From autonomous driving to package delivery, ensuring safe yet efficient multi-agent interaction is challenging as the interaction dynamics are influenced by hard-to-model factors such as social norms and contextual cues. Understanding these influences can aid in the design and evaluation of socially-aware autonomous agents whose behaviors are aligned with human values. In this work, we seek to codify factors governing safe multi-agent interactions via the lens of responsibility, i.e., an agent’s willingness to deviate from their desired control to accommodate safe interaction with others. Specifically, we propose a data-driven modeling approach based on control barrier functions and differentiable optimization that efficiently learns agents’ responsibility allocation from data. We demonstrate on synthetic and real-world datasets that we can obtain an interpretable and quantitative understanding of how much agents adjust their behavior to ensure the safety of others given their current environment.
@inproceedings{RemyFridovichKeilEtAl2025,author={Remy, I. and Fridovich-Keil, D. and Leung, K.},booktitle={{American Control Conference}},title={Learning responsibility allocations for multi-agent interactions: A differentiable optimization approach with control barrier functions},year={2025},arxiv={2410.07409},category={structure},img={RemyFridovichKeilEtAl2024.png},selected={true},keywords={accepted},owner={karenl7}}
STLCG++: A Masking Approach for Differentiable Signal Temporal Logic Specification
Signal Temporal Logic (STL) offers a concise yet expressive framework for specifying and reasoning about spatio-temporal behaviors of robotic systems. Attractively, STL admits the notion of robustness, the degree to which an input signal satisfies or violates an STL specification, thus providing a nuanced evaluation of system performance. Notably, the differentiability of STL robustness enables direct integration to robotics workflows that rely on gradient-based optimization, such as trajectory optimization and deep learning. However, existing approaches to evaluating and differentiating STL robustness rely on recurrent computations, which become inefficient with longer sequences, limiting their use in time-sensitive applications. In this paper, we present STLCG++, a masking-based approach that parallelizes STL robustness evaluation and backpropagation across timesteps, achieving more than 1000x faster computation time than the recurrent approach. We also introduce a smoothing technique for differentiability through time interval bounds, expanding STL’s applicability in gradient-based optimization tasks over spatial and temporal variables. Finally, we demonstrate STLCG++’s benefits through three robotics use cases and provide open-source Python libraries in JAX and PyTorch for seamless integration into modern robotics workflows.
@inproceedings{KapoorMizutaEtAl2025,author={Kapoor, P. and Mizuta, K. and Kang, E. and Leung, K.},title={{STLCG++}: A Masking Approach for Differentiable Signal Temporal Logic Specification},year={2025},arxiv={2501.04194},category={structure},img={KapoorMizutaEtAl2025.png},selected={true},note={{preprint}},keywords={preprint},owner={karenl7}}
2024
Legible and Proactive Robot Planning for Prosocial Human-Robot Interactions
Geldenbott, J.,
and Leung, K.
In Proc. IEEE Conf. on Robotics and Automation,
2024
Humans have a remarkable ability to fluently engage in joint collision avoidance in crowded navigation tasks despite the complexities and uncertainties inherent in human behavior. Underlying these interactions is a mutual understanding that (i) individuals are \textitprosocial, that is, there is equitable responsibility in avoiding collisions, and (ii) individuals should behave \textitlegibly, that is, move in a way that clearly conveys their intent to reduce ambiguity in how they intend to avoid others. Toward building robots that can safely and seamlessly interact with humans, we propose a general robot trajectory planning framework for synthesizing legible and proactive behaviors and demonstrate that our robot planner naturally leads to prosocial interactions. Specifically, we introduce the notion of a \textitmarkup factor to incentivize legible and proactive behaviors and an \textitinconvenience budget constraint to ensure equitable collision avoidance responsibility. We evaluate our approach against well-established multi-agent planning algorithms and show that using our approach produces safe, fluent, and prosocial interactions. We demonstrate the real-time feasibility of our approach with human-in-the-loop simulations.
@inproceedings{GeldenbottLeung2024,author={Geldenbott, J. and Leung, K.},booktitle={{Proc.\ IEEE Conf.\ on Robotics and Automation}},title={Legible and Proactive Robot Planning for Prosocial Human-Robot Interactions},year={2024},arxiv={2404.03734},category={interaction},img={GeldenbottLeung2024.png},selected={true},owner={karenl7}}
Semantically-Driven Object Search Using Partially Observed 3D Scene Graphs
@inproceedings{RemyGuptaEtAl2024,author={Remy, I. and Gupta, A. and Leung, K.},title={Semantically-Driven Object Search Using Partially Observed {3D} Scene Graphs},year={2024},img={RemyGuptaEtAl2024.png},note={(preprint)},keywords={preprint},owner={karenl7}}
Beyond Visual Line-of-Sight Uncrewed Aerial Vehicle for Search and Locate Operations
Madewell, E.,
Pollack, E.,
Kuni, H.,
Johri, S.,
Broyles, D.,
Vagners, J.,
and Leung, K.
The deployment of Uncrewed Aerial Vehicles (UAV) in wilderness search and locate operations has gained attention in the past few years. To help expand the effective search radius and provide more flexible UAV search capabilities, we propose a Reliable Uninterrupted Communications Kit for UAV Search (RUCKUS), a backpackable Beyond Visual Line-of-Sight UAV system utilizing an intermediate "relay UAV" to provide an uninterrupted communications link between the ground station and the search UAV. The proposed system is designed to be self-contained, modular, and affordable and can provide continuous sensor data and control flow between the search UAV and ground station, enabling the users to receive real-time video feedback from the search UAV and dynamically update the UAV’s search strategy. In this paper, we describe the proposed system architecture and characterization of the signal strength via a number of experimental flight tests. The end goal is to develop a flexible, cost-effective, and portable BVLOS solution to aid first responders and alike in safety-critical operations where extending the operational range can significantly improve mission success.
@inproceedings{MadewellPollackEtAl2024,author={Madewell, E. and Pollack, E. and Kuni, H. and Johri, S. and Broyles, D. and Vagners, J. and Leung, K.},booktitle={{AIAA Scitech Forum}},title={Beyond Visual Line-of-Sight Uncrewed Aerial Vehicle for Search and Locate Operations},year={2024},category={afsl},img={MadewellPollackEtAl2024.png},owner={karenl7}}
CoBL-Diffusion: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions
Mizuta, K.,
and Leung, K.
