Riemannian Motion Policies

A reactive control framework where each sub-goal contributes a desired acceleration and an importance matrix, combined by weighted sum.

RMPs were introduced by Nathan Ratliff, Dieter Fox, and colleagues at NVIDIA in 2018. An RMP is a pair (a, M): a is a desired acceleration defined in some task space — such as the end-effector reaching for a goal, a link moving away from an obstacle, or a joint staying away from its limit — and M is a Riemannian metric, roughly ‘how important this sub-goal is in each direction.’ Each sub-policy is defined in its own space, pulled back into joint space through a Jacobian, and combined into a single joint acceleration weighted by M. This lets conflicting requirements be handled in a unified way, with the weights changing as the state changes — the closer the robot gets to an obstacle, the more avoidance dominates. RMPflow, published the same year, organizes this composition into an automated computation graph and provides stability conditions. RMPs are recomputed every control cycle, so they can react to moving targets and obstacles, but they are purely local and still need a global planner for complex scenes. NVIDIA's later Geometric Fabrics work continues this line.

ExampleIsaac Sim's Lula motion generation toolkit uses RMPflow as its core, combining goal-reaching, collision-avoidance, joint-limit, and damping RMPs so an arm's end-effector can follow a moving target in real time while avoiding obstacles. As of September 2026, NVIDIA's official documentation recommends new development use the experimental Robot Motion API instead.

Also called

RMP, RMPflow, Riemannian Motion Policy

Related

Geometric Fabrics · Operational Space Control · Obstacle Avoidance · Artificial Potential Field · NVIDIA Isaac Sim · cuRobo (NVIDIA GPU-accelerated motion planning)

Sources

Ratliff et al., Riemannian Motion Policies (arXiv:1801.02854)
Cheng et al., RMPflow: A Computational Graph for Automatic Motion Policy Generation (arXiv:1811.07049, WAFR 2018)
Isaac Sim Documentation: RMPflow

As of

2026-09