GlobMP: Continuous-Time Constrained Motion Planning

Method

Planning and steering as one continuous-time program

GlobMP represents each motion as a piecewise polynomial, so every constraint, whether an obstacle, a separation between robots, or closeness to a learned policy's proposal, becomes a polynomial that must stay nonnegative over the whole motion, not only at sampled times. A gradient projection method alternates a step that lowers the smoothness cost with a restoration step that makes the curve feasible again. Every iterate stays feasible, and under mild assumptions the cost approaches the global optimum as the number of pieces grows.

Two robots, A and B, planned jointly among ellipsoidal obstacles. Top: each robot's path. Bottom: clearance to each obstacle and to the other robot over time; below zero is a collision. (1) The direct paths collide. (2) Checking the constraints at 8 sample times misses collisions between them. (3) GlobMP's curves keep every clearance nonnegative over the whole motion.

Experiments

Tightness and cost on synthetic instances

Steering

Steering tactile-reactive dexterous policies on a bimanual humanoid

GlobMP steers the action chunks of a learned policy (GR00T N1.7, π_0.5) on a bimanual robot with two XHAND1 hands. A meta-reasoner picks the constraint blocks once per episode, and GlobMP returns a curve that meets every block at every instant while staying close to the policy.

Bag into box

Tissue-box handover

Pull a tissue

Pick up a full or empty cup

Force magnitude per fingertip (raw sensor units), above its resting value. Dashed lines: first and last frame with motion.

Steered motion planning, handover — Steered motion planning, illustrated on the handover task: the meta-reasoner sets keep-out, keep-in and grip blocks once; GlobMP returns a smooth, collision-free curve close to the policy.

Steered rollouts on the robot and real-robot results: coming soon

Obstacle avoidance

Collision-free motion in end-effector space (D3IL avoiding-v0)

A planar end-effector must reach the goal while avoiding pillars. GlobMP is the projection step of DiRecT's diffusion sampler, compared with ten diffusion planners over 100 rollouts each.

GlobMP rollouts on avoiding-v0 (seed 0, 100 episodes: 95 safe, 98 reach the goal), replayed in the simulator. Blue: test-time constraints. The robot runs four rollouts, then all 100 paths appear, safe in navy and violating in red.

(c) safety rate against task success — Safety rate against task success, 100 episodes per method. Only the upper right both reaches the goal and avoids.

Maze2D

Safe navigation in a nonconvex maze (D4RL maze2d-large)

A point robot crosses a nonconvex maze while avoiding keep-out regions. GlobMP picks a corridor by breadth-first search and enforces the keep-outs in continuous time; GlobMP is deterministic, the ten baselines run 10 episodes each.

Broad setting. Dark stretches marked × are inside a keep-out; the badge counts runs that entered one.

Narrow setting, with six keep-outs.

Quick Start

Code on GitHub and Hugging Face

git clone https://github.com/GlobalMotionPlanning/GlobMP.git
cd globmp
pip install -e .
python -m pytest globmp/tests    # about 10 s on one CPU core

BibTeX

@misc{amiri2026globmp,
  title={Continuous-Time Motion Planning and Steering with Global Convergence},
  author={Amiri, Mohsen and Didari, Sima and Ataee Tarzanagh, Davoud and Moon, Hankyu and Kwon, Yeongdae},
  year={2026},
  note={Equal contribution: Amiri, Didari, Ataee Tarzanagh}
}

GlobMP