In IEEE/RSJ Int. Conf. on Intelligent Robots & Systems,
2024
@inproceedings{MizutaLeung2024,author={Mizuta, K. and Leung, K.},booktitle={{IEEE/RSJ Int.\ Conf.\ on Intelligent Robots \& Systems}},title={{CoBL-Diffusion}: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions},year={2024},arxiv={2406.05309},category={interaction},img={MizutaLeung2024.png},selected={true},owner={karenl7}}
CoBL-Diffusion: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions
Mizuta, K.,
and Leung, K.
In Proc. IEEE Conf. on Robotics and Automation: Long-term Human Motion Prediction Workshop,
2024
@inproceedings{MizutaLeung2024b,author={Mizuta, K. and Leung, K.},booktitle={{Proc.\ IEEE Conf.\ on Robotics and Automation}: Long-term Human Motion Prediction Workshop},title={{CoBL-Diffusion}: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions},year={2024},img={MizutaLeung2024.png},owner={karenl7}}
Continuous-Time Line-of-Sight Constrained Trajectory Planning for 6-Degree of Freedom Systems
Hayner, C. R.,
Carson, J.,
Açıkmeşe, B.,
and Leung, K.
Perception algorithms are ubiquitous in modern autonomy stacks, providing necessary environmental information to operate in the real world. Many of these algorithms depend on the visibility of keypoints, which must remain within the robot’s line-of-sight (LoS), for reliable operation. This paper tackles the challenge of maintaining LoS on such keypoints during robot movement. We propose a novel method that addresses these issues by ensuring applicability to various sensor footprints, adaptability to arbitrary nonlinear dynamics, and constant enforcement of LoS throughout the robot’s path. Through our experiments, we show that the proposed approach achieves significantly reduced LoS violation and runtime compared to existing state-of-the-art methods in several representative and challenging scenarios.
@inproceedings{HaynerCarsonEtAl2024,author={Hayner, C.~R. and Carson, J. and A\c{c}{\i}kme\c{s}e, B. and Leung, K.},title={Continuous-Time Line-of-Sight Constrained Trajectory Planning for 6-Degree of Freedom Systems},year={2024},arxiv={2410.22596},category={safetycritical},img={HaynerCarsonEtAl2024.png},selected={true},note={{preprint}},html={https://haynec.github.io/papers/los/},keywords={preprint},owner={karenl7}}
2023
Learning Autonomous Vehicle Safety Concepts from Demonstrations
Leung, K.,
Veer, S.,
Schmerling, E.,
and Pavone, M.
Evaluating the safety of an autonomous vehicle (AV) depends on the behavior of surrounding agents which can be heavily influenced by factors such as environmental context and informally-defined driving etiquette. A key challenge is in determining a minimum set of assumptions on what constitutes reasonable foreseeable behaviors of other road users for the development of AV safety models and techniques. In this paper, we propose a data-driven AV safety design methodology that first learns "reasonable" behavioral assumptions from data, and then synthesizes an AV safety concept using these learned behavioral assumptions. We borrow techniques from control theory, namely high order control barrier functions and Hamilton-Jacobi reachability, to provide inductive bias to aid interpretability, verifiability, and tractability of our approach. In our experiments, we learn an AV safety concept using demonstrations collected from a highway traffic-weaving scenario, compare our learned concept to existing baselines, and showcase its efficacy in evaluating real-world driving logs.
@inproceedings{LeungVeerEtAl2023,author={Leung, K. and Veer, S. and Schmerling, E. and Pavone, M.},booktitle={{American Control Conference}},title={Learning Autonomous Vehicle Safety Concepts from Demonstrations},year={2023},arxiv={2210.02761},category={structure},img={LeungVeerEtAl2022.png},selected={true},owner={karenl7}}
HALO: Hazard-Aware Landing Optimization for Autonomous Systems
Hayner, C. R.,
Buckner, S. C.,
Broyles, D.,
Madewell, E.,
Leung, K.,
and Açıkmeşe, B.
In Proc. IEEE Conf. on Robotics and Automation,
2023
With autonomous aerial vehicles enacting safety-critical missions, such as the Mars Science Laboratory Curiosity rover’s entry, descent, and landing on Mars, awareness and reasoning regarding potentially hazardous landing sites is paramount. This paper presents a coupled perception-planning solution which address the real-time hazard detection, optimal landing trajectory generation, and contingency planning challenges encountered when landing in uncertain environments. The perception and planning components are addressed by the proposed Hazard-Aware Landing Site Selection (HALSS) framework and Adaptive Deferred-Decision Trajectory Optimization (Adaptive-DDTO) algorithm respectively. The HALSS framework processes point clouds through a segmentation network to predict a binary safety map which is analyzed using the medial axis transform to efficiently identify circular, safe landing zones. The Adaptive-DDTO algorithm address the need for contingency planning during target failure scenarios through adaptively recomputed multi-target trajectory optimization. Overall, Adaptive-DDTO achieves 18.16% increase in terms of landing success rate and 0.4% decrease in cumulative control effort compared to its predecessor, DDTO, while computing near real-time solutions, when coupled with HALSS, in a simulated environment.
@inproceedings{HaynerBucknerEtAl2023,author={Hayner, C. R. and Buckner, S. C. and Broyles, D. and Madewell, E. and Leung, K. and A\c{c}{\i}kme\c{s}e, B.},booktitle={{Proc.\ IEEE Conf.\ on Robotics and Automation}},title={{HALO}: Hazard-Aware Landing Optimization for Autonomous Systems},year={2023},arxiv={2304.01583},category={safetycritical},img={HaynerBucknerEtAl2023.png},selected={true},owner={karenl7}}
Receding Horizon Planning with Rule Hierarchies for Autonomous Vehicles
Veer, S.,
Leung, K.,
Cosner, R.,
Chen, Y.,
and Pavone, M.
In Proc. IEEE Conf. on Robotics and Automation,
2023
Autonomous vehicles must often contend with conflicting planning requirements, e.g., safety and comfort could be at odds with each other if avoiding a collision calls for slamming the brakes. To resolve such conflicts, assigning importance ranking to rules (i.e., imposing a rule hierarchy) has been proposed, which, in turn, induces rankings on trajectories based on the importance of the rules they satisfy. On one hand, imposing rule hierarchies can enhance interpretability, but introduce combinatorial complexity to planning; while on the other hand, differentiable reward structures can be leveraged by modern gradient-based optimization tools, but are less interpretable and unintuitive to tune. In this paper, we present an approach to equivalently express rule hierarchies as differentiable reward structures amenable to modern gradient-based optimizers, thereby, achieving the best of both worlds. We achieve this by formulating rank-preserving reward functions that are monotonic in the rank of the trajectories induced by the rule hierarchy; i.e., higher ranked trajectories receive higher reward. Equipped with a rule hierarchy and its corresponding rank-preserving reward function, we develop a two-stage planner that can efficiently resolve conflicting planning requirements. We demonstrate that our approach can generate motion plans in 7-10 Hz for various challenging road navigation and intersection negotiation scenarios.
