Constrained Iterative Linear Quadratic Regulator (CILQR), a variant of ILQR, has been recently proposed for motion planning problems of autonomous vehicles to deal with constraints such as obstacle avoidance and reference tracking. However, the previous work considers either deterministic trajectories or persistent prediction for target dynamical obstacles. The other drawback is lack of generality - it requires manual weight tuning for different scenarios. In this paper, two significant improvements are achieved. Firstly, a two-stage uncertainty-aware prediction is proposed. The short-term prediction with safety guarantee based on reachability analysis is responsible for dealing with extreme maneuvers conducted by target vehicles. The long-term prediction leveraging an adaptive least square filter preserves the long-term optimality of the planned trajectory since using reachability only for long-term prediction is too pessimistic and makes the planner over-conservative. Secondly, to allow a wider coverage over different scenarios and to avoid tedious parameter tuning case by case, this paper designs a scenario-based analytical function taking the states from the ego vehicle and the target vehicle as input, and carrying weights of a cost function as output. It allows the ego vehicle to execute multiple behaviors (such as lane-keeping and overtaking) under a single planner. We demonstrate safety, effectiveness, and real-time performance of the proposed planner in simulations.
The Hong Kong University of Science and Technology（香港科技大学）
Developments in cooperative trajectory planning of connected autonomous vehicles (CAVs) have gathered considerable momentum and research attention. Generally, such problems present strong non-linearity and non-convexity, rendering great difficulties in finding the optimal solution. Existing methods typically suffer from low computational efficiency, and this hinders the appropriate applications in large-scale scenarios involving an increasing number of vehicles. To tackle this problem, we propose a novel decentralized iterative linear quadratic regulator (iLQR) algorithm by leveraging the dual…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Raytheon BBN Technologies（雷神BBN技术公司）
In this work, we develop a scalable, local trajectory optimization algorithm that enables robots to interact with other robots. It has been shown that agents' interactions can be successfully captured in game-theoretic formulations, where the interaction outcome can be best modeled via the equilibria of the underlying dynamic game. However, it is typically challenging to compute equilibria of dynamic games as it involves simultaneously solving a set of coupled optimal control problems. Existing solvers operate in a centralized fashion and do not scale up tractably to multiple interacting agent…
Many robotic applications involve interactions between multiple agents where an agent's decisions affect the behavior of other agents. Such behaviors can be captured by the equilibria of differential games which provide an expressive framework for modeling the agents' mutual influence. However, finding the equilibria of differential games is in general challenging as it involves solving a set of coupled optimal control problems. In this work, we propose to leverage the special structure of multi-agent interactions to generate interactive trajectories by simply solving a single optimal control …
Trajectory optimization is a popular strategy for planning trajectories for robotic systems. However, many robotic tasks require changing contact conditions, which is difficult due to the hybrid nature of the dynamics. The optimal sequence and timing of these modes are typically not known ahead of time. In this work, we extend the Iterative Linear Quadratic Regulator (iLQR) method to a class of piecewise smooth hybrid dynamical systems by allowing for changing hybrid modes in the forward pass, using the saltation matrix to update the gradient information in the backwards pass, and using a refe…
Tencent Technology (Beijing) Company Limited（腾讯科技（北京）有限公司）
Collision avoidance is one of the most challenging tasks people need to consider for developing the self-driving technology. In this paper we propose a new spatiotemporal motion planning algorithm that efficiently solves a constrained nonlinear optimal control problem using the iterative linear quadratic regulator (iLQR), which takes into account the uncertain driving behaviors of the traffic vehicles and minimizes the collision risks between the self-driving vehicle (referred to as the "ego" vehicle) and the traffic vehicles such that the ego vehicle is able to maintain sufficiently large dis…
Katholieke Universiteit Leuven（鲁汶天主教大学）；University of Melbourne（墨尔本大学）
