH: Heuristic-based, computationally light, no explicit dynamics model.
• MPC: Optimization-based, handles complex dynamics and constraints, but is more computationally demanding.
• MPC can produce smoother, more optimal trajectories than purely reactive methods.

VFH requires a map to know where obstacles are relative to the goal. SLAM builds and updates that map in real-time while simultaneously estimating the robot's pose. Without SLAM, VFH can only wander aimlessly or follow a pre-built map.

• SLAM provides the global occupancy grid for the global planner.
• SLAM corrects for odometry drift, ensuring the robot's position in the VFH costmap is accurate.

Once VFH selects a safe steering direction, a lower-level controller must execute it. Pure Pursuit is a geometric path-tracking algorithm that calculates the steering angle needed to follow a look-ahead point on the desired path.

• VFH outputs a desired heading.
• Pure Pursuit computes the steering command to achieve that heading, assuming an Ackermann-steered vehicle.
• Together, they form a complete sense-plan-act loop for mobile robots.