Belief-space planning

Plan over uncertainty, not only a best estimate#

A robot rarely knows its exact pose, object state, or contact condition. Its belief is a probability distribution over those possibilities, updated from actions and observations. Belief-space planning treats that distribution as the planning state.

This changes the value of an action. A direct reach may be short but leave an object's pose ambiguous, while a small camera or contact motion may reduce uncertainty before the grasp. The resulting plan can include information-gathering behaviour associated with active perception, not just motion toward a geometric goal.

Future observations make the problem stochastic#

The planner does not yet know which measurements it will receive. Each action can change both the physical state and the distribution of possible future observations, so belief dynamics are high-dimensional and stochastic.

Platt and colleagues formulate partially observable control as planning in belief space. Their method assumes maximum-likelihood future observations to construct nominal belief dynamics, treats departures as noise, and applies control and planning methods to a planar localisation-and-grasping problem. They show an exact result for their linear-Gaussian case and use local approximation and replanning for nonlinear systems.

Approximation is usually unavoidable#

Belief-space planning differs from ordinary motion planning with a safety margin. A margin inflates geometry around one estimate; a belief-space method models how uncertainty itself evolves and how observations can reduce it.

Exact belief distributions can be too large to represent, so implementations may assume Gaussians, use a particle filter, keep only selected hypotheses, or approximate future observations. Those choices can miss multimodality or become overconfident after ambiguous measurements. Sensor bias, data association, and an incorrect observation model can make an apparently informative action misleading. A plan's value is therefore conditional on both its physical model and its model of what the robot expects to learn.