We propose a safety-guaranteed planning and control framework for unmanned surface vessels (USVs), using Gaussian processes (GPs) to learn uncertainties. The uncertainties encountered by USVs, including external disturbances and model mismatches, are potentially state-dependent, time-varying, and hard to capture with constant models. GP is a powerful learning-based tool that can be integrated with a model-based planning and control framework, which employs a Hamilton-Jacobi differential game formulation. Such a combination yields less conservative trajectories and safety-guaranteeing control s…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Autonomous robots that are capable of operating safely in the presence of imperfect model knowledge or external disturbances are vital in safety-critical applications. In this paper, we present a planner-agnostic framework to design and certify safe tubes around desired trajectories that the robot is always guaranteed to remain inside of. By leveraging recent results in contraction analysis and $\mathcal{L}_1$-adaptive control we synthesize an architecture that induces safe tubes for nonlinear systems with state and time-varying uncertainties. We demonstrate with a few illustrative examples ho…
This paper presents a new trajectory planning method for multiple quadrotors in obstacle-dense environments. We suggest a relative safe flight corridor (RSFC) to model safe region between a pair of agents, and it is used to generate linear constraints for inter-collision avoidance by utilizing the convex hull property of relative Bernstein polynomial. Our approach employs a graph-based multi-agent pathfinding algorithm to generate an initial trajectory, which is used to construct a safe flight corridor (SFC) and RSFC. We express the trajectory as a piecewise Bernstein polynomial and formulate …
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
Consider a robot operating in an uncertain environment with stochastic, dynamic obstacles. Despite the clear benefits for trajectory optimization, it is often hard to keep track of each obstacle at every time step due to sensing and hardware limitations. We introduce the Safely motion planner, a receding-horizon control framework, that simultaneously synthesizes both a trajectory for the robot to follow as well as a sensor selection strategy that prescribes trajectory-relevant obstacles to measure at each time step while respecting the sensing constraints of the robot. We perform the motion pl…
Nanyang Technological University（南洋理工大学）；New York University（纽约大学）；University of British Columbia（不列颠哥伦比亚大学）；Harvard University（哈佛大学）
In this paper, we study a navigation problem where a mobile robot needs to locate a mmWave wireless signal. Using the directionality properties of the signal, we propose an estimation and path planning algorithm that can efficiently navigate in cluttered indoor environments. We formulate Extended Kalman filters for emitter location estimation in cases where the signal is received in line-of-sight or after reflections. We then propose to plan motion trajectories based on belief-space dynamics in order to minimize the uncertainty of the position estimates. The associated non-linear optimization …
We present the design of a motion planning algorithm that ensures safety for an autonomous vehicle. In particular, we consider a multimodal distribution over uncertainties; for example, the uncertain predictions of future trajectories of surrounding vehicles reflect discrete decisions, such as turning or going straight at intersections. We develop a computationally efficient, scenario-based approach that solves the motion planning problem with high confidence given a quantifiable number of samples from the multimodal distribution. Our approach is based on two preprocessing steps, which 1) sepa…
RTD-RAX: Fast, Safe Trajectory Planning for Systems under Unknown Disturbances
Georgia Institute of Technology（佐治亚理工学院）；School of Electrical and Computer Engineering（电子与计算机工程学院）；School of Mechanical Engineering（机械工程学院）；School of Civil and Environmental Engineering（土木与环境工程学院）
Peking University（北京大学）；College of Engineering, Peking University（北京大学工学院）
This paper addresses the online motion planning problem of mobile robots under complex high-level tasks. The robot motion is modeled as an uncertain Markov Decision Process (MDP) due to limited initial knowledge, while the task is specified as Linear Temporal Logic (LTL) formulas. The proposed framework enables the robot to explore and update the system model in a Bayesian way, while simultaneously optimizing the asymptotic costs of satisfying the complex temporal task. Theoretical guarantees are provided for the synthesized outgoing policy and safety policy. More importantly, instead of greed…
Seoul National University（首尔大学）；Automation and Systems Research Institute（自动化与系统研究所）
This paper presents a new online multi-agent trajectory planning algorithm that guarantees to generate safe, dynamically feasible trajectories in a cluttered environment. The proposed algorithm utilizes a linear safe corridor (LSC) to formulate the distributed trajectory optimization problem with only feasible constraints, so it does not resort to slack variables or soft constraints to avoid optimization failure. We adopt a priority-based goal planning method to prevent the deadlock without an additional procedure to decide which robot to yield. The proposed algorithm can compute the trajector…
Control Barrier Functions (CBF) are widely used to enforce the safety-critical constraints on nonlinear systems. Recently, these functions are being incorporated into a path planning framework to design safety-critical path planners. However, these methods fall short of providing a realistic path considering both the algorithm's run-time complexity and enforcement of the safety-critical constraints. This paper proposes a novel motion planning approach using the well-known Rapidly Exploring Random Trees (RRT) algorithm that enforces both CBF and the robot Kinodynamic constraints to generate a s…
