HT-LIP Model based Robust Control of Quadrupedal Robot Locomotion under Unknown Vertical Ground Motion

This paper presents a hierarchical control framework that enables robust quadrupedal locomotion on a dynamic rigid surface (DRS) with general and unknown vertical motions. The key novelty of the framework lies in its higher layer, which is a discrete-time, provably stabilizing footstep controller. The basis of the footstep controller is a new hybrid, time-varying, linear inverted pendulum (HT-LIP) model that is low-dimensional and accurately captures the essential robot dynamics during DRS locomotion. A new set of sufficient stability conditions are then derived to directly guide the controller design for ensuring the asymptotic stability of the HT-LIP model under general, unknown, vertical DRS motions. Further, the footstep controller is cast as a computationally efficient quadratic program that incorporates the proposed HT-LIP model and stability conditions. The middle layer takes the desired footstep locations generated by the higher layer as input to produce kinematically feasible full-body reference trajectories, which are then accurately tracked by a lower-layer torque controller. Hardware experiments on a Unitree Go1 quadrupedal robot confirm the robustness of the proposed framework under various unknown, aperiodic, vertical DRS motions and uncertainties (e.g., slippery and uneven surfaces, solid and liquid loads, and sudden pushes).

Driving Everywhere with Large Language Model Policy Adaptation

Adapting driving behavior to new environments, customs, and laws is a long-standing problem in autonomous driving, precluding the widespread deployment of autonomous vehicles (AVs). In this paper, we present LLaDA, a simple yet powerful tool that enables human drivers and autonomous vehicles alike to drive everywhere by adapting their tasks and motion plans to traffic rules in new locations. LLaDA achieves this by leveraging the impressive zero-shot generalizability of large language models (LLMs) in interpreting the traffic rules in the local driver handbook. Through an extensive user study, we show that LLaDA's instructions are useful in disambiguating in-the-wild unexpected situations. We also demonstrate LLaDA's ability to adapt AV motion planning policies in real-world datasets; LLaDA outperforms baseline planning approaches on all our metrics. Please check our website for more details: https://boyiliee.github.io/llada.

PAC-Bayes Generalization Certificates for Learned Inductive Conformal Prediction

Inductive Conformal Prediction (ICP) provides a practical and effective approach for equipping deep learning models with uncertainty estimates in the form of set-valued predictions which are guaranteed to contain the ground truth with high probability. Despite the appeal of this coverage guarantee, these sets may not be efficient: the size and contents of the prediction sets are not directly controlled, and instead depend on the underlying model and choice of score function. To remedy this, recent work has proposed learning model and score function parameters using data to directly optimize the efficiency of the ICP prediction sets. While appealing, the generalization theory for such an approach is lacking: direct optimization of empirical efficiency may yield prediction sets that are either no longer efficient on test data, or no longer obtain the required coverage on test data. In this work, we use PAC-Bayes theory to obtain generalization bounds on both the coverage and the efficiency of set-valued predictors which can be directly optimized to maximize efficiency while satisfying a desired test coverage. In contrast to prior work, our framework allows us to utilize the entire calibration dataset to learn the parameters of the model and score function, instead of requiring a separate hold-out set for obtaining test-time coverage guarantees. We leverage these theoretical results to provide a practical algorithm for using calibration data to simultaneously fine-tune the parameters of a model and score function while guaranteeing test-time coverage and efficiency of the resulting prediction sets. We evaluate the approach on regression and classification tasks, and outperform baselines calibrated using a Hoeffding bound-based PAC guarantee on ICP, especially in the low-data regime.

