Encoder Resolution

Encoder resolution is specified differently for the two primary encoder types:

• Absolute Encoders: Report a unique digital code for each shaft position within a single revolution. Resolution is specified in bits (e.g., 12-bit, 16-bit). A 12-bit encoder provides 2^12 = 4,096 distinct positions per revolution.
• Incremental Encoders: Output a pulse train as the shaft rotates. Resolution is specified in Pulses Per Revolution (PPR). Higher PPR means finer position detection. Many systems use quadrature decoding to multiply this count by 4, effectively increasing resolution.

Resolution defines the smallest angular or linear change the encoder can detect.

• Angular Resolution: For an absolute encoder, this is 360° / (2^bits). A 14-bit encoder has a resolution of 360° / 16,384 = ~0.022°. For an incremental encoder, it's 360° / (PPR * quadrature factor).
• Linear Resolution: For a linear encoder or a rotary encoder driving a lead screw, linear resolution is (Screw Lead) / (Encoder Counts per Revolution). A 5mm lead screw with a 2500 PPR encoder has a linear resolution of 5mm / (2500*4) = 0.0005mm.

Inaccurate encoder modeling directly degrades sim-to-real transfer.

• Low-Resolution Effects: Coarse quantization introduces measurement noise and limit cycles in closed-loop control (e.g., PID), causing the actuator to 'hunt' around a setpoint. This must be modeled in simulation.
• Simulation Modeling: A high-fidelity actuator model includes not just the ideal resolution but also non-idealities like signal jitter, missing counts, and electrical noise on the pulse train. Omitting these creates an overfit policy that fails on real hardware.

Resolution can be virtually enhanced through signal processing.

• Electronic Interpolation: Specialized encoder interface chips multiply the base PPR by factors (2x, 4x, etc.) by analyzing the analog shape of the sinusoidal encoder signals, providing sub-precision.
• Electronic Gearing: In multi-axis systems, a master encoder's signal can be used to command a slave axis with a precise ratio, requiring very high effective resolution for smooth following. This must be replicated in the simulation's control loop.

Choosing encoder resolution involves trade-offs between cost, bandwidth, and required precision.

• Rule of Thumb: Resolution should be at least 4-10 times finer than the required positioning accuracy of the system to allow the controller to converge smoothly.
• Bandwidth Limitation: Higher PPR generates more pulses per second at high speed, which may exceed the maximum frequency of the counter or interface. The max RPM is (Max Frequency [Hz] * 60) / (PPR * quadrature factor).
• Simulation Parameter: In a URDF or SDF model, encoder resolution is a key parameter in the <joint> or <sensor> definition for the simulated encoder plugin.

Resolution is distinct from, but interacts with, other encoder performance metrics.

• Accuracy: The difference between the reported position and the true absolute position. Affected by mechanical mounting, disk imperfections, and temperature drift. An encoder can have high resolution but poor accuracy.
• Repeatability: The ability to return to the same reported position. This is often better than absolute accuracy and is more directly influenced by resolution.
• Sim-to-Real Gap: In simulation, encoders are often modeled as perfectly accurate and repeatable with only quantization noise. Domain randomization should be applied to resolution, signal dropout, and bias to train robust policies.

Proprioception is a robot's internal sense of its own body's position, orientation, and movement. It is derived from sensors like joint encoders, IMUs, and torque sensors. In simulation, accurate proprioceptive models are built by combining high-fidelity encoder resolution with actuator dynamics and noise models to replicate a real robot's internal state awareness.

Sensor noise refers to random, unwanted variations in a sensor's output signal that obscure the true measurement. For encoders, this includes:

• Quantization error inherent in digital resolution.
• Electrical noise from signal conditioning circuits.
• Mechanical noise from gear backlash or vibration. Simulations model this statistically (e.g., with Gaussian noise) to prevent policies from overfitting to perfect, noise-free data.

An actuator model is a mathematical representation of a physical motor's dynamics. It defines the relationship between a control input (e.g., voltage, desired position) and the resulting output (torque, velocity). A high-fidelity model includes:

• Electrical characteristics (resistance, inductance, back-EMF).
• Mechanical limitations (saturation, torque-speed curves).
• Non-linear effects like friction and stiction. Encoder resolution provides the feedback necessary to close the control loop within this model.

Torque control is a low-level actuation mode where a motor driver directly commands a desired output torque or current. This enables compliant, force-sensitive robot behavior essential for safe human interaction and delicate manipulation. In simulation, implementing torque control requires an accurate actuator model and high-resolution encoder feedback to calculate the current joint state and the torque error for closed-loop control.

Forward kinematics is the computation of the position and orientation of a robot's end-effector given the angles or displacements of all its joints. This calculation is foundational for simulation rendering and task planning. The precision of the result is directly dependent on the assumed accuracy of the joint positions, which are provided by the simulated encoder readings. Higher encoder resolution reduces error propagation through the kinematic chain.

In simulation, ground truth refers to the perfectly accurate, noise-free data about the state of the world known by the simulator. For proprioception, this is the exact joint angle or position. The simulated sensor (e.g., the encoder model) then generates a noisy, quantized measurement based on this ground truth, using parameters like resolution, noise models, and bias. Ground truth data is used to train and evaluate perception algorithms.