Riemannian motion policy

Local policies can live in different task spaces#

A high-degree-of-freedom robot may need to move a hand toward a goal, keep its elbow away from an obstacle, and maintain a comfortable posture at the same time. Each objective is easier to describe in its own coordinates. A Riemannian motion policy pairs a desired acceleration with a metric that says how strongly different directions matter at the current state.

The metric is more than a fixed priority number. It can make motion toward an obstacle highly important while assigning less weight to directions that do not reduce clearance. RMPflow uses a computational graph to pull these task-space quantities back through transformations and combine them into one configuration-space policy, as set out by Cheng and colleagues.

RMPflow is reactive policy synthesis#

RMPflow produces a motion command from the current state. It can combine goal attraction, collision avoidance, and other local behaviours without first producing a complete time-indexed path. This makes an RMP different from a global motion planner, although a robot system can use both.

The framework also provides structure for learned policies. RMP2 reformulates the computation using automatic differentiation so that task maps and policy components can be trained end to end. Its experiments show one way to add learned components; learning is not required by the RMP definition.

Composition depends on design choices#

An RMP system needs suitable task maps, local policies, and metrics. A poorly shaped obstacle metric can create undesirable local behaviour, while conflicting objectives can still produce a compromise that fails the task. Stability results apply only when their mathematical conditions hold.

Reactive control also does not by itself reason over long sequences such as opening a door before entering a room. A humanoid may use RMPflow for fast local motion while a higher-level planner chooses goals, contacts, or task order.