Robot Motion Generation

While modular robots offer versatility, excessive joint torque during locomotion poses a significant risk of mechanical failure, especially for detachable joints. To address this, we propose an optimization framework using the NSGA-III algorithm. Unlike conventional approaches that prioritize mobility alone, our method derives Pareto optimal solutions to minimize joint load while maintaining necessary locomotion speed and stability. Simulations and physical experiments demonstrate that our approach successfully generates gait motions for diverse environments, such as slopes and steps, ensuring structural integrity without compromising overall mobility.

Learning motion priors for physics-based humanoid control is an active research topic. Existing approaches mainly include variational autoencoders (VAE) and adversarial motion priors (AMP). VAE introduces information loss, and random latent sampling may sometimes produce invalid behaviors. AMP suffers from mode collapse and struggles to capture diverse motion skills. We present the Spherical Latent Motion Prior (SLMP), a two-stage method for learning motion priors. In the first stage, we train a high-quality motion tracking controller. In the second stage, we distill the tracking controller into a spherical latent space. A combination of distillation, a discriminator, and a discriminator-guided local semantic consistency constraint shapes a structured latent action space, allowing stable random sampling without information loss. To evaluate SLMP, we collect a two-hour human combat motion capture dataset and show that SLMP preserves fine motion detail without information loss, and random sampling yields semantically valid and stable behaviors. When applied to a two-agent physics-based combat task, SLMP produces human-like and physically plausible combat behaviors only using simple rule-based rewards. Furthermore, SLMP generalizes across different humanoid robot morphologies, demonstrating its transferability beyond a single simulated avatar.

Trajectory generation for mobile robots in unstructured environments faces a critical dilemma: balancing kinematic smoothness for safe execution with terminal precision for fine-grained tasks. Existing generative planners often struggle with this trade-off, yielding either smooth but imprecise paths or geometrically accurate but erratic motions. To address the aforementioned shortcomings, this article proposes DRIFT (Diffusion-based Rule-Inferred for Trajectories), a conditional diffusion framework designed to generate high-fidelity reference trajectories by integrating two complementary inductive biases. First, a Relational Inductive Bias, realized via a GNN-based Structured Scene Perception (SSP) module, encodes global topological constraints to ensure holistic smoothness. Second, a Temporal Attention Bias, implemented through a novel Graph-Conditioned Time-Aware GRU (GTGRU), dynamically attends to sparse obstacles and targets for precise local maneuvering. In the end, quantitative results demonstrate that DRIFT reconciles these conflicting objectives, achieving centimeter-level imitation fidelity (0.041m FDE) and competitive smoothness (27.19 Jerk). This balance yields highly executable reference plans for downstream control.

In this paper, we present an online method for converting an arbitrary geometric path, represented by a sequence of states, and generated by any planner (e.g., sampling-based planners such as RRT or PRM, search-based planners such as ARA*, etc.), into a kinematically feasible, jerk-limited trajectory. The method generates a sequence of quintic/quartic splines that can be discretized at a user-specified control rate and streamed to a low-level robot controller. Our approach enables real-time adaptation to environmental changes and can be re-invoked at any instant to generate a new trajectory from the robot's current state to a desired target state or sequence of states. Under a bounded-obstacle-velocity assumption, the method provides conditional stopping-safety guarantees over a finite time interval in dynamic environments, while allowing bounded geometric deviation from the original path. Kinematic constraints, including jerk limits, are explicitly considered. We validate the approach in a comparative simulation study against a competing method, demonstrating favorable behavior w.r.t. smoothness, computational time, and real-time performance, particularly with frequent target-state changes (up to 1 [kHz]). Real-robot experiments demonstrate applicability in real-world scenarios, including scenarios with a human as an obstacle.

Robotic manipulation requires policies that are smooth and responsive to evolving observations. However, synchronous inference in the raw action space introduces several challenges, including intra-chunk jitter, inter-chunk discontinuities, and stop-and-go execution. These issues undermine a policy's smoothness and its responsiveness to environmental changes. We propose ABPolicy, an asynchronous flow-matching policy that operates in a B-spline control-point action space. First, the B-spline representation ensures intra-chunk smoothness. Second, we introduce bidirectional action prediction coupled with refitting optimization to enforce inter-chunk continuity. Finally, by leveraging asynchronous inference, ABPolicy delivers real-time, continuous updates. We evaluate ABPolicy across seven tasks encompassing both static settings and dynamic settings with moving objects. Empirical results indicate that ABPolicy reduces trajectory jerk, leading to smoother motion and improved performance. Project website: https://teee000.github.io/ABPolicy/.

