Towards Provably Not-at-Fault Control of Autonomous Robots in Arbitrary Dynamic Environments

As autonomous robots increasingly become part of daily life, they will often encounter dynamic environments while only having limited information about their surroundings. Unfortunately, due to the possible presence of malicious dynamic actors, it is infeasible to develop an algorithm that can guarantee collision-free operation. Instead, one can attempt to design a control technique that guarantees the robot is not-at-fault in any collision. In the literature, making such guarantees in real time has been restricted to static environments or specific dynamic models. To ensure not-at-fault behavior, a robot must first correctly sense and predict the world around it within some sufficiently large sensor horizon (the prediction problem), then correctly control relative to the predictions (the control problem). This paper addresses the control problem by proposing Reachability-based Trajectory Design for Dynamic environments (RTD-D), which guarantees that a robot with an arbitrary nonlinear dynamic model correctly responds to predictions in arbitrary dynamic environments. RTD-D first computes a Forward Reachable Set (FRS) offline of the robot tracking parameterized desired trajectories that include fail-safe maneuvers. Then, for online receding-horizon planning, the method provides a way to discretize predictions of an arbitrary dynamic environment to enable real-time collision checking. The FRS is used to map these discretized predictions to trajectories that the robot can track while provably not-at-fault. One such trajectory is chosen at each iteration, or the robot executes the fail-safe maneuver from its previous trajectory which is guaranteed to be not at fault. RTD-D is shown to produce not-at-fault behavior over thousands of simulations and several real-world hardware demonstrations on two robots: a Segway, and a small electric vehicle.

[1]  Matthew Johnson-Roberson,et al.  Bridging the gap between safety and real-time performance in receding-horizon trajectory design for mobile robots , 2018, Int. J. Robotics Res..

[2]  Matthew Johnson-Roberson,et al.  Safe Trajectory Synthesis for Autonomous Driving in Unforeseen Environments , 2017, ArXiv.

[3]  Matthias Althoff,et al.  Provably safe motion of mobile robots in human environments , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[4]  Huei Peng,et al.  Obstacle Avoidance for Low-Speed Autonomous Vehicles With Barrier Function , 2018, IEEE Transactions on Control Systems Technology.

[5]  Siddhartha S. Srinivasa,et al.  A Unifying Formalism for Shortest Path Problems with Expensive Edge Evaluations via Lazy Best-First Search over Paths with Edge Selectors , 2016, ICAPS.

[6]  Dan Halperin,et al.  Minkowksi Sums and Offset Polygons , 2011 .

[7]  Li Wang,et al.  Control Barrier Certificates for Safe Swarm Behavior , 2015, ADHS.

[8]  Ian M. Mitchell The Flexible, Extensible and Efficient Toolbox of Level Set Methods , 2008, J. Sci. Comput..

[9]  Matthew Johnson-Roberson,et al.  Occlusion-Aware Risk Assessment for Autonomous Driving in Urban Environments , 2018, IEEE Robotics and Automation Letters.

[10]  Russ Tedrake,et al.  Funnel libraries for real-time robust feedback motion planning , 2016, Int. J. Robotics Res..

[11]  Matthias Althoff,et al.  Online Verification of Automated Road Vehicles Using Reachability Analysis , 2014, IEEE Transactions on Robotics.

[12]  Wolfgang Hess,et al.  Real-time loop closure in 2D LIDAR SLAM , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[13]  Amnon Shashua,et al.  On a Formal Model of Safe and Scalable Self-driving Cars , 2017, ArXiv.

[14]  Christos Katrakazas,et al.  Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions , 2015 .

[15]  G. Strang The Width of a Chair , 1982 .

[16]  William Whittaker,et al.  Autonomous driving in urban environments: Boss and the Urban Challenge , 2008, J. Field Robotics.

[17]  Mikel Sagardia,et al.  A New Fast and Robust Collision Detection and Force Computation Algorithm Applied to the Physics Engine Bullet: Method, Integration, and Evaluation , 2014, EuroVR.

[18]  Anca D. Dragan,et al.  A Scalable Framework For Real-Time Multi-Robot, Multi-Human Collision Avoidance , 2018, 2019 International Conference on Robotics and Automation (ICRA).

[19]  Paulo Tabuada,et al.  Correctness Guarantees for the Composition of Lane Keeping and Adaptive Cruise Control , 2016, IEEE Transactions on Automation Science and Engineering.

[20]  Matthew McNaughton,et al.  Parallel Algorithms for Real-time Motion Planning , 2011 .

[21]  Mo Chen,et al.  FaSTrack: A modular framework for fast and guaranteed safe motion planning , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[22]  Alexandre M. Bayen,et al.  A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games , 2005, IEEE Transactions on Automatic Control.

[23]  Matthew Johnson-Roberson,et al.  Real-Time Certified Probabilistic Pedestrian Forecasting , 2017, IEEE Robotics and Automation Letters.

[24]  Russ Tedrake,et al.  Convex optimization of nonlinear feedback controllers via occupation measures , 2013, Int. J. Robotics Res..

[25]  J. Lasserre Moments, Positive Polynomials And Their Applications , 2009 .

[26]  Stewart Worrall,et al.  Identifying robust landmarks in feature-based maps , 2018, 2019 IEEE Intelligent Vehicles Symposium (IV).

[27]  Pengcheng Zhao,et al.  Optimal Control for Nonlinear Hybrid Systems via Convex Relaxations , 2017, 1702.04310.

[28]  Ruzena Bajcsy,et al.  Convex computation of the reachable set for controlled polynomial hybrid systems , 2014, 53rd IEEE Conference on Decision and Control.