Motion Primitives

Quality-diversity (QD) algorithms have been gaining traction in robot learning, where diverse motion primitive libraries allow robots to adapt zero-shot to constraints at deployment time. However, such methods typically require expert designers to write the success condition, fitness and diversity metrics, and this strongly limits the robot's autonomy. On the other hand, existing LLM-based reward-shaping techniques allow robots to learn autonomously but only output single high-performing solutions, limiting the robot's adaptability. In this paper, we propose an approach designed to output diverse motion primitive archives by autonomously leveraging quality-diversity algorithms, only requiring a free-form description of the task in common language. To address the difficulty of designing relevant fitness and diversity metrics, we propose an autonomous exploration mechanism able to reliably output sets of functionals covering the fitness and behavior descriptor (BD) space. First, we pose policy exploration as a functional design problem, where the functional spaces are lower-dimensional than the full BD and fitness spaces, and propose an LLM-based exploration scheme to sample from these low-dimensional spaces without any task-specific prompts, fine-tuning or expert intervention. We adapt a multi-BD variant of the MAP-Elites success (MES) algorithm, designed to leverage the heterogeneous BD samples. Finally, through experiments based on the genesis simulator, we show that our method effectively generates archives of diverse motion primitives, outperforming classical QD algorithms with inferred and hand-written parametrizations on a set of $4$ robotic manipulation tasks.

Terminal interfaces to conversational agents report rich internal state (listening, thinking, executing tools, awaiting input, failing) almost entirely through text, while the motion channel beside it, the one peripheral vision monitors without reading, carries a single bit: alive. We present the Signal Rail, a one-row terminal status instrument that gives that channel a grammar. Four ideas govern it: spatial semantics (input, processing, and output zones, with direction as meaning), a motion grammar (one kinetic rule per state, never color alone), determinism (frames as a pure function of explicit inputs, golden-frame testable), and honesty (no invented progress or activity). We contribute a 45-section normative specification and a reference implementation inside a working full-duplex local voice agent driven by real signals.

This work presents a human-centered collaborative framework that integrates Preference-Based Optimization (PBO) and Dynamic Movement Primitives (DMPs) to optimize robot-assisted tasks such as painting. The system allows the operator to perform the process while the robot adapts its behavior in real-time, dynamically adjusting the orientation of the piece in order to match the orientation of the operator's hand. The PBO framework leverages the GLISp algorithm to iteratively refine control parameters such as execution time, robot responsiveness, and rotation amplification through human feedback. Moreover, DMPs have been modified to enhance the reactive behavior of the robot and its adaptability to ergonomic requirements. The method was validated with a heterogeneous group of participants executing \rev{painting tasks}. The results show that our strategy effectively reduces operator effort while optimizing process outcomes.

Reinforcement learning can produce robust humanoid controllers, but each new task is typically trained as a separate policy with its own reward design and training process. Motion imitation provides an alternative source of motor competence by training policies to track retargeted human motions, yet the resulting controllers remain reference trackers and are not directly usable as task policies. We propose a three-stage pipeline that turns motion-imitation skills into a reusable hybrid motion prior (HMP) for humanoid locomotion. First, an expert policy is trained to imitate retargeted human motion-capture clips. Second, the expert is distilled into a frozen architecture composed of a proprioceptive encoder, a residual vector-quantized (RVQ) codebook, and an action decoder. Third, task-level policies are trained to solve locomotion tasks by selecting discrete codebook entries while the HMP remains frozen. We evaluate the method on velocity tracking, point-goal navigation, and fall-recovery velocity tracking in simulation, and deploy the velocity-tracking policy on a real Unitree G1 robot. The distillation process preserves the tracking behavior of the expert, while the resulting HMP can be reused without retraining as the action interface for different downstream locomotion policies. The learned HMP reveals an interpretable codebook structure in which the number of active RVQ stages modulates the available gait patterns. We further show that training the codebook with the rotation trick improves latent organization and reduces downstream falls compared with a standard straight-through estimator.