Leveraging auditory and visual feedback for attention reorientation is essential for natural gaze shifts in social interaction. However, enabling humanoid robots to perform natural and context-appropriate gaze shifts in unconstrained human--robot interaction (HRI) remains challenging, as it requires the coupling of cognitive attention mechanisms and biomimetic motion generation. In this work, we propose the Robot Gaze-Shift (RGS) framework, which integrates these two components into a unified pipeline. First, RGS employs a vision--language model (VLM)-based gaze reasoning pipeline to infer context-appropriate gaze targets from multimodal interaction cues, ensuring consistency with human gaze-orienting regularities. Second, RGS introduces a conditional Vector Quantized-Variational Autoencoder (VQ-VAE) model for eye--head coordinated gaze-shift motion generation, producing diverse and human-like gaze-shift behaviors. Experiments validate that RGS effectively replicates human-like target selection and generates realistic, diverse gaze-shift motions.

Physics-based humanoid control relies on training with motion datasets that have diverse data distributions. However, the fixed difficulty distribution of datasets limits the performance ceiling of the trained control policies. Additionally, the method of acquiring high-quality data through professional motion capture systems is constrained by costs, making it difficult to achieve large-scale scalability. To address these issues, we propose a closed-loop automated motion data generation and iterative framework. It can generate high-quality motion data with rich action semantics, including martial arts, dance, combat, sports, gymnastics, and more. Furthermore, our framework enables difficulty iteration of policies and data through physical metrics and objective evaluations, allowing the trained tracker to break through its original difficulty limits. On the PHC single-primitive tracker, using only approximately 1/10 of the AMASS dataset size, the average failure rate on the test set (2201 clips) is reduced by 45% compared to the baseline. Finally, we conduct comprehensive ablation and comparative experiments to highlight the rationality and advantages of our framework.

Reactive motion generation in dynamic and unstructured scenarios is typically subject to essentially static perception and system dynamics. Reliably modeling dynamic obstacles and optimizing collision-free trajectories under perceptive and control uncertainty are challenging. This article focuses on revealing tight connection between reactive planning and dynamic mapping for manipulators from a model-based perspective. To enable efficient particle-based perception with expressively dynamic property, we present a tensorized particle weight update scheme that explicitly maintains obstacle velocities and covariance meanwhile. Building upon this dynamic representation, we propose an obstacle-aware MPPI-based planning formulation that jointly propagates robot-obstacle dynamics, allowing future system motion to be predicted and evaluated under uncertainty. The model predictive method is shown to significantly improve safety and reactivity with dynamic surroundings. By applying our complete framework in simulated and noisy real-world environments, we demonstrate that explicit modeling of robot-obstacle dynamics consistently enhances performance over state-of-the-art MPPI-based perception-planning baselines avoiding multiple static and dynamic obstacles.

This paper presents a smooth trajectory generation method for a four-degree-of-freedom parallel kinematic milling robot. The proposed approach integrates B-spline and Quaternion interpolation techniques to manage decoupled position and orientation data points. The synchronization of orientation and arc-length-parameterized position data is achieved through the fitting of smooth piece-wise Bezier curves, which describe the non-linear relationship between path length and tool orientation, solved via sequential quadratic programming. By leveraging the convex hull properties of Bezier curves, the method ensures spatial and temporal separation constraints for multi-agent trajectory generation. Unit quaternions are employed for orientation interpolation, providing a robust and efficient representation that avoids gimbal lock and facilitates smooth, continuous rotation. Modifier polynomials are used for position interpolation. Temporal trajectories are optimized using minimum jerk, time-optimal piece-wise Bezier curves in two stages: task space followed by joint space, implemented on a low-cost microcontroller. Experimental results demonstrate that the proposed method offers enhanced accuracy, reduced velocity fluctuations, and computational efficiency compared to conventional interpolation methods.

