Zero Moment Point vs Capture Point for Dynamic Balance

Mathematically proven stability: Ensures the robot is dynamically balanced as long as the ZMP remains strictly within the support polygon. This provides a hard safety guarantee for quasi-static walking. Matters most for industrial humanoids performing precise, slow manipulation tasks on known, rigid surfaces where a fall cannot be tolerated.

Predictable computational load: ZMP-based walking pattern generation is typically solved via Quadratic Programming (QP) with a well-defined preview control horizon. This allows for deterministic real-time performance on embedded hardware. Matters for safety-certified systems where execution timing must be guaranteed and validated.

Inherently limits agility: The ZMP criterion breaks down when the support polygon shrinks to a point (running) or vanishes entirely (jumping). It forces a flat-footed, quasi-static motion, limiting the robot's ability to recover from large pushes or traverse rough terrain. This makes it a poor fit for highly dynamic locomotion.

Directly models fall prevention: The Capture Point is the point on the ground where the robot must step to bring its Center of Mass to a complete stop. This provides an actionable metric for reactive stepping, enabling robust push recovery and walking over uneven terrain. Matters for humanoids operating in unstructured, human-centric environments.

Decouples stability from a flat foot: Unlike ZMP, the Capture Point concept naturally extends to running, jumping, and walking with a non-flat foot. It focuses on the instantaneous capturability of the state, making it the superior framework for generating highly dynamic and aperiodic maneuvers.

Requires precise state estimation: Effective Capture Point control depends on an accurate, low-latency estimate of the Center of Mass velocity. This demands high-quality sensor fusion (e.g., Factor Graph Optimization) and more complex whole-body controllers, increasing the software complexity and computational cost compared to a simple ZMP preview controller.

Mathematically proven stability: ZMP ensures the Center of Pressure (CoP) stays strictly within the support polygon. This provides a deterministic stability guarantee for quasi-static walking on flat terrain, making it the gold standard for industrial humanoids like Honda's ASIMO where a fall is unacceptable. The constraint is explicit and verifiable in real-time.

Low computational overhead: ZMP-based walking pattern generation can be solved efficiently using preview control or Linear Inverted Pendulum Model (LIPM) cart-table models. This allows for 1 kHz+ real-time control loops on embedded hardware. The extensive literature and proven implementations reduce integration risk for teams moving from simulation to hardware.

Restricts agility: ZMP requires the CoP to remain strictly inside the support polygon. This constraint breaks down during dynamic gaits like running or jumping where the foot is not flat on the ground. For highly dynamic locomotion, ZMP acts as an artificial limiter, preventing the natural under-actuated phases that Capture Point strategies exploit for energy efficiency and speed.

Assumes a known, flat ground plane: ZMP calculation relies on accurate force/torque sensing at the ankles and a known support polygon. On rough terrain, stairs, or deformable surfaces, the support polygon shrinks or becomes ill-defined. This leads to overly conservative or incorrect stability margins, often causing the robot to freeze or fall when a Capture Point step would have recovered balance.