Istanbul Technical University（伊斯坦布尔理工大学）；Turkish-German University（土耳其-德国大学）
We investigate how to utilize predictive models for selecting appropriate motion planning strategies based on perception uncertainty estimation for agile unmanned aerial vehicle (UAV) navigation tasks. Although there are variety of motion planning and perception algorithms for such tasks, the impact of perception uncertainty is not explicitly handled in many of the current motion algorithms, which leads to performance loss in real-life scenarios where the measurement are often noisy due to external disturbances. We develop a novel framework for embedding perception uncertainty to high level mo…
Istituto di Sistemi e Tecnologie Industriali Intelligenti per il Manifatturiero Avanzato, Consiglio Nazionale delle Ricerche（意大利国家研究委员会先进制造智能工业系统与技术研究所）；University of Brescia（布雷西亚大学）
Human awareness in robot motion planning is crucial for seamless interaction with humans. Many existing techniques slow down, stop, or change the robot's trajectory locally to avoid collisions with humans. Although using the information on the human's state in the path planning phase could reduce future interference with the human's movements and make safety stops less frequent, such an approach is less widespread. This paper proposes a novel approach to embedding a human model in the robot's path planner. The method explicitly addresses the problem of minimizing the path execution time, inclu…
University of California San Diego（加州大学圣地亚哥分校）；San Diego State University（圣地亚哥州立大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Safety is a critical concern for the success of urban air mobility, especially in dynamic and uncertain environments. This paper proposes a path planning algorithm based on RRT in conjunction with chance constraints in the presence of uncertain obstacles. The chance-constrained formulation for Gaussian distributed obstacles is developed by converting the probabilistic constraints to deterministic constraints in terms of distribution parameters. The probabilistic feasible region at every time step can be established through the simulation of the system state and the evaluation of convex constra…
Otto von Guericke University（奥托·冯·格里克大学）；German Aerospace Center (DLR)（德国航空航天中心（DLR））；Technical University of Darmstadt（达姆施塔特工业大学）
Planning and control for autonomous vehicles usually are hierarchical separated. However, increasing performance demands and operating in highly dynamic environments requires an frequent re-evaluation of the planning and tight integration of control and planning to guarantee safety. We propose an integrated hierarchical predictive control and planning approach to tackle this challenge. Planner and controller are based on the repeated solution of moving horizon optimal control problems. The planner can choose different low-layer controller modes for increased flexibility and performance instead…
Safety guarantees in motion planning for autonomous driving typically involve certifying the trajectory to be collision-free under any motion of the uncontrollable participants in the environment, such as the human-driven vehicles on the road. As a result they usually employ a conservative bound on the behavior of such participants, such as reachability analysis. We point out that planning trajectories to rigorously avoid the entirety of the reachable regions is unnecessary and too restrictive, because observing the environment in the future will allow us to prune away most of them; disregardi…
Motion planning in environments with multiple agents is critical to many important autonomous applications such as autonomous vehicles and assistive robots. This paper considers the problem of motion planning, where the controlled agent shares the environment with multiple uncontrolled agents. First, a predictive model of the uncontrolled agents is trained to predict all possible trajectories within a short horizon based on the scenario. The prediction is then fed to a motion planning module based on model predictive control. We proved generalization bound for the predictive model using three …
We present a method for learning to satisfy uncertain constraints from demonstrations. Our method uses robust optimization to obtain a belief over the potentially infinite set of possible constraints consistent with the demonstrations, and then uses this belief to plan trajectories that trade off performance with satisfying the possible constraints. We use these trajectories in a closed-loop policy that executes and replans using belief updates, which incorporate data gathered during execution. We derive guarantees on the accuracy of our constraint belief and probabilistic guarantees on plan s…
ETH Zurich（苏黎世联邦理工学院）；Katholieke Universiteit Leuven（鲁汶大学）
This paper presents a game-theoretic path-following formulation where the opponent is an adversary road model. This formulation allows us to compute safe sets using tools from viability theory, that can be used as terminal constraints in an optimization-based motion planner. Based on the adversary road model, we first derive an analytical discriminating domain, which even allows guaranteeing safety in the case when steering rate constraints are considered. Second, we compute the discriminating kernel and show that the output of the gridding based algorithm can be accurately approximated by a f…
