robot motion planners

Abstract: For practical motion generation, it is essential to handle multimodality (multiple actions can be correct for the same observation) while maintaining low inference cost and strong generalization from limited demonstrations. We introduce an attentive mixture-density policy trained with the Energy Score that represents future visuomotor trajectories as explicit probability distributions with a single forward pass. Concretely, we output Gaussian mixture parameters for joint commands (and optionally attention points) and optimize them with the Energy Score (computed as a sum of 1D CRPS under a diagonal covariance assumption) instead of the negative log-likelihood (NLL) to avoid MDN singularities and gradient-scale instabilities. Our architecture couples explicit spatial attention with mixture-density outputs, enabling robust multimodal behavior selection under visual noise and small-data regimes. On an 8-DOF manipulator, the method generates distinct avoidance trajectories and stabilizes learning in obstacle avoidance. Moreover, in a randomized moving-object grasping task, where spatiotemporal multimodality and fast timing decisions are required, the proposed model outperforms Diffusion Policy by 15-25% under several unseen conditions, demonstrating superior generalization and real-time feasibility.

Abstract: Multiple second-order control barrier function constraints can exhaust their common control authority under bounded acceleration, even when the current state remains feasible. We define a signed local joint-feasibility margin whose sign exactly identifies whether the current barrier half-spaces intersect the admissible input set. For unit-scaled distance constraints, it has acceleration units and a support-function dual that identifies weighted constraint conflicts. We predict the margin one sample ahead for nine task-directed candidates, selecting either the least-deviating candidate that attains a desired margin or the candidate with the largest predicted margin before solving the same hard HOCBF quadratic program. A controlled one-step case shows that, at the state predicted under the hard-QP command, two constraints remain individually feasible but become jointly infeasible, whereas the margin-feedback controller retains a positive next margin. Separately, across 20 paired initial conditions, the margin-feedback controller retains the hard-QP command in a low-pressure task and acts at positive margin in a critical task before the hard-QP problem becomes infeasible; its trajectories remain feasible at that time and complete the task. Source code is publicly available. https://github.com/xirhxq/cbf/tree/robio2026-preventive-regulation

Abstract: Signal Temporal Logic (STL) specifies robot tasks with spatio-temporal requirements, and its robustness semantics allow planning by trajectory optimization. In practice, robots estimate their state from noisy measurements, and when the information gained from a measurement depends on the state, the robot can actively reduce its uncertainty by planning in the belief space. The resulting problem is, however, generally non-convex, for which gradient-based methods are neither complete nor globally optimal. In this paper, we consider Risk STL (RiSTL) planning in Gaussian belief space and show that an information-form parameterization of the belief, together with a convex relaxation of the belief dynamics, yields a mixed-integer convex program (MICP). We prove that the MICP is sound and complete, and that the relaxation preserves the globally optimal input trajectories. We validate the effectiveness of our method in numerical simulations.

Abstract: We establish uniform score bounds and Lipschitz continuity for truncated Gaussian, Cauchy, Boltzmann, and softmax policies under explicitly stated parameterizations.

Abstract: Translating language into humanoid motion requires coordinating body parts, determining motion duration, and producing references suitable for robot execution. We introduce PartiGen, a part-aware latent diffusion framework that incorporates anatomical structure into a shared whole-body motion representation. Part-specific attention processes anatomically masked frame features, and its outputs are fused to combine local limb information with whole-body context. Conditioned on text and motion history, the model generates motion primitives autoregressively. Forward-kinematics supervision encourages kinematic consistency, while a learned end-of-sequence predictor selects a frame-level endpoint after generation. On HumanML3D retargeted to the Unitree G1, PartiGen achieves a segment-level FID of 3.165, a 16.8% reduction over TextOp, and improves R@1 by 1.4 percentage points. In the duration study with 16-frame primitives, endpoint prediction reduces mean absolute duration error from 12.471 to 3.080 frames compared with a fixed-length cutoff. We further evaluate robot execution using a pretrained, frozen GRIT tracker: 409 of 500 generated references (81.8%) pass the posture-based stability screen in MuJoCo. Following simulation screening and manual selection, 26 of 27 attempted motions are judged successful on the real G1.

Abstract: We present Fluid-Gen-Zero, a training-free framework for physics-aware fluid-object interaction video generation that decouples physical reasoning from appearance synthesis. Our key insight is to delegate motion dynamics to a physics simulator while preserving the appearance modeling capacity of pretrained video generators. We bridge these two domains through a two-level agentic workflow: generation-time planning, where a vision-language model (VLM) agent interprets intent and the simulation rollout to organize generation clips, and latent-space guidance, which injects simulation signals into denoising through region-aware latent wrapping. This plug-and-play design is compatible with current video foundation models. We further introduce a benchmark for fluid-object interaction video generation. Across Tora (CogVideoX-based), VACE and WanMove (Wan-based), Fluid-Gen-Zero consistently improves simulation alignment, reducing object trajectory error by 26.7%-81.5% and fluid fEPE (fluid flow endpoint error) by 67.9%-84.0%, while largely preserving perceptual quality. In a human preference study, raters favor Fluid-Gen-Zero in 55.1%-74.4% of same-backbone comparisons across three backbones, and in 90.4%-94.2% of comparisons against simulation-based methods. Code and data will be released upon acceptance.