@inproceedings{VeerLeungEtAl2023,author={Veer, S. and Leung, K. and Cosner, R. and Chen, Y. and Pavone, M.},booktitle={{Proc.\ IEEE Conf.\ on Robotics and Automation}},title={Receding Horizon Planning with Rule Hierarchies for Autonomous Vehicles},year={2023},arxiv={2212.03323},category={safetycritical},img={VeerLeungEtAl2023.png},selected={true},owner={karenl7}}
Learning Responsibility Allocations for Safe Human-Robot Interaction with Applications to Autonomous Driving
Cosner, R.,
Chen, Y.,
Leung, K.,
and Pavone, M.
In Proc. IEEE Conf. on Robotics and Automation,
2023
Drivers have a responsibility to exercise reasonable care to avoid collision with other road users. This assumed responsibility allows interacting agents to maintain safety without explicit coordination. Thus to enable safe autonomous vehicle (AV) interactions, AVs must understand what their responsibilities are to maintain safety and how they affect the safety of nearby agents. In this work we seek to understand how responsibility is shared in multi-agent settings where an autonomous agent is interacting with human counterparts. We introduce Responsibility-Aware Control Barrier Functions (RA-CBFs) and present a method to learn responsibility allocations from data. By combining safety-critical control and learning-based techniques, RA-CBFs allow us to account for scene-dependent responsibility allocations and synthesize safe and efficient driving behaviors without making worst-case assumptions that typically result in overly-conservative behaviors. We test our framework using real-world driving data and demonstrate its efficacy as a tool for both safe control and forensic analysis of unsafe driving.
@inproceedings{CosnerChenEtAl2023,author={Cosner, R. and Chen, Y. and Leung, K. and Pavone, M.},booktitle={{Proc.\ IEEE Conf.\ on Robotics and Automation}},title={Learning Responsibility Allocations for Safe Human-Robot Interaction with Applications to Autonomous Driving},year={2023},arxiv={2303.03504},category={structure},img={CosnerChenEtAl2023.png},selected={true},owner={karenl7}}
Task-Aware Risk Estimation of Perception Failures for Autonomous Vehicles
Antonante, P.,
Veer, S.,
Leung, K.,
Weng, X.,
Carlone, L.,
and Pavone, M.
Safety and performance are key enablers for autonomous driving: on the one hand we want our autonomous vehicles (AVs) to be safe, while at the same time their performance (e.g., comfort or progression) is key to adoption. To effectively walk the tight-rope between safety and performance, AVs need to be risk-averse, but not entirely risk-avoidant. To facilitate safe-yet-performant driving, in this paper, we develop a task-aware risk estimator that assesses the risk a perception failure poses to the AV’s motion plan. If the failure has no bearing on the safety of the AV’s motion plan, then regardless of how egregious the perception failure is, our task-aware risk estimator considers the failure to have a low risk; on the other hand, if a seemingly benign perception failure severely impacts the motion plan, then our estimator considers it to have a high risk. In this paper, we propose a task-aware risk estimator to decide whether a safety maneuver needs to be triggered. To estimate the task-aware risk, first, we leverage the perception failure - detected by a perception monitor - to synthesize an alternative plausible model for the vehicle’s surroundings. The risk due to the perception failure is then formalized as the "relative" risk to the AV’s motion plan between the perceived and the alternative plausible scenario. We employ a statistical tool called copula, which models tail dependencies between distributions, to estimate this risk. The theoretical properties of the copula allow us to compute probably approximately correct (PAC) estimates of the risk. We evaluate our task-aware risk estimator using NuPlan and compare it with established baselines, showing that the proposed risk estimator achieves the best F1-score (doubling the score of the best baseline) and exhibits a good balance between recall and precision, i.e., a good balance of safety and performance.
@inproceedings{AntonanteVeerEtAl2023,author={Antonante, P. and Veer, S. and Leung, K. and Weng, X. and Carlone, L. and Pavone, M.},booktitle={{Robotics: Science and Systems}},title={Task-Aware Risk Estimation of Perception Failures for Autonomous Vehicles},year={2023},arxiv={2305.01870},category={safetycritical},img={AntonanteVeerEtAl2023.png},owner={karenl7}}
MISFIT-V: Misaligned Image Synthesis and Fusion using Information from Thermal and Visual
Detecting humans from airborne visual and thermal imagery is a fundamental challenge for Wilderness Search-and-Rescue (WiSAR) teams, who must perform this function accurately in the face of immense pressure. The ability to fuse these two sensor modalities can potentially reduce the cognitive load on human operators and/or improve the effectiveness of computer vision object detection models. However, the fusion task is particularly challenging in the context of WiSAR due to hardware limitations and extreme environmental factors. This work presents Misaligned Image Synthesis and Fusion using Information from Thermal and Visual (MISFIT-V), a novel two-pronged unsupervised deep learning approach that utilizes a Generative Adversarial Network (GAN) and a cross-attention mechanism to capture the most relevant features from each modality. Experimental results show MISFIT-V offers enhanced robustness against misalignment and poor lighting/thermal environmental conditions compared to existing visual-thermal image fusion methods.
@inproceedings{ChauhanRemyEtAl2023,author={Chauhan, A. and Remy, I. and Broyles, D. and Leung, K.},title={{MISFIT-V}: Misaligned Image Synthesis and Fusion using Information from Thermal and Visual},year={2023},arxiv={2309.13216},category={afsl},img={ChauhanRemyEtAl2023.png},note={(submitted)},keywords={preprint},owner={karenl7}}
Refining Obstacle Perception Safety Zones via Maneuver-Based Decomposition
Topan, S.,
Chen, Y.,
Schmerling, E.,
Leung, K.,
Nilsson, J.,
Cox, M.,
and Pavone, M.