Interactive Motion Planning for Autonomous Vehicles with Joint Optimization

In highly interactive driving scenarios, the actions of one agent greatly influences those of its neighbors. Planning safe motions for autonomous vehicles in such interactive environments, therefore, requires reasoning about the impact of the ego's intended motion plan on nearby agents' behavior. Deep-learning-based models have recently achieved great success in trajectory prediction and many models in the literature allow for ego-conditioned prediction. However, leveraging ego-conditioned prediction remains challenging in downstream planning due to the complex nature of neural networks, limiting the planner structure to simple ones, e.g., sampling-based planner. Despite their ability to generate fine-grained high-quality motion plans, it is difficult for gradient-based planning algorithms, such as model predictive control (MPC), to leverage ego-conditioned prediction due to their iterative nature and need for gradient. We present Interactive Joint Planning (IJP) that bridges MPC with learned prediction models in a computationally scalable manner to provide us the best of both the worlds. In particular, IJP jointly optimizes over the behavior of the ego and the surrounding agents and leverages deep-learned prediction models as prediction priors that the join trajectory optimization tries to stay close to. Furthermore, by leveraging homotopy classes, our joint optimizer searches over diverse motion plans to avoid getting stuck at local minima. Closed-loop simulation result shows that IJP significantly outperforms the baselines that are either without joint optimization or running sampling-based planning.

Multi-Predictor Fusion: Combining Learning-based and Rule-based Trajectory Predictors

Trajectory prediction modules are key enablers for safe and efficient planning of autonomous vehicles (AVs), particularly in highly interactive traffic scenarios. Recently, learning-based trajectory predictors have experienced considerable success in providing state-of-the-art performance due to their ability to learn multimodal behaviors of other agents from data. In this paper, we present an algorithm called multi-predictor fusion (MPF) that augments the performance of learning-based predictors by imbuing them with motion planners that are tasked with satisfying logic-based rules. MPF probabilistically combines learning- and rule-based predictors by mixing trajectories from both standalone predictors in accordance with a belief distribution that reflects the online performance of each predictor. In our results, we show that MPF outperforms the two standalone predictors on various metrics and delivers the most consistent performance.

Task-Aware Risk Estimation of Perception Failures for Autonomous Vehicles

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.

Reactive Gait Composition with Stability: Dynamic Walking amidst Static and Moving Obstacles

This paper presents a modular approach to motion planning with provable stability guarantees for robots that move through changing environments via periodic locomotion behaviors. We focus on dynamic walkers as a paradigm for such systems, although the tools developed in this paper can be used to support general compositional approaches to robot motion planning with Dynamic Movement Primitives (DMPs). Our approach ensures a priori that the suggested plan can be stably executed. This is achieved by formulating the planning process as a Switching System with Multiple Equilibria (SSME) and proving that the system's evolution remains within explicitly characterized trapping regions in the state space under suitable constraints on the frequency of switching among the DMPs. These conditions effectively encapsulate the low-level stability limitations in a form that can be easily communicated to the planner to guarantee that the suggested plan is compatible with the robot's dynamics. Furthermore, we show how the available primitives can be safely composed online in a receding horizon manner to enable the robot to react to moving obstacles. The proposed framework is applied on 3D bipedal walking models under common modeling assumptions, and offers a modular approach towards stably integrating readily available low-level locomotion control and high-level planning methods.

Real-Time Walking Pattern Generation of Quadrupedal Dynamic-Surface Locomotion based on a Linear Time-Varying Pendulum Model

This study introduces an analytically tractable and computationally efficient model of the legged robot dynamics associated with locomotion on a dynamic rigid surface (DRS), and develops a real-time motion planner based on the proposed model and its analytical solution. This study first theoretically extends the classical linear inverted pendulum (LIP) model from legged locomotion on a static surface to DRS locomotion, by relaxing the LIP's underlying assumption that the surface is static. The resulting model, which we call "DRS-LIP", is explicitly time-varying. After converting the DRS-LIP into Mathieu's equation, an approximate analytical solution of the DRS-LIP is obtained, which is reasonably accurate with a low computational cost. Furthermore, to illustrate the practical uses of the analytical results, they are exploited to develop a hierarchical motion planner that efficiently generates physically feasible trajectories for DRS locomotion. Finally, the effectiveness of the proposed theoretical results and motion planner is demonstrated both through PyBullet simulations and experimentally on a Laikago quadrupedal robot that walks on a rocking treadmill. The videos of simulations and hardware experiments are available at https://youtu.be/u2Q_u2pR99c.

Receding Horizon Planning with Rule Hierarchies for Autonomous Vehicles

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.