Understanding the computational basis of action recognition is a central challenge in social cognition as well as in human-robot interaction. Inspired by the Mirror Neuron System (MNS), we propose a two-level architecture for motor primitive discovery and online phase recognition applied to the NICO humanoid robot. At the first level, two Self-Organising Maps (SOMs) learn topographic representations of arm kinematics (A-SOM) and hand kinematics (H-SOM) from simulated trials covering seven motor actions. The maps are trained on non-redundant features identified through hierarchical correlation analysis of motion trajectories. The results show that the two SOMs encode complementary aspects of motor behaviour. At the second level, an Echo State Network (ESN) evaluates whether temporal trajectories of SOM activations, represented by consecutive best-matching units, are sufficient for online recognition of the currently executed movement phase. The results show that SOM-based trajectories preserve the dominant phase-discriminative structure of the movement, while contextual information provides only a secondary refinement. Our contribution is the integration of established SOM and ESN methods within an MNS-inspired architecture for motor primitive representation and online phase recognition. The results are compatible with the computational hypothesis that self-organised motor representations, when temporally integrated, can support accurate online recognition of ongoing movement phases.

Learning from demonstration (LfD) enables robots to learn manipulation skills directly from expert demonstrations but remains challenging for contact-rich tasks involving geometric constraints and force interaction. Existing approaches typically require multiple complete demonstrations and do not support reverse skill execution. In this paper, we present a unified one-shot framework for constrained manipulation that learns both forward and reverse execution from a single, possibly unfinished demonstration. Our method decomposes demonstrations into non-contact and contact phases, with non-contact motion encoded with dynamic movement primitives (DMP), and contact motion represented as a sequence of screw motion primitives segmented by our proposed geometry-driven twist-direction segmentation algorithm. During execution, screw primitives are executed sequentially under admittance-guided pose correction and speed regulation, enabling task completion beyond the demonstrated trajectory length as well as reverse skill execution without additional learning data. Experiments on peg insertion, battery insertion, lock opening, and screw driving tasks demonstrate improved success rates and robustness over segmentation and one-shot trajectory learning baselines. Details are available on the project website: https://tuwien-asl.github.io/LfD-Screw/.

Compositionality, by organizing complex behavior as combinations of simpler elements, enables robot learning that is scalable and data efficient. Leveraging this principle, we propose a generative learning-from-demonstration framework that enables compositional modeling of robotic behavior by connecting perception and motion through shared object-level representations. We render scenes from object-centric neural representations that integrate canonical neural fields with latent-conditioned deformations, capturing positional and geometric variations in a smooth, consistent, and interpretable way. For motion generation, a temporal mixture-of-experts (MoE) employs a gating mechanism to combine object-conditioned movement primitives over time, producing complete trajectories. This spatial-temporal compositionality maintains the data efficiency of movement primitives while grounding motion in visual structure, enabling systematic generalization across diverse scene configurations. In simulation, long-horizon manipulation tasks are successfully completed using the proposed model, which requires significantly less training data than other image-based baselines. Real-world experiments further demonstrate the method's robustness to noise, its ability to generalize at the category level through language-based segmentation models, and its capacity to operate directly on 3D scene representations.

Robot imitation learning for manipulation should preserve demonstrated task geometry while producing dynamically admissible robot motions. Existing pipelines often learn task-dependent trajectories and impose execution limits afterward through filtering, smoothing, clipping, or time scaling, which may distort task-critical end-effector paths. We propose the Spectral Movement Primitive (SMP), a frequency-domain imitation learning framework that couples task-space skill generation with joint-space execution regulation. Demonstrations are represented by truncated finite-horizon Fourier coefficients. An empirically selected low-frequency task band captures the dominant motion geometry, while higher harmonics contribute disproportionately to derivative growth. A frame-aware context-conditioned GMM/GMR prior predicts the task-band coefficients in a canonical task frame, and the resulting Cartesian trajectory is mapped to joint space through sequential inverse kinematics. A phase-coupled regulator then limits the requested phase progression without modifying the spectral coefficients, thereby enforcing joint velocity and acceleration limits while preserving the represented path. Experiments evaluate task-band reconstruction, robustness to composite demonstration corruption, out-of-distribution cross-board generalization, joint-space dynamic admissibility, end-effector path preservation, and deployment on a Franka Panda robot. Results show compact geometric reconstruction, consistent transfer across unseen task frames, substantial reductions in dynamic violations and jerk, and preservation of the intended end-effector path during phase regulation.

This paper proposes a novel method that extends the Model Predictive Path Integral (MPPI) method with motion primitives for additional structured sampling, which enhances the convergence towards a globally optimal solution. By evaluating motion primitives and perturbed control sequences in a real-time sampling-based optimization loop, this work addresses the limitations of the path planning capabilities of sampling-based controllers. The algorithm is implemented on a quadcopter simulator and tested on an obstacle field navigation task. It is demonstrated that the proposed approach enhances exploration of the control space while maintaining the fast, reactive behavior required for real-time control.