A critical task for developing safe autonomous driving stacks is to determine whether an obstacle is safety-critical, i.e., poses an imminent threat to the autonomous vehicle. Our previous work showed that Hamilton Jacobi reachability theory can be applied to compute interaction-dynamics-aware perception safety zones that better inform an ego vehicle’s perception module which obstacles are considered safety-critical. For completeness, these zones are typically larger than absolutely necessary, forcing the perception module to pay attention to a larger collection of objects for the sake of conservatism. As an improvement, we propose a maneuver-based decomposition of our safety zones that leverages information about the ego maneuver to reduce the zone volume. In particular, we propose a "temporal convolution" operation that produces safety zones for specific ego maneuvers, thus limiting the ego’s behavior to reduce the size of the safety zones. We show with numerical experiments that maneuver-based zones are significantly smaller (up to 76% size reduction) than the baseline while maintaining completeness.
@inproceedings{TopanChenEtAl2023,author={Topan, S. and Chen, Y. and Schmerling, E. and Leung, K. and Nilsson, J. and Cox, M. and Pavone, M.},booktitle={{IEEE Intelligent Vehicles Symposium}},title={Refining Obstacle Perception Safety Zones via Maneuver-Based Decomposition},year={2023},arxiv={2308.06337},category={safetycritical},img={TopanChenEtAl2023.png},selected={true},owner={karenl7}}
Interpretable Trajectory Prediction for Autonomous Vehicles Via Counterfactual Responsibility
Hsu, K-C.,
Leung, K.,
Chen, Y.,
Fisac, J.,
and Pavone, M.
In IEEE/RSJ Int. Conf. on Intelligent Robots & Systems,
2023
The ability to anticipate surrounding agents’ behaviors is critical to enable safe and seamless autonomous vehicles (AVs). While phenomenological methods have successfully predicted future trajectories from scene context, these predictions lack interpretability. On the other hand, ontological approaches assume an underlying structure able to describe the interaction dynamics or agents’ internal decision processes. Still, they often suffer from poor scalability or cannot reflect diverse human behaviors. This work proposes an interpretability framework for a phenomenological method through responsibility evaluations. We formulate responsibility as a measure of how much an agent takes into account the welfare of other agents through counterfactual reasoning. Additionally, this framework abstracts the computed responsibility sequences into different responsibility levels and grounds these latent levels into reward functions. The proposed responsibility-based interpretability framework is modular and easily integrated into a wide range of prediction models. To demonstrate the utility of the proposed framework in providing added interpretability, we adapt an existing AV prediction model and perform a simulation study on a real-world nuScenes traffic dataset. Experimental results show that we can perform offline ex-post traffic analysis by incorporating the responsibility signal and rendering interpretable but accurate online trajectory predictions.
@inproceedings{HsuLeungEtAl2023,author={Hsu, K-C. and Leung, K. and Chen, Y. and Fisac, J. and Pavone, M.},booktitle={{IEEE/RSJ Int.\ Conf.\ on Intelligent Robots \& Systems}},title={Interpretable Trajectory Prediction for Autonomous Vehicles Via Counterfactual Responsibility},year={2023},category={structure},img={HsuLeungEtAl2023.png},owner={karenl7},paper={https://ieeexplore.ieee.org/document/10341712}}
2022
Backpropagation through signal temporal logic specifications: Infusing logical structure into gradient-based methods
This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics of STL provide a robustness metric, i.e., how much a signal satisfies or violates an STL specification. In this work, we devise a systematic methodology for translating STL robustness formulas into computation graphs. With this representation, and by leveraging off-the-shelf automatic differentiation tools, we are able to efficiently backpropagate through STL robustness formulas and hence enable a natural and easy-to-use integration of STL specifications with many gradient-based approaches used in robotics. Through a number of examples stemming from various robotics applications, we demonstrate that STLCG is versatile, computationally efficient, and capable of incorporating human-domain knowledge into the problem formulation.
@article{LeungArechigaEtAl2021,author={Leung, K. and Ar\'{e}chiga, N. and Pavone, M.},journal={{Int.\ Journal of Robotics Research}},title={Backpropagation through signal temporal logic specifications: Infusing logical structure into gradient-based methods},year={2022},arxiv={2008.00097},category={structure},img={LeungArechigaEtAl2021.png},selected={true}}
Towards the Unification and Data-Driven Synthesis of Autonomous Vehicle Safety Concepts
Leung, K.*,
Bajcsy, A.*,
Schmerling, E.,
and Pavone, M.
As safety-critical autonomous vehicles (AVs) will soon become pervasive in our society, a number of safety concepts for trusted AV deployment have been recently proposed throughout industry and academia. Yet, agreeing upon an "appropriate" safety concept is still an elusive task. In this paper, we advocate for the use of Hamilton Jacobi (HJ) reachability as a unifying mathematical framework for comparing existing safety concepts, and propose ways to expand its modeling premises in a data-driven fashion. Specifically, we show that (i) existing predominant safety concepts can be embedded in the HJ reachability framework, thereby enabling a common language for comparing and contrasting modeling assumptions, and (ii) HJ reachability can serve as an inductive bias to effectively reason, in a data-driven context, about two critical, yet often overlooked aspects of safety: responsibility and context-dependency.
@article{LeungBajcsyEtAl2022,author={Leung, K.* and Bajcsy, A.* and Schmerling, E. and Pavone, M.},journal={{{Available at }\url{https://arxiv.org/abs/2107.14412}}},title={Towards the Unification and Data-Driven Synthesis of Autonomous Vehicle Safety Concepts},year={2022},arxiv={2107.14412},category={structure},img={BajcsyLeungEtAl2021.png},selected={true},keywords={preprint}}
Semi-Supervised Trajectory-Feedback Controller Synthesis for Signal Temporal Logic Specifications
There are spatio-temporal rules that dictate how robots should operate in complex environments, e.g., road rules govern how (self-driving) vehicles should behave on the road. However, seamlessly incorporating such rules into a robot control policy remains challenging especially for real-time applications. In this work, given a desired spatio-temporal specification expressed in the Signal Temporal Logic (STL) language, we propose a semi-supervised controller synthesis technique that is attuned to human-like behaviors while satisfying desired STL specifications. Offline, we synthesize a trajectory-feedback neural network controller via an adversarial training scheme that summarizes past spatio-temporal behaviors when computing controls, and then online, we perform gradient steps to improve specification satisfaction. Central to the offline phase is an imitation-based regularization component that fosters better policy exploration and helps induce naturalistic human behaviors. Our experiments demonstrate that having imitation-based regularization leads to higher qualitative and quantitative performance compared to optimizing an STL objective only as done in prior work. We demonstrate the efficacy of our approach with an illustrative case study and show that our proposed controller outperforms a state-of-the-art shooting method in both performance and computation time.