Robot motion distributions often exhibit multi-modality and require flexible generative models for accurate representation. Streaming Flow Policies (SFPs) have recently emerged as a powerful paradigm for generating robot trajectories by integrating learned velocity fields directly in action space, enabling smooth and reactive control. However, existing formulations lack mechanisms for adapting trajectories post-training to enforce safety and task-specific constraints. We propose Constraint-Aware Streaming Flow (CASF), a framework that augments streaming flow policies with constraint-dependent metrics that reshape the learned velocity field during execution. CASF models each constraint, defined in either the robot's workspace or configuration space, as a differentiable distance function that is converted into a local metric and pulled back into the robot's control space. Far from restricted regions, the resulting metric reduces to the identity; near constraint boundaries, it smoothly attenuates or redirects motion, effectively deforming the underlying flow to maintain safety. This allows trajectories to be adapted in real time, ensuring that robot actions respect joint limits, avoid collisions, and remain within feasible workspaces, while preserving the multi-modal and reactive properties of streaming flow policies. We demonstrate CASF in simulated and real-world manipulation tasks, showing that it produces constraint-satisfying trajectories that remain smooth, feasible, and dynamically consistent, outperforming standard post-hoc projection baselines.

Humans intuitively move to sound, but current humanoid robots lack expressive improvisational capabilities, confined to predefined motions or sparse commands. Generating motion from audio and then retargeting it to robots relies on explicit motion reconstruction, leading to cascaded errors, high latency, and disjointed acoustic-actuation mapping. We propose RoboPerform, the first unified audio-to-locomotion framework that can directly generate music-driven dance and speech-driven co-speech gestures from audio. Guided by the core principle of "motion = content + style", the framework treats audio as implicit style signals and eliminates the need for explicit motion reconstruction. RoboPerform integrates a ResMoE teacher policy for adapting to diverse motion patterns and a diffusion-based student policy for audio style injection. This retargeting-free design ensures low latency and high fidelity. Experimental validation shows that RoboPerform achieves promising results in physical plausibility and audio alignment, successfully transforming robots into responsive performers capable of reacting to audio.

Visual traversability estimation is central to autonomous navigation, yet most approaches either rely on prompt-driven Vision-Language Model (VLM) or decouple traversability from trajectory planning, requiring separate planners with heavy mapping, manual tuning, and extended deployment time. We propose EmbodiedDiffusion, a diffusion-based framework that simultaneously predicts traversability maps and generates feasible trajectories from RGB images using planner-free synthetic supervision and embodiment conditioning for cross-platform transfer. The framework distills category-level traversability semantics from a VLM teacher into a lightweight student model during training, enabling prompt-free, real-time inference at deployment. A modular FiLM-based conditioning mechanism isolates embodiment-specific reasoning into a compact trainable subset of the network, allowing rapid adaptation to new robot platforms without retraining the visual backbone or the trajectory diffusion model. Across indoor environments with quadruped and aerial robots, EmbodiedDiffusion achieves 80-100% navigation success in the full-data regime with real-time inference (90 ms) and adapts to new platforms using only 10 min of visual data collection, demonstrating scalable, unified traversability reasoning and trajectory generation for heterogeneous robots.

Learning coordinated behaviors for multi-robot systems from only a few demonstrations is difficult because temporal task dependencies and spatial trajectory generation are tightly coupled, which increases the hypothesis space and often yields unstable generalization in data-scarce regimes. We present DDACE, a structured few-shot learning framework that introduces a structural inductive bias by explicitly decoupling temporal coordination from spatial trajectory synthesis. Demonstrations are first processed via spectral clustering to extract coordination structure and form interaction graphs. A Temporal Graph Network predicts action dependencies and sequences, while Gaussian Process models generate progress-parameterized geometric trajectories that adapt to new start/goal configurations. This factorized design reduces hypothesis coupling and improves data efficiency for few-shot multi-robot coordination. Extensive simulation studies and real-robot experiments show that DDACE produces stable coordinated executions from a small number of demonstrations and improves trajectory consistency compared to end-to-end imitation baselines under limited data. Additional materials are available at https://sites.google.com/view/ddace.

This paper presents a three-stage offline command generation framework for reproducing human lower-limb motion on a suspended bipedal robot while matching torque trajectories computed from the robot dynamic model. First, State-Dependent Riccati Equation (SDRE) control derives the reference torque trajectory for the measured motion. Second, parameterized optimization converts this trajectory into trapezoidal joint velocity commands under motor speed and acceleration limits. Third, a proportional-integral-derivative linear quadratic regulator (PID-LQR) compensation scheme refines these commands using experimental tracking data. The platform executes the resulting profiles to reproduce human walking and squatting motions recorded by a Vicon system, allowing evaluation of tracking accuracy and repeatability. Results show that the average root mean square error (RMSE) and standard deviation (STD) of joint angles across repeated trials remain below 7° and 0.33°, respectively. Joint angle and torque trajectory comparisons show lower maximum RMSE and STD values than those for MPC and IPSO-PID in every reported case. The framework enables accurate and repeatable motion reproduction within actuator limits, providing controlled and measurable conditions that can reduce reliance on human participation and associated risks during preliminary evaluation of devices for assistive walking, gait training, and rehabilitation.

Generative models have become increasingly powerful tools for robot motion generation, enabling flexible and multimodal trajectory generation across various tasks. Yet, most existing approaches remain limited in handling multiple types of constraints, such as collision avoidance, actuation limits, and dynamic consistency, which are typically addressed individually or heuristically. In this work, we propose UniConFlow, a unified constrained flow matching-based framework for trajectory generation that systematically incorporates both equality and inequality constraints. Moreover, UniConFlow introduces a novel prescribed-time zeroing function that shapes a time-varying guidance field during inference, allowing the generation process to adapt to varying system models and task requirements. Furthermore, to further address the computational challenges of long-horizon and high-dimensional trajectory generation, we propose two practical strategies for the terminal constraint enforcement and inference process: a violation-segment extraction protocol that precisely localizes and refines only the constraint-violating portions of trajectories, and a trajectory compression method that accelerates optimization in a reduced-dimensional space while preserving high-fidelity reconstruction after decoding. Empirical validation across three experiments, including a double inverted pendulum, a real-to-sim car racing task, and a sim-to-real manipulation task, demonstrates that UniConFlow outperforms state-of-the-art generative planners and conventional optimization baselines, achieving superior performance on certified motion planning metrics such as safety, kinodynamic consistency, and action feasibility. Project page is available at: https://uniconflow.github.io.

This paper addresses conservatism, limited numerical accuracy, and high computational effort in existing methods ensuring safety by design in online model-based motion generation. The presented method employs a novel captivity-escape zero-sum differential game to adapt the planning model's performance so that resulting reference trajectories are trackable within a prescribed safety margin by a jointly synthesized safety controller. A numerical example demonstrates orders-of-magnitude faster computation and improved numerical accuracy compared to the state of the art.

Embodied robots have achieved strong performance in many real-world manipulation tasks, yet agile dynamic manipulation remains challenging due to high sensitivity to motion parameters and sparse outcome-level feedback. Tasks such as shooting a basketball into a hoop require precise control of fast open-loop motions, where small trajectory variations can lead to large outcome deviations, making data-efficient adaptation difficult for existing methods that rely on large-scale interaction, reward engineering, or accurate dynamic modeling. We propose Prior Reinforce (P.R.), a simple and practical framework for goal-conditioned dynamic manipulation. The method first learns a structured motion manifold from a small set of demonstrations using a conditional diffusion model, and then adapts motions toward new goals through feedback-driven optimization in a low-dimensional condition space. By separating motion generation from outcome-driven adaptation, the framework enables efficient refinement using only a small number of real-world trials under noisy perception. Experiments on multiple real-world dynamic manipulation tasks demonstrate that P.R. reliably achieves new goals within as few as ten total trials while remaining robust to perception noise and hardware uncertainty, suggesting a practical approach for low-trial real-world robot adaptation. Project website: https://adap-robotics.github.io/.

Motion retargeting for specific robot from existing motion datasets is one critical step in transferring motion patterns from human behaviors to and across various robots. However, inconsistencies in topological structure, geometrical parameters as well as joint correspondence make it difficult to handle diverse embodiments with a unified retargeting architecture. In this work, we propose a novel unified graph-conditioned diffusion-based motion generation framework for retargeting reference motions across diverse embodiments. The intrinsic characteristics of heterogeneous embodiments are represented with graph structure that effectively captures topological and geometrical features of different robots. Such a graph-based encoding further allows for knowledge exploitation at the joint level with a customized attention mechanisms developed in this work. For lacking ground truth motions of the desired embodiment, we utilize an energy-based guidance formulated as retargeting losses to train the diffusion model. As one of the first cross-embodiment motion retargeting methods in robotics, our experiments validate that the proposed model can retarget motions across heterogeneous embodiments in a unified manner. Moreover, it demonstrates a certain degree of generalization to both diverse skeletal structures and similar motion patterns.