Robots deployed in safety-critical environments must execute motions that are simultaneously robust to disturbances and provably safe from collisions. Dynamic Movement Primitives (DMPs) offer inherent stability, temporal flexibility, and efficient trajectory generalization from single demonstrations, but they lack formal safety certificates. Conversely, Hamilton-Jacobi (HJ) Reachability analysis provides a principled framework for computing worst-case safety margins and forward-invariant safe sets, but classical grid-based methods suffer from the curse of dimensionality and are impractical for real-time control. This paper introduces HJ-SafeDMP, a framework that integrates DMPs with learned HJ Reachability-based safety value functions to achieve provably safe, robust, and computationally efficient robot motion. We learn a Control Barrier Value Function (CBVF) from offline demonstration data using a model-free, finite-difference HJ recursion and deploy it as a real-time safety filter via a closed-form control law that modulates the DMP output. Unlike optimization-based CBF-QP approaches, our method achieves safety filtering without online quadratic program solves, preserving the computational efficiency of DMPs. We further incorporate an expectile-based offline learning objective that avoids querying out-of-distribution actions, and a conformal prediction calibration step that provides finite-sample probabilistic safety coverage. Experimental evaluation on a 7-DOF robot manipulator demonstrates that HJ-SafeDMP achieves formal safety guarantees with orders-of-magnitude faster execution than optimization-based baselines, while maintaining the robustness and adaptability of DMPs for human-robot interaction.

Motion forecasting is essential for autonomous driving systems to enable safe decision-making and planning in complex driving scenarios. While existing predictors excel at minimizing standard displacement errors, they often overlook the adherence to lane topology of multimodal predictions, particularly for lower-probability modes. Consequently, predicted trajectories may violate physical and logical constraints, making the prediction set unreliable for safety-critical planning. In this paper, we propose LAMP (Lane-Aligned Motion Primitives), a topology-aware forecasting framework that anchors multimodal prediction to structured motion primitives aligned with lane topology. Specifically, we use a VQ-VAE to learn shape-aware motion primitives as discrete intention queries, capturing spatiotemporal patterns beyond endpoint-based intentions. We further introduce a feasibility-aware intention selector trained with a lane-topology prior for filtering unreachable intention queries, guiding the decoder to prioritize topology-consistent intentions while preserving behavioral diversity. Extensive experiments on the Argoverse 2 dataset demonstrate that LAMP achieves prediction accuracy comparable to state-of-the-art baselines while outperforming them in feasibility and diversity metrics.

Enabling robots to understand and execute tasks from natural language commands while maintaining data efficiency remains challenging. Foundation models such as vision-language-action (VLA) and vision-language models (VLMs) provide intuitive interaction channels but require extensive data; task-parameterized imitation learning achieves data efficiency but lacks natural language grounding. This work bridges this gap through a modular architecture combining task-parameterized kernelized movement primitives (TP-KMPs) with pretrained VLMs. During learning, skills are acquired from 2 to 5 kinesthetic demonstrations, and the VLM generates skill schemas describing each skill's parameters and preconditions. During execution, the VLM interprets commands to select skills, reason about parameter bindings, and create novel behaviors through covariance-weighted composition. When no skill or composition suffices, the system identifies capability gaps and requests targeted demonstrations, all without fine-tuning. Validation on a 7-DoF manipulator shows success rates of 73.3%-100% in scenarios requiring skill selection, composition, and active learning.

Diffusion-based imitation learning methods have driven rapid progress in robot dexterous manipulation tasks. However, they have limitations when applied to tasks that involve complex free-form surface constraints because of their lack of explicit surface geometry constraint modeling and the dynamic feasibility issue, resulting in stochastic action generation that fails to achieve reliable surface alignment and maintain stable contact. To address these limitations, we propose a novel surface constraint policy (SCP) for generating robot actions that satisfy free-form surface constraints on the basis of human demonstrations and real-time visual observations. First, the surface geometry constraint is encoded using a two-dimensional weighted Gaussian kernel function that is derived from demonstrations. Building on the encoded surface geometry constraints, the diffusion-based policy is used to infer task-level action intentions from multimodal sensory inputs, including visual observations and robot state feedback. These intentions are further transformed into surface-constrained dynamic movement primitives (DMPs) through a similarity-based action mapping method, thereby enabling smooth and compliant motion execution. The SCP achieves generation of structured surface geometric intent and dynamically admissible actions. The proposed method is validated on multiple surface manipulation tasks and compared with existing techniques. The experimental results demonstrate superior task success rates and contact stability under surface constraints.