@inproceedings{LeungPavone2022,author={Leung, K. and Pavone, M.},booktitle={{American Control Conference}},title={Semi-Supervised Trajectory-Feedback Controller Synthesis for Signal Temporal Logic Specifications},year={2022},arxiv={2202.01997},category={structure},img={LeungPavone2022.png}}
Interaction-Dynamics-Aware Perception Zones for Obstacle Detection Safety Evaluation
Topan, S.,
Leung, K.,
Chen, Y.,
Tupekar, P.,
Schmerling, E.,
Nilsson, J.,
Cox, M.,
and Pavone, M.
To enable safe autonomous vehicle (AV) operations, it is critical that an AV’s obstacle detection module can reliably detect obstacles that pose a safety threat (i.e., are safety-critical). It is therefore desirable that the evaluation metric for the perception system captures the safety-criticality of objects. Unfortunately, existing perception evaluation metrics tend to make strong assumptions about the objects and ignore the dynamic interactions between agents, and thus do not accurately capture the safety risks in reality. To address these shortcomings, we introduce an interaction-dynamics-aware obstacle detection evaluation metric by accounting for closed-loop dynamic interactions between an ego vehicle and obstacles in the scene. By borrowing existing theory from optimal control theory, namely Hamilton-Jacobi reachability, we present a computationally tractable method for constructing a "safety zone": a region in state space that defines where safety-critical obstacles lie for the purpose of defining safety metrics. Our proposed safety zone is mathematically complete, and can be easily computed to reflect a variety of safety requirements. Using an off-the-shelf detection algorithm from the nuScenes detection challenge leaderboard, we demonstrate that our approach is computationally lightweight, and can better capture safety-critical perception errors than a baseline approach.
@inproceedings{TopanLeungEtAl2022,author={Topan, S. and Leung, K. and Chen, Y. and Tupekar, P. and Schmerling, E. and Nilsson, J. and Cox, M. and Pavone, M.},booktitle={{IEEE Intelligent Vehicles Symposium}},title={Interaction-Dynamics-Aware Perception Zones for Obstacle Detection Safety Evaluation},year={2022},arxiv={2206.12471},category={safetycritical},img={TopanLeungEtAl2022.png},owner={karenl7}}
WiSARD: A Labeled Visual and Thermal Image Dataset for Wilderness Search and Rescue
Broyles, D.*,
Hayner, C.*,
and Leung, K.
In IEEE/RSJ Int. Conf. on Intelligent Robots & Systems,
2022
Sensor-equipped unoccupied aerial vehicles (UAVs) have the potential to help reduce search times and alleviate safety risks for first responders carrying out Wilderness Search and Rescue (WiSAR) operations, the process of finding and evacuating person(s) lost in wilderness areas. Unfortunately, visual sensors alone do not address the need for robustness across all the possible terrains, weather, and lighting conditions that WiSAR operations can be conducted in. The use of multi-modal sensors, specifically visual-thermal imagers, is critical in enabling WiSAR UAVs to perform in diverse operating conditions. However, due to the unique challenges posed by the wilderness context, existing dataset benchmarks are inadequate for developing vision-based algorithms for autonomous WiSAR UAVs. To this end, we present WiSARD, more than 56,000 labeled visual and thermal images collected from UAV flights in various terrains, seasons, weather, and lighting conditions. To the best of our knowledge, WiSARD is the first large-scale dataset collected with multi-modal sensors for autonomous WiSAR operations. We envision that our dataset will provide researchers with a diverse and challenging benchmark that can test the robustness of their algorithms when applied to real-world (life-saving) applications.Sensor-equipped unoccupied aerial vehicles (UAVs) have the potential to help reduce search times and alleviate safety risks for first responders carrying out Wilderness Search and Rescue (WiSAR) operations, the process of finding and evacuating person(s) lost in wilderness areas. Unfortunately, visual sensors alone do not address the need for robustness across all the possible terrains, weather, and lighting conditions that WiSAR operations can be conducted in. The use of multi-modal sensors, specifically visual-thermal imagers, is critical in enabling WiSAR UAVs to perform in diverse operating conditions. However, due to the unique challenges posed by the wilderness context, existing dataset benchmarks are inadequate for developing vision-based algorithms for autonomous WiSAR UAVs. To this end, we present WiSARD, more than 56,000 labeled visual and thermal images collected from UAV flights in various terrains, seasons, weather, and lighting conditions. To the best of our knowledge, WiSARD is the first large-scale dataset collected with multi-modal sensors for autonomous WiSAR operations. We envision that our dataset will provide researchers with a diverse and challenging benchmark that can test the robustness of their algorithms when applied to real-world (life-saving) applications.
@inproceedings{BroylesHaynerEtAl2022,author={Broyles, D.* and Hayner, C.* and Leung, K.},booktitle={{IEEE/RSJ Int.\ Conf.\ on Intelligent Robots \& Systems}},title={{WiSARD}: A Labeled Visual and Thermal Image Dataset for Wilderness Search and Rescue},year={2022},arxiv={2309.04453},category={afsl},img={BroylesHaynerEtAl2022.jpg},html={https://sites.google.com/uw.edu/wisard/},owner={karenl7}}
Task-Relevant Failure Detection for Trajectory Predictors in Autonomous Vehicles
Farid, A.,
Veer, S.,
Ivanovic, B.,
Leung, K.,
and Pavone, M
In modern autonomy stacks, prediction modules are paramount to planning motions in the presence of other mobile agents. However, failures in prediction modules can mislead the downstream planner into making unsafe decisions. Indeed, the high uncertainty inherent to the task of trajectory forecasting ensures that such mispredictions occur frequently. Motivated by the need to improve safety of autonomous vehicles without compromising on their performance, we develop a probabilistic run-time monitor that detects when a harmful prediction failure occurs, i.e., a task-relevant failure detector. We achieve this by propagating trajectory prediction errors to the planning cost to reason about their impact on the AV. Furthermore, our detector comes equipped with performance measures on the false-positive and the false-negative rate and allows for data-free calibration. In our experiments we compared our detector with various others and found that our detector has the highest area under the receiver operator characteristic curve.
