Reactive Locomotion

Reflex-based controllers implement low-latency, state-triggered feedback loops that directly map sensor readings to actuator commands, bypassing high-level planning. These are inspired by biological reflexes and are crucial for handling sudden disturbances.

• Example: A load cell in a robot's leg detects an unexpected drop in ground reaction force, triggering an immediate leg extension command to prevent a fall.
• Key Property: Operates on the order of milliseconds, far faster than trajectory re-planning cycles.
• Implementation: Often encoded as if-then rules or proportional-derivative (PD) gains that are switched based on contact state.

While MPC is a planning algorithm, its receding horizon implementation makes it a powerful reactive tool. At each control cycle (e.g., 1-10 ms), it solves a finite-time optimization based on the current state, allowing it to react to new sensor data immediately.

• Mechanism: Uses an internal dynamic model (like centroidal dynamics) to predict future states over a short horizon (~0.5 seconds).
• Reactivity: The optimization is re-solved at every time step, incorporating the latest estimates of terrain height or external forces.
• Output: Directly computes optimal ground reaction forces and foot placements for the immediate future, enabling recovery from pushes.

The Divergent Component of Motion is a stability metric derived from the Linear Inverted Pendulum Model (LIPM). Controlling the DCM enables reactive balance by dictating where to place the foot to arrest the robot's falling motion.

• Definition: The DCM (ξ) is a point that diverges from the Center of Mass (CoM) if left uncontrolled. Its dynamics are inherently unstable.
• Reactive Strategy: The controller constantly measures the current DCM. To recover from a disturbance, it computes the Capture Point—the foot placement on the ground where stepping will bring the DCM and CoM to a stop.
• Use Case: Fundamental to push recovery algorithms for bipeds, allowing single-step stabilization.

These are force-reactive control paradigms that allow a robot's body to comply with unexpected contact forces, crucial for traversing uneven terrain or withstanding impacts.

• Impedance Control: Regulates the dynamic relationship between position error and force. The robot behaves like a mass-spring-damper system. When a foot hits a rock early, the "spring" compresses, absorbing the shock without breaking contact.
• Admittance Control: Maps sensed forces to a desired motion. An external push generates a velocity command, allowing the robot to "yield" appropriately.
• Implementation: Often layered within a Whole-Body Control (WBC) framework to distribute compliant behavior across all joints while maintaining primary tasks.

Reactive locomotion requires real-time perception of ground properties. Terrain adaptation algorithms fuse proprioceptive sensing to estimate critical surface features and trigger gait adjustments.

• Proprioceptive Sensors: Joint torque sensors, IMUs, and foot load cells provide direct data on interaction forces.
• Estimation Process: Algorithms infer ground inclination, surface stiffness, and friction coefficients from patterns in sensor data during the stance phase.
• Reactive Adjustments: Based on estimates, the system can:
  • Modulate step height to clear obstacles.
  • Adjust leg stiffness via impedance control for soft ground.
  • Shift the Center of Pressure (CoP) to prevent slipping on low-friction surfaces.

A Central Pattern Generator is a network of coupled oscillators that produces rhythmic signals for gaits. When augmented with sensory feedback, it becomes a reactive system capable of online gait modulation.

• Base Operation: The CPG generates stable, periodic phase signals for each limb, defining a default trot, walk, or pace gait.
• Reactive Modulation: Phase resetting and amplitude modulation inputs from sensors can instantly alter the rhythm.
• Example: A leg hitting an obstacle receives a high load signal, which resets its oscillator phase to initiate a faster swing motion, effectively lifting the leg over the obstruction without stopping the overall gait cycle.

Whole-Body Control is a hierarchical optimization framework that coordinates all of a robot's joints to execute multiple prioritized tasks simultaneously. It is the higher-level controller that often sends torque commands to the joints to realize the balance and stepping adjustments computed by reactive strategies.

• Primary Role: Integrates tasks like center of mass tracking, foot placement, and swing leg control into a single quadratic program.
• Relationship to Reactivity: WBC provides the actuation layer for reactive policies. A reactive step adjustment from a Capture Point calculation is executed by the WBC, which computes the precise joint torques needed while managing other constraints.

Model Predictive Control is an advanced control method that uses an internal dynamic model to predict the robot's future state over a short time horizon and solves an optimization problem at each control cycle for the best sequence of inputs. It bridges planning and reaction.

• Predictive vs. Reactive: While purely reactive control acts on the current state error, MPC is predictively reactive. It anticipates future disturbances (e.g., an upcoming slope) and optimizes a sequence of actions (e.g., body posture adjustments) to handle them smoothly.
• Application: Used for center of mass trajectory optimization in response to predicted forces, making it a key component in modern reactive locomotion stacks that plan over a ~200ms horizon.

These are low-level force-reactive control strategies that define how a robot's leg or joint responds to physical interactions, forming the foundational "reflex arc" for locomotion.

• Impedance Control: Regulates the dynamic relationship between position error and output force. It makes a joint or foot behave like a programmable spring-damper system. This is crucial for absorbing impacts and maintaining stable contact on uncertain terrain.
• Admittance Control: Regulates the relationship between measured force and resulting motion. An external push (force) generates a compliant positional adjustment (admittance). This is often used for safe human-robot interaction and gentle terrain adaptation.
• Role: These controllers execute the physical compliance required by higher-level reactive strategies.

A Reduced-Order Model is a simplified mathematical representation of a robot's dynamics that captures only the most essential states for locomotion planning and control, enabling fast real-time computation.

• Examples: The Linear Inverted Pendulum Model (LIPM) and Spring-Loaded Inverted Pendulum (SLIP) are quintessential ROMs.
• Purpose in Reactivity: Reactive algorithms rely on ROMs because they are computationally tractable. For instance, calculating a Capture Point for instant step adjustment uses the LIPM, not the full 30+ degree-of-freedom robot model. They provide the analytical basis for reflex rules.

Push recovery is the specific capability of a legged robot to maintain balance after an unexpected external force is applied to its torso. It is a canonical test case and application for reactive locomotion systems.

• Strategies: Encompasses a hierarchy of reactions:
  • Ankle Strategy: Small adjustments using Center of Pressure modulation via impedance control.
  • Hip Strategy: Angular momentum generation by swinging the torso or arms.
  • Step Strategy: The most definitive reactive action—taking a rapid recovery step to a new Capture Point to re-establish balance.
• Implementation: Relies on state estimation to detect the push and the entire reactive toolkit (ROMs, WBC) to execute the counter-movement.

Terrain adaptation is the real-time adjustment of gait parameters, foot placement, and leg compliance to traverse uneven, slippery, or deformable ground. It is a primary objective of reactive locomotion systems.

• Sensory Input: Driven by proprioception (joint torque, foot contact) and sometimes exteroception (vision, lidar) to detect terrain changes.
• Reactive Mechanisms:
  • Foot Force Control: Adjusting leg impedance to prevent foot slip on ice or sinkage in sand.
  • Reflexive Leg Retraction: Quickly lifting a leg if a planned foothold is unexpectedly lost.
  • Body Posture Adjustment: Tilting the torso to keep the center of mass over uncertain footholds.
• Outcome: Enables robust traversal without a perfect prior map of the environment.