Vision-Language-Action (VLA) models offer a promising paradigm for generalist robotic policies, yet their adaptation is hindered by data inefficiency and poor generalization. We argue that these bottlenecks stem from the prevailing Direct Instruction-to-Control Mapping, which forces models to memorize monolithic trajectories rather than reusable motion patterns, i.e., primitives. We propose PrimitiveVLA, a framework that shifts this paradigm toward a Primitive-Centric Disassemble & Assemble paradigm. Supported by a shared Multimodal Canonical Representation (MCR), PrimitiveVLA unifies two phases: (1) Fine-tuning-phase Disassembly, which uses an automated pipeline to disassemble demonstrations into reusable primitives; and (2) Inference-phase Assembly, which employs a VLM-based planner and an LLM-generated switch module for robust closed-loop execution. By disassembling tasks into reusable primitives, PrimitiveVLA enables VLA models to learn invariant motion patterns instead of task-specific trajectories. Extensive experiments show that our framework improves data efficiency and achieves superior zero-shot generalization across unseen and long-horizon tasks.

AR smart glasses need continuous behavioral context to offer proactive assistance, yet their most practical always-on sensor, the head-mounted Inertial Measurement Unit (IMU), detects only motion primitives such as walking or standing. We push beyond motion primitives to behavioral-level recognition, defining five categories that balance AR application need with sensor observability. To this end, we construct a 160K-sample Ego4D dataset with a four-tier quality assurance framework spanning 8 activity scenarios, and propose HiT-HAR, a 703K-parameter hierarchical model that outperforms prior head-mounted IMU models on five-class action and eight-class scenario recognition. We further map the observability frontier of head-mounted IMU through per-class separability analysis, identifying which behavioral categories are reliably observable (Locomotion), which benefit from temporal context (Object Transfer, Task Operation), and where scenario-dependent signal overlap poses remaining challenges. Our results indicate that architectural choices exploiting temporal context and scenario structure outperform simply scaling model size. The code and dataset are publicly available at https://github.com/Harvard-AI-and-Robotics-Lab/HiT-HAR.

Embodied trajectories, such as the executable motion sequences of robotic manipulators, underwater vehicles, and mobile robots, are a fundamental output of embodied AI. Modern generative models often treat them as a dense, monolithic signal generated point by point, fitting an intricate high-dimensional posterior while leaving the data's latent structure unmodeled, the same sample inefficiency long identified by the structured generative model literature. We argue that a compositional latent structure is a natural choice: many embodied tasks share recurring motion fragments that can be made explicit as a finite repertoire of reusable motion primitives, and compositional units naturally align with subtask boundaries to support task decomposition. Existing compositional generators, however, compose in a latent space and rely on post-hoc decoding to relate sampled units to actual trajectory segments. We instead compose directly in the physical trajectory space through a flow-matching framework with two coupled designs. Motion-Primitive Dictionary Learning equips each atom with a learnable length mask and binary starting indicators so the atom itself is the primitive, reused verbatim wherever it is placed. Structural Sparse Flow Matching with Geometric Constraints then generates a binary placement matrix using duration-aware tokenization and a differentiable geometric loss that enforces spatial continuity and temporal contiguity where adjacent primitives meet. On Open X-Embodiment and 3DMoTraj, the framework attains state-of-the-art accuracy and reduces the FDE/ADE ratio from 1.8 to 1.07, improving ADE by 19.2% and FDE by 21.0% over the strongest baseline.