Massachusetts Institute of Technology（麻省理工学院）；Ford Motor Company（福特汽车公司）
Density of the reachable states can help understand the risk of safety-critical systems, especially in situations when worst-case reachability is too conservative. Recent work provides a data-driven approach to compute the density distribution of autonomous systems' forward reachable states online. In this paper, we study the use of such approach in combination with model predictive control for verifiable safe path planning under uncertainties. We first use the learned density distribution to compute the risk of collision online. If such risk exceeds the acceptable threshold, our method will p…
The empirical success of derivative-free methods in reinforcement learning for planning through contact seems at odds with the perceived fragility of classical gradient-based optimization methods in these domains. What is causing this gap, and how might we use the answer to improve gradient-based methods? We believe a stochastic formulation of dynamics is one crucial ingredient. We use tools from randomized smoothing to analyze sampling-based approximations of the gradient, and formalize such approximations through the gradient bundle. We show that using the gradient bundle in lieu of the grad…
Efficient and Real-Time Motion Planning for Robotics Using Projection-Based Optimization
Department of Control Science and Engineering, Zhejiang University（控制科学与工程系，浙江大学）；Swiss Cobotics Competence Center（瑞士协作机器人能力建设中心）；Idiap Research Institute（Idiap研究机构）；EPFL（瑞士联邦理工学院）
Manipal Institute of Technology（马尼帕尔理工学院）；Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）
Motion Planning under uncertainty is critical for safe self-driving. In this paper, we propose a unified obstacle avoidance framework that deals with 1) uncertainty in ego-vehicle motion; and 2) prediction uncertainty of dynamic obstacles from environment. A two-stage traffic participant trajectory predictor comprising short-term and long-term prediction is used in the planning layer to generate safe but not over-conservative trajectories for the ego vehicle. The prediction module cooperates well with existing planning approaches. Our work showcases its effectiveness in a Frenet frame planner.…
Lattice-based motion planning is a hybrid planning method where a plan made up of discrete actions simultaneously is a physically feasible trajectory. The planning takes both discrete and continuous aspects into account, for example action pre-conditions and collision-free action-duration in the configuration space. Safe motion planing rely on well-calibrated safety-margins for collision checking. The trajectory tracking controller must further be able to reliably execute the motions within this safety margin for the execution to be safe. In this work we are concerned with introspective learni…
This paper reports on developing an integrated framework for safety-aware informative motion planning suitable for legged robots. The information-gathering planner takes a dense stochastic map of the environment into account, while safety constraints are enforced via Control Barrier Functions (CBFs). The planner is based on the Incrementally-exploring Information Gathering (IIG) algorithm and allows closed-loop kinodynamic node expansion using a Model Predictive Control (MPC) formalism. Robotic exploration and information gathering problems are inherently path-dependent problems. That is, the …
Autonomous vehicles need to plan at the task level to compute a sequence of symbolic actions, such as merging left and turning right, to fulfill people's service requests, where efficiency is the main concern. At the same time, the vehicles must compute continuous trajectories to perform actions at the motion level, where safety is the most important. Task-motion planning in autonomous driving faces the problem of maximizing task-level efficiency while ensuring motion-level safety. To this end, we develop algorithm Task-Motion Planning for Urban Driving (TMPUD) that, for the first time, enable…
We present a method to solve planning problems involving sequential decision making in unpredictable environments while accomplishing a high level task specification expressed using the formalism of linear temporal logic. Our method improves the state of the art by introducing a pruning step that preserves correctness while significantly reducing the time needed to compute an optimal policy. Our theoretical contribution is coupled with simulations substantiating the value of the proposed method.
Cornell Tech（康奈尔理工学院）；University of Pennsylvania（宾夕法尼亚大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
In this paper, we introduce a new probabilistically safe local steering primitive for sampling-based motion planning in complex high-dimensional configuration spaces. Our local steering procedure is based on a new notion of a convex probabilistically safe corridor that is constructed around a configuration using tangent hyperplanes of confidence ellipsoids of Gaussian mixture models learned from prior collision history. Accordingly, we propose to expand a random motion planning graph towards a sample goal using its projection onto probabilistically safe corridors, which efficiently exploits th…