@inproceedings{FaridVeerEtAl2022,author={Farid, A. and Veer, S. and Ivanovic, B. and Leung, K. and Pavone, M},booktitle={{Conf.\ on Robot Learning}},title={Task-Relevant Failure Detection for Trajectory Predictors in Autonomous Vehicles},year={2022},arxiv={2207.12380},category={safetycritical},img={FaridVeerEtAl2022.png},owner={karenl7}}
2021
Multimodal Deep Generative Models for Trajectory Prediction: A Conditional Variational Autoencoder Approach
Ivanovic, B.*,
Leung, K.*,
Schmerling, E.,
and Pavone, M.
Human behavior prediction models enable robots to anticipate how humans may react to their actions, and hence are instrumental to devising safe and proactive robot planning algorithms. However, modeling complex interaction dynamics and capturing the possibility of many possible outcomes in such interactive settings is very challenging, which has recently prompted the study of several different approaches. In this work, we provide a self-contained tutorial on a conditional variational autoencoder (CVAE) approach to human behavior prediction which, at its core, can produce a multimodal probability distribution over future human trajectories conditioned on past interactions and candidate robot future actions. Specifically, the goals of this tutorial paper are to review and build a taxonomy of state-of-the-art methods in human behavior prediction, from physics-based to purely data-driven methods, provide a rigorous yet easily accessible description of a data-driven, CVAE-based approach, highlight important design characteristics that make this an attractive model to use in the context of model-based planning for human-robot interactions, and provide important design considerations when using this class of models.
@article{IvanovicLeungEtAl2020,author={Ivanovic, B.* and Leung, K.* and Schmerling, E. and Pavone, M.},journal={{IEEE Robotics and Automation Letters}},number={2},pages={295--302},title={Multimodal Deep Generative Models for Trajectory Prediction: A Conditional Variational Autoencoder Approach},volume={6},arxiv={2008.03880},category={interaction},img={IvanovicLeungEtAl2020.jpg},selected={true},year={2021}}
Leveraging Neural Network Gradients within Trajectory Optimization for Proactive Human-Robot Interactions
Schaefer, S.,
Leung, K.,
Ivanovic, B.,
and Pavone, M.
In Proc. IEEE Conf. on Robotics and Automation,
2021
To achieve seamless human-robot interactions, robots need to intimately reason about complex interaction dynamics and future human behaviors within their motion planning process. However, there is a disconnect between state-of-the-art neural network-based human behavior models and robot motion planners—either the behavior models are limited in their consideration of downstream planning or a simplified behavior model is used to ensure tractability of the planning problem. In this work, we present a framework that fuses together the interpretability and flexibility of trajectory optimization (TO) with the predictive power of state-of-the-art human trajectory prediction models. In particular, we leverage gradient information from data-driven prediction models to explicitly reason about human-robot interaction dynamics within a gradient-based TO problem. We demonstrate the efficacy of our approach in a multi-agent scenario whereby a robot is required to safely and efficiently navigate through a crowd of up to ten pedestrians. We compare against a variety of planning methods, and show that by explicitly accounting for interaction dynamics within the planner, our method offers safer and more efficient behaviors, even yielding proactive and nuanced behaviors such as waiting for a pedestrian to pass before moving.
@inproceedings{SchaeferLeungEtAl2021,author={Schaefer, S. and Leung, K. and Ivanovic, B. and Pavone, M.},booktitle={{Proc.\ IEEE Conf.\ on Robotics and Automation}},title={Leveraging Neural Network Gradients within Trajectory Optimization for Proactive Human-Robot Interactions},year={2021},arxiv={2012.01027},category={interaction},img={SchaeferLeungEtAl2021.jpeg}}
2020
On Infusing Reachability-Based Safety Assurance within Planning Frameworks for Human-Robot Vehicle Interactions
Leung, K.,
Schmerling, E.,
Zhang, M.,
Chen, M.,
Talbot, J.,
Gerdes, J. C.,
and Pavone, M.
Action anticipation, intent prediction, and proactive behavior are all desirable characteristics for autonomous driving policies in interactive scenarios. Paramount, however, is ensuring safety on the road—a key challenge in doing so is accounting for uncertainty in human driver actions without unduly impacting planner performance. This paper introduces a minimally-interventional safety controller operating within an autonomous vehicle control stack with the role of ensuring collision-free interaction with an externally controlled (e.g., human-driven) counterpart while respecting static obstacles such as a road boundary wall. We leverage reachability analysis to construct a real-time (100Hz) controller that serves the dual role of (1) tracking an input trajectory from a higher-level planning algorithm using model predictive control, and (2) assuring safety through maintaining the availability of a collision-free escape maneuver as a persistent constraint regardless of whatever future actions the other car takes. A full-scale steer-by-wire platform is used to conduct traffic weaving experiments wherein two cars, initially side-by-side, must swap lanes in a limited amount of time and distance, emulating cars merging onto/off of a highway. We demonstrate that, with our control stack, the autonomous vehicle is able to avoid collision even when the other car defies the planner’s expectations and takes dangerous actions, either carelessly or with the intent to collide, and otherwise deviates minimally from the planned trajectory to the extent required to maintain safety.
@article{LeungSchmerlingEtAl2020,author={Leung, K. and Schmerling, E. and Zhang, M. and Chen, M. and Talbot, J. and Gerdes, J. C. and Pavone, M.},journal={{Int.\ Journal of Robotics Research}},pages={1326--1345},title={On Infusing Reachability-Based Safety Assurance within Planning Frameworks for Human-Robot Vehicle Interactions},volume={39},arxiv={2012.03390},category={interaction},img={LeungSchmerlingEtAl2020.png},selected={true},year={2020},issue={10--11}}
Infusing Reachability-Based Safety into Planning and Control for Multi-agent Interactions
Wang, X.*,
Leung, K.*,
and Pavone, M.
In IEEE/RSJ Int. Conf. on Intelligent Robots & Systems,
2020
Within a robot autonomy stack, the planner and controller are typically designed separately, and serve different purposes. As such, there is often a diffusion of responsibilities when it comes to ensuring safety for the robot. We propose that a planner and controller should share the same interpretation of safety but apply this knowledge in a different yet complementary way. To achieve this, we use Hamilton-Jacobi (HJ) reachability theory at the planning level to provide the robot planner with the foresight to avoid entering regions with possible inevitable collision. However, this alone does not guarantee safety. In conjunction with this HJ reachability-infused planner, we propose a minimally-interventional multi-agent safety-preserving controller also derived via HJ-reachability theory. The safety controller maintains safety for the robot without unduly impacting planner performance. We demonstrate the benefits of our proposed approach in a multi-agent highway scenario where a robot car is rewarded to navigate through traffic as fast as possible, and we show that our approach provides strong safety assurances yet achieves the highest performance compared to other safety controllers.
