Distributionally Robust CVaR-Based Safety Filtering for Motion Planning in Uncertain Environments

Safety is a core challenge of autonomous robot motion planning, especially in the presence of dynamic and uncertain obstacles. Many recent results use learning and deep learning-based motion planners and prediction modules to predict multiple possible obstacle trajectories and generate obstacle-aware ego robot plans. However, planners that ignore the inherent uncertainties in such predictions incur collision risks and lack formal safety guarantees. In this paper, we present a computationally efficient safety filtering solution to reduce the collision risk of ego robot motion plans using multiple samples of obstacle trajectory predictions. The proposed approach reformulates the collision avoidance problem by computing safe halfspaces based on obstacle sample trajectories using distributionally robust optimization (DRO) techniques. The safe halfspaces are used in a model predictive control (MPC)-like safety filter to apply corrections to the reference ego trajectory thereby promoting safer planning. The efficacy and computational efficiency of our approach are demonstrated through numerical simulations

Distributionally Robust RRT with Risk Allocation

An integration of distributionally robust risk allocation into sampling-based motion planning algorithms for robots operating in uncertain environments is proposed. We perform non-uniform risk allocation by decomposing the distributionally robust joint risk constraints defined over the entire planning horizon into individual risk constraints given the total risk budget. Specifically, the deterministic tightening defined using the individual risk constraints is leveraged to define our proposed exact risk allocation procedure. Our idea of embedding the risk allocation technique into sampling based motion planning algorithms realises guaranteed conservative, yet increasingly more risk feasible trajectories for efficient state space exploration

Robust trajectory planning for unmanned aerial vehicles in uncertain environments

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (leaves 145-153).As unmanned aerial vehicles (UAVs) take on more prominent roles in aerial missions, it becomes necessary to increase the level of autonomy available to them within the mission planner. In order to complete realistic mission scenarios, the UAV must be capable of operating within a complex environment, which may include obstacles and other no-fly zones. Additionally, the UAV must be able to overcome environmental uncertainties such as modeling errors, external disturbances, and an incomplete situational awareness. By utilizing planners which can autonomously navigate within such environments, the cost-effectiveness of UAV missions can be dramatically improved.This thesis develops a UAV trajectory planner to efficiently identify and execute trajectories which are robust to a complex, uncertain environment. This planner, named Efficient RSBK, integrates previous mixed-integer linear programming (MILP) path planning algorithms with several implementation innovations to achieve provably robust on-line trajectory optimization. Using the proposed innovations, the planner is able to design intelligent long-term plans using a minimal number of decision variables. The effectiveness of this planner is demonstrated with both simulation results and flight experiments on a quadrotor testbed.Two major components of the Efficient RSBK framework are the robust model predictive control (RMPC) scheme and the low-level planner. This thesis develops a generalized framework to investigate RMPC affine feedback policies on the disturbance, identify relative strengths and weaknesses, and assess suitability for the UAV trajectory planning problem. A simple example demonstrates that even with a conventional problem setup, the closed-loop performance may not always improve with additional decision variables, despite the resulting increase in computational complexity. A compatible low-level troller is also introduced which significantly improves trajectory-following accuracy, as demonstrated by additional flight experiments.by Brandon Luders.S.M

Fast Second-order Cone Programming for Safe Mission Planning

This paper considers the problem of safe mission planning of dynamic systems operating under uncertain environments. Much of the prior work