Belief-Space Planning
- Also called: planning in belief space
- Category: Planning & manipulation › Motion planning
- Tags: planning-under-uncertainty, pomdp, state-estimation, active-sensing, probabilistic-robotics
Planning over probability distributions of the robot's state rather than a single estimate, so that actions can be chosen to reduce uncertainty as well as to reach the goal.
Definition
A robot rarely knows its state exactly: its pose, the positions of objects and the outcome of contacts are known only through noisy sensing. A belief is a probability distribution over possible states given the history of actions and observations, and belief space is the space of all such distributions. Belief-space planning chooses actions by predicting how they will change the belief, not only the nominal state. This lets the planner trade progress toward the goal against reducing uncertainty, for example by passing near a landmark to localize before entering a narrow doorway, or by touching an object to find its position before grasping it.
Formally, belief-space planning is a way of solving partially observable Markov decision processes (POMDPs). The POMDP is the problem formulation; recasting it over beliefs turns it into a fully observable decision problem in which the belief plays the role of the state. Belief spaces are high-dimensional, and for continuous states infinite-dimensional, so exact solutions are rarely practical for robots and methods approximate. Gaussian belief-space planners represent the belief by a mean and covariance, propagate it with an extended Kalman filter, and then search or optimize over these compact beliefs, as in belief roadmaps and LQG-based motion planning. Particle-based methods represent beliefs with weighted samples, and online POMDP solvers search a tree of action and observation sequences from the current belief. Many systems simplify further by assuming the most likely observation during planning and replanning when the real observations arrive.
Belief-space planning differs from planning on the mean state with safety margins, which treats uncertainty as fixed. In belief space, actions can deliberately reduce uncertainty, so plans may include information-gathering moves that a deterministic planner would never choose. The cost is computation, and plan quality depends on how accurately the sensor and motion models predict future beliefs. In some tasks, reactive controllers that respond to the current estimate without look-ahead perform comparably at much lower cost, which is why belief-space planners are often used as baselines for such methods.
Why it matters
Robots that plan only on their best state estimate can commit to actions that fail when that estimate is wrong, such as grasping where an object is believed to be. Belief-space planning makes uncertainty part of the decision, producing plans that localize, sense or probe when that is cheaper than failing, and giving a principled way to decide when more sensing is worth the time.
Key applications
- Navigation with active localization where landmarks are sparse
- Manipulation under object pose uncertainty, including touch-based localization
- Insertion and other contact tasks where position error exceeds the clearance
- Search and exploration that trades information gain against travel cost
- Decision making for vehicles that are uncertain about other agents' intentions
- Grasping in clutter with partial occlusion
In practice
A robot must insert a key into a lock whose position is known from a camera only to within a few millimeters, more than the insertion clearance. A planner working on the mean estimate would move straight to the believed position and often miss. A belief-space planner represents the lock position as a Gaussian, predicts how each candidate motion and contact would shrink the covariance, and finds that sliding the key along the lock face until it meets the edge cheaply removes the uncertainty along one axis. The plan therefore includes a guarded probing motion before the insertion. During execution, an extended Kalman filter updates the belief with force readings, and the planner replans from the new belief whenever observations differ from its predictions.
Common misconceptions
- Belief-space planning is just planning with error margins — margins treat uncertainty as fixed, while belief-space planners can choose actions that reduce it
- A belief is the same as a state estimate — a state estimate is usually a single point such as the mean, while the belief is the whole distribution, including its spread and shape
- Belief-space planning requires solving the full POMDP exactly — practical methods rely on approximations such as Gaussian beliefs, particles or most-likely-observation assumptions
Who should know this
- Motion and task planning researchers working under uncertainty
- Manipulation engineers dealing with object pose uncertainty
- Autonomous navigation engineers
- Students of probabilistic robotics
Related technologies
- Extended Kalman Filter
- Particle Filter
- Online POMDP Solvers
- Belief Roadmap
- LQG Motion Planning
- Information Gain Metrics
Related terms
- Partially Observable Markov Decision Process (POMDP)
- Extended Kalman Filter
- Particle Filter
- Interactive Perception
- Robotic information gathering
- Task and Motion Planning