Text- and image-conditioned video generation models have achieved strong visual fidelity and temporal coherence, but they often fail to generate motion governed by kinematic and geometric constraints. In these settings, object parts must remain rigid, maintain contact or coupling with neighboring components, and transfer motion consistently across connected parts. These requirements are especially explicit in articulated mechanical assemblies, where motion is constrained by rigid-link geometry, contact/coupling relations, and transmission through kinematic chains. A generated video may therefore appear plausible while violating the intended mechanism, such as rotating a part that should translate, deforming a rigid component, breaking coupling between parts, or failing to move downstream components. To evaluate this gap, We introduce MechVerse, a benchmark for mechanically consistent image-to-video generation. MechVerse contains 21,156 synthetic clips from 1,357 mechanical assemblies across 141 categories, organized into three tiers of increasing kinematic complexity: independent articulation, pairwise coupling, and densely coupled multi-part mechanisms. Each clip is paired with a structured prompt describing part identities, stationary supports, moving components, motion primitives, direction, speed/extent, and inter-part dependencies. We evaluate proprietary, open-source, and fine-tuned image-to-video models using standard video metrics, instruction-following scores, and human judgments of motion correctness and kinematic coupling. Results show that current models can preserve appearance and smoothness while failing to generate mechanically admissible motion, with errors increasing as coupling complexity grows. MechVerse provides a benchmark for measuring and improving mechanism-aware video generation from image and language inputs.

Lower limb exoskeletons (LLEs) present the potential to make motor-impaired individuals walk again. Their application in real-world environments is still limited by the lack of effective adaptive gait planning. Indeed, current exoskeletons are meant to walk only on a flat and even terrain. Generating environment-aware, physiologically consistent gait trajectories in real-time is an open challenge. To overcome this, we propose a novel Kernelized Movement Primitives (KMP)-based framework for adaptive gait generation (AGG) across multiple indoor terrains. The proposed approach learns a probabilistic representation of human gait in both the joint and task spaces from a limited number of human demonstrations, representing natural gait characteristics and ensuring kinematic feasibility. In addition, the learned trajectories are adapted using environmental information extracted from an onboard RGB-D camera by treating the AGG as a linearly constrained optimization problem with via-points. The proposed method has been thoroughly validated first in simulations for gait generation in different scenarios, such as flat-ground walking, slopes, stairs, and obstacles crossing. Finally, the effectiveness and robustness of the method have been demonstrated with experiments on a commercial LLE in real-world scenarios. The results obtained demonstrate the feasibility of an environment-aware gait planning system for a new generation of intelligent lower limb exoskeletons for assisting people with disabilities in their every-day life.

Multi-agent motion planning (MAMP) is an important problem for autonomous systems with multiple agents. In this work we propose a two-step method for finding optimized and kinematically feasible solutions to MAMP problems. The first step finds an initial feasible solution using state-of-the-art methods such as conflict-based search (CBS) or priority-based search (PBS), and the second step is an improvement step which improves the solution by solving a multi-phase optimal control problem (OCP) where the initial solution is used to warm-start the solver. We also propose a method for generating motion primitives in an optimized way under the constraint that the primitive durations are all multiples of the same sample time. We evaluate our proposed framework on a MAMP problem for tractor-trailer systems. We extend the safe interval path planning with interval projections (SIPP-IP) algorithm so it can handle more general cost functions and larger agents, but our results show that for the tractor-trailer system a simple lattice-based planner performs better due to less conservative collision checks. Our experiments also indicate that CBS performs better than PBS for this system as it achieves a higher success rate in environments with obstacles and had a lower average runtime, although both planners achieve solutions of similar quality after the improvement step.

Motion forecasting often requires trading interpretability for predictive accuracy. Standard anchor-based architectures rely on opaque latent queries that are highly prone to latent collapse, or naive trajectory sampling that limits multi-modal diversity. We propose an end-to-end differentiable framework that grounds predictions in a comprehensive "motion bank", a structured embedding space of physically realizable trajectories constructed via contrastive learning. Rather than regressing paths from a blank slate, our architecture dynamically retrieves explicit motion priors using a novel Anchor Retrieval Layer. This module adapts orthogonally initialized queries via a Dual-Level Gated Cross-Attention mechanism and executes discrete trajectory selection using a Straight-Through Gumbel-Softmax estimator to preserve continuous gradient flow. The retrieved semantically grounded anchors are then geometrically refined by a DETR-style decoder, optimized jointly with a Winner-Takes-All (WTA) kinematic Gaussian Mixture Model (GMM), a latent diversity penalty, and a soft-min weighted endpoint loss. By strictly conditioning the decoding phase on diverse, interpretable motion primitives, our approach eliminates the "black box" of standard latent queries while achieving competitive multi-modal accuracy on the Argoverse 2 and Waymo Open Motion datasets. Code is available at: https://github.com/abviv/recall2predict