Abstract: In this note, we study the problem of designing a feedback law that globally steers a system to a prescribed target configuration. Even if the system is fully actuated, topological obstructions generally prevent the existence of globally asymptotically stabilizing continuous feedback laws. We revisit this problem in a stochastic setting by allowing noise to enter through the control channels. Using a criterion for asymptotic stability in the large that combines local Lyapunov stability with positive recurrence, we constructively show that one can construct elementary feedback laws that achieve global asymptotic stability in the large, of the target equilibrium point in connected Euclidean domains with obstacles and manifolds without boundary. For Euclidean domains with obstacles, we also show that the method extends naturally to the problem of finding the minimizer of a strongly convex function with non-convex constraints. Numerical experiments illustrate the effectiveness of the approach for Euclidean domains with circular obstacles and the two dimensional sphere. Additionally, we study the role noise strength when there is a non-convex obstacle, in which case the system might show metastability.

Abstract: We consider a matching problem in which the cost of each edge is a vector with $k$ components. The cost of a matching is the sum of the bottlenecks over all components, and we ask whether there is a perfect matching of cost at most some value $Z$. This type of matching has applications in heavily synchronized job-shop scheduling problems and in reconfiguration problems, where movement is restricted to a single direction per step. In this paper, we analyze the problem from a parameterized complexity perspective and provide various results including FPT-membership for parameters $k$ and $Z$ combined, as well as W[P]-membership and W[SAT]-hardness for each of the two parameters individually. The reduction also implies para-NP-hardness parameterized by either maximum degree or treewidth. We further show hardness of approximation within a super-logarithmic factor for the optimization variant and provide a $k/d$-approximation algorithm for any constant $d \leq k$ as well as an efficient approximation scheme parameterized by $k$. With parameter $Z$, we show that no FPT-time $F(Z)$-approximation algorithm is possible for any computable function $F$, unless W[1] = FPT.

Abstract: Flow-based Vision-Language-Action (VLA) policies generate action chunks by transporting samples from a task-agnostic isotropic Gaussian source. As this source is conditioned on neither recent execution nor predicted future evolution, (i) it discards the local continuity established by recently executed motion. (ii) Even when predictive world representations are introduced, they often only condition the transport dynamics rather than determine where generation starts, how far it may deviate, or along which action directions it may expand. Building on this observation, we introduce ProAct, a world-calibrated proposal-to-action framework that makes the generative source itself predictable. (i) To preserve motion continuity, a lightweight Proposal Expert converts recent actions into a scene-aware hypothesis via one motion-anchored endpoint flow-matching step, initializing generation near the demonstrated action manifold. (ii) To jointly capture intended scene evolution and proposal-future compatibility, a prospective World Expert treats the hypothesis as a soft motion prior while predicting the task-consistent latent future. (iii) From this compatibility, the model calibrates a proposal-centered anisotropic source, where a bounded per-step extent controls the allowed deviation and a trace-normalized low-rank geometry under a condition-number budget allocates refinement over coupled translation, rotation, and gripper directions. Compared with $π_{0.5}$, ProAct improves performance across simulation and real-world tasks while reducing denoising steps by 50%, inference latency by up to 25.8%, and increasing throughput by up to 34.8%.

Abstract: Performing complex medical procedures with continuum robots requires careful selection of their geometric design parameters. The robot should have high dexterity in the specific anatomical environment of its procedure. This work presents a design optimization method that considers both dexterity and anatomy. We introduce the Reachable Volumetric Dexterous Solid Angle (RVDSA) metric as our objective, which measures the ability of a robot's end effector to reach the points in a goal volume from different directions via collision-free paths from a start configuration. We present a computationally efficient motion planner to compute this objective function for a given robotic design, and we use an asymptotically optimal simulated annealing optimizer to compute an optimized design. We applied our new method to optimize the design of a bimanual dexterous sheaths robot for performing procedures on cancerous polyps in colon anatomies, achieving a 78% higher RVDSA on average than optimizing for 3D voxel coverage alone.

Abstract: This paper studies the minimum time trajectoriesvof a car-like mobile robot navigating in an obstacle free environment. The robot, with forward and backward speeds, is controlled by bounded front-wheels acceleration and limited front-wheels steering rate. The paper extends previous results which solved this problem for the kinematic car-like robot. However, the kinematic model assumes pure rolling at the wheels ground contacts. This assumption requires non-sliding constraints for the front and rear wheels that can only be handled by the robot dynamics. This paper formulates the non-sliding constraints based on the robot dynamics then augments the kinematic model time-optimal path primitives with three new path primitives associated with the non-sliding constraints. The three non-sliding path primitives together with the kinematic model twelve path primitives form the car-like robot time optimal trajectories. Approximate analytic solutions for the non-sliding path primitives are also provided. Examples study the time-optimal path primitives along representative maneuvers, illustrating how the non-sliding constraints influence the time optimal trajectories of the car-like robot.