@inproceedings{WangLeungEtAl2020,author={Wang, X.* and Leung, K.* and Pavone, M.},booktitle={{IEEE/RSJ Int.\ Conf.\ on Intelligent Robots \& Systems}},title={Infusing Reachability-Based Safety into Planning and Control for Multi-agent Interactions},year={2020},arxiv={2008.00067},category={interaction},img={WangLeungEtAl2020.png}}
Back-propagation through signal temporal logic specifications: Infusing logical structure into gradient-based methods
Leung, K.,
Aréchiga, N.,
and Pavone, M.
In Workshop on Algorithmic Foundations of Robotics,
2020
This paper presents a technique, named stlcg, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. This provides a platform which enables the incorporation of logic-based specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics of STL provide a robustness metric, i.e., how much a signal satisfies or violates an STL specification. In this work we devise a systematic methodology for translating STL robustness formulas into computation graphs. With this representation, and by leveraging off-the-shelf auto-differentiation tools, we are able to back-propagate through STL robustness formulas and hence enable a natural and easy-to-use integration with many gradient-based approaches used in robotics. We demonstrate, through examples stemming from various robotics applications, that the technique is versatile, computationally efficient, and capable of injecting human-domain knowledge into the problem formulation.
@inproceedings{LeungArechigaEtAl2020,author={Leung, K. and Ar\'{e}chiga, N. and Pavone, M.},booktitle={{Workshop on Algorithmic Foundations of Robotics}},title={Back-propagation through signal temporal logic specifications: Infusing logical structure into gradient-based methods},year={2020},arxiv={2008.00097},category={structure},img={LeungArechigaEtAl2020.png}}
Interpretable Policies from Formally-Specified Temporal Properties
DeCastro, J.,
Leung, K.,
Aréchiga, N.,
and Pavone, M.
In Proc. IEEE Int. Conf. on Intelligent Transportation Systems,
2020
We present an approach for interpreting parameterized policies based on a formally-specified abstract description of the importance of certain behaviors or observed outcomes of a policy. The standard way to deploy data-driven policies usually involves sampling from the set of outcomes produced by the policy. Our approach leverages parametric signal temporal logic (pSTL) formulas to construct an interpretable view on the modeling parameters via a sequence of variational inference problems; one to solve for the pSTL parameters and another to construct a new parameterization satisfying the specification. We perform clustering using a finite set of examples, either real or simulated, and combine computational graph learning and normalizing flows to form a relationship between these parameters and pSTL formulas either derived by hand or inferred from data. We illustrate the utility of our approach to model selection for validation of the safety properties of an autonomous driving system, using a learned generative model of the surrounding agents.
@inproceedings{DeCastroLeungEtAl2020,author={DeCastro, J. and Leung, K. and Ar\'{e}chiga, N. and Pavone, M.},booktitle={{Proc.\ IEEE Int.\ Conf.\ on Intelligent Transportation Systems}},title={Interpretable Policies from Formally-Specified Temporal Properties},year={2020},category={structure},img={DeCastroLeungEtAl2020.png},pdf={papers/DeCastro.Leung.ea.ITSC20.pdf}}
2019
Backpropagation for Parametric STL
Leung, K.,
Aréchiga, N.,
and Pavone, M.
In IEEE Intelligent Vehicles Symposium: Workshop on Unsupervised Learning for Automated Driving,
2019
Signal Temporal Logic (STL) is an expressive language used to describe logical and temporal properties of signals, both continuous and discrete. Inferring STL formulas from behavior traces can provide powerful insights into complex systems. These insights can help system designers better understand and improve the systems they develop (e.g., long-term behaviors of time series data), yet this is a very challenging and often intractable problem. This work presents a method for evaluating STL formulas using computation graphs, hence bridging a connection between STL and many modern machine learning frameworks that depend on computation graphs, such as deep learning. We show that this approach is particularly effective for solving parameteric STL (pSTL) problems, the problem of parameter fitting for a given signal. We provide a relaxation technique that makes this method more tractable when solving general pSTL formulas. By using computation graphs, we can leverage the benefits and the computational prowess of modern day machine learning tools. Motivated by the problem of learning explanatory factors and safety assurance for complex cyber-physical systems, we demonstrate our proposed method on an autonomous driving case study.
@inproceedings{LeungArechigaEtAl2019,author={Leung, K. and Ar\'{e}chiga, N. and Pavone, M.},booktitle={{IEEE Intelligent Vehicles Symposium: Workshop on Unsupervised Learning for Automated Driving}},title={Backpropagation for Parametric {STL}},year={2019},category={structure},img={LeungArechigaEtAl2019.png},pdf={papers/Leung.Arechiga.ea.ULAD19.pdf}}
2018
Multimodal Probabilistic Model-Based Planning for Human-Robot Interaction
Schmerling, E.,
Leung, K.,
Vollprecht, W.,
and Pavone, M.
In Proc. IEEE Conf. on Robotics and Automation,
2018
This paper presents a method for constructing human-robot interaction policies in settings where multimodality, i.e., the possibility of multiple highly distinct futures, plays a critical role in decision making. We are motivated in this work by the example of traffic weaving, e.g., at highway onramps/offramps, where entering and exiting cars must swap lanes in a short distance — a challenging negotiation even for experienced drivers due to the inherent multimodal uncertainty of who will pass whom. Our approach is to learn multimodal probability distributions over future human actions from a dataset of human-human exemplars and perform real-time robot policy construction in the resulting environment model through massively parallel sampling of human responses to candidate robot action sequences. Direct learning of these distributions is made possible by recent advances in the theory of conditional variational autoencoders (CVAEs), whereby we learn action distributions simultaneously conditioned on the present interaction history, as well as candidate future robot actions in order to take into account response dynamics. We demonstrate the efficacy of this approach with a human-in-the-loop simulation of a traffic weaving scenario.
@inproceedings{SchmerlingLeungEtAl2018,author={Schmerling, E. and Leung, K. and Vollprecht, W. and Pavone, M.},booktitle={{Proc.\ IEEE Conf.\ on Robotics and Automation}},title={Multimodal Probabilistic Model-Based Planning for Human-Robot Interaction},year={2018},arxiv={1710.09483},category={interaction},img={SchmerlingLeungEtAl2018.png},selected={true}}
Generative Modeling of Multimodal Multi-Human Behavior
Ivanovic, B.,
Schmerling, E.,
Leung, K.,
and Pavone, M.
In IEEE/RSJ Int. Conf. on Intelligent Robots & Systems,
2018
This work presents a methodology for modeling and predicting human behavior in settings with N humans interacting in highly multimodal scenarios (i.e. where there are many possible highly-distinct futures). A motivating example includes robots interacting with humans in crowded environments, such as self-driving cars operating alongside human-driven vehicles or human-robot collaborative bin packing in a warehouse. Our approach to model human behavior in such uncertain environments is to model humans in the scene as nodes in a graphical model, with edges encoding relationships between them. For each human, we learn a multimodal probability distribution over future actions from a dataset of multi-human interactions. Learning such distributions is made possible by recent advances in the theory of conditional variational autoencoders and deep learning approximations of probabilistic graphical models. Specifically, we learn action distributions conditioned on interaction history, neighboring human behavior, and candidate future agent behavior in order to take into account response dynamics. We demonstrate the performance of such a modeling approach in modeling basketball player trajectories, a highly multimodal, multi-human scenario which serves as a proxy for many robotic applications.
@inproceedings{IvanovicSchmerlingEtAl2018,author={Ivanovic, B. and Schmerling, E. and Leung, K. and Pavone, M.},booktitle={{IEEE/RSJ Int.\ Conf.\ on Intelligent Robots \& Systems}},title={Generative Modeling of Multimodal Multi-Human Behavior},year={2018},arxiv={1803.02015},category={interaction},img={IvanovicSchmerlingEtAl2018.png}}
On Infusing Reachability-Based Safety Assurance within Probabilistic Planning Frameworks for Human-Robot Vehicle Interactions
Leung, K.*,
Schmerling, E.*,
Chen, M.,
Talbot, J.,
Gerdes, J. C.,
and Pavone, M.
Action anticipation, intent prediction, and proactive behavior are all desirable characteristics for autonomous driving policies in interactive scenarios. Paramount, however, is ensuring safety on the road — a key challenge in doing so is accounting for uncertainty in human driver actions without unduly impacting planner performance. This paper introduces a minimally-interventional safety controller operating within an autonomous vehicle control stack with the role of ensuring collision-free interaction with an externally controlled (e.g., human-driven) counterpart. We leverage reachability analysis to construct a real-time (100Hz) controller that serves the dual role of (1) tracking an input trajectory from a higher-level planning algorithm using model predictive control, and (2) assuring safety through maintaining the availability of a collision-free escape maneuver as a persistent constraint regardless of whatever future actions the other car takes. A full-scale steer-by-wire platform is used to conduct traffic weaving experiments wherein the two cars, initially side-by-side, must swap lanes in a limited amount of time and distance, emulating cars merging onto/off of a highway. We demonstrate that, with our control stack, the autonomous vehicle is able to avoid collision even when the other car defies the planner’s expectations and takes dangerous actions, either carelessly or with the intent to collide, and otherwise deviates minimally from the planned trajectory to the extent required to maintain safety.
@inproceedings{LeungSchmerlingEtAl2018,author={Leung, K.* and Schmerling, E.* and Chen, M. and Talbot, J. and Gerdes, J. C. and Pavone, M.},booktitle={{Int.\ Symp.\ on Experimental Robotics}},title={On Infusing Reachability-Based Safety Assurance within Probabilistic Planning Frameworks for Human-Robot Vehicle Interactions},year={2018},arxiv={1812.11315},category={interaction},img={LeungSchmerlingEtAl2018.png}}
2017
Nonlinear Stabilization via Control Contraction Metrics: A Pseudospectral Approach for Computing Geodesics
Real-time nonlinear stabilization techniques are often limited by inefficient or intractable online and/or offline computations, or a lack guarantee for global stability. In this paper, we explore the use of Control Contraction Metrics (CCM) for nonlinear stabilization because it offers tractable offline computations that give formal guarantees for global stability. We provide a method to solve the associated online computation for a CCM controller - a pseudospectral method to find a geodesic. Through a case study of a stiff nonlinear system, we highlight two key benefits: (i) using CCM for nonlinear stabilization and (ii) rapid online computations amenable to real-time implementation. We compare the performance of a CCM controller with other popular feedback control techniques, namely the Linear Quadratic Regulator (LQR) and Nonlinear Model Predictive Control (NMPC). We show that a CCM controller using a pseudospectral approach for online computations is a middle ground between the simplicity of LQR and stability guarantees for NMPC.
@inproceedings{LeungManchester2017,author={Leung, K. and Manchester, I. R.},booktitle={{American Control Conference}},title={Nonlinear Stabilization via Control Contraction Metrics: A Pseudospectral Approach for Computing Geodesics},year={2017},arxiv={1607.04340},img={LeungManchester2017.png}}
2016
The Diver with a Rotor
Bharadwaj, S.,
Duignan, N.,
Dullin, H.,
Leung, K.,
and Tong, W.
We present and analyse a simple model for the twisting somersault. The model is a rigid body with a rotor attached which can be switched on and off. This makes it simple enough to devise explicit analytical formulas whilst still maintaining sufficient complexity to preserve the shape-changing dynamics essential for twisting somersaults in springboard and platform diving. With ‘rotor on’ and with ‘rotor off’ the corresponding Euler-type equations can be solved, and the essential quantities characterising the dynamics, such as the periods and rotation numbers, can be computed in terms of complete elliptic integrals. Thus we arrive at explicit formulas for how to achieve a dive with m somersaults and n twists in a given total time. This can be thought of as a special case of a geometric phase formula due to Cabrera 2007.
@article{LeungDullinEtAl2016,author={Bharadwaj, S. and Duignan, N. and Dullin, H. and Leung, K. and Tong, W.},journal={{Indagationes Mathematicae}},number={5},pages={1147--1161},title={The Diver with a Rotor},volume={27},arxiv={1510.02978},img={LeungDullinEtAl2016.png},year={2016}}
CoBL-Diffusion: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov FunctionsIn Proc. IEEE Conf. on Robotics and Automation: Long-term Human Motion Prediction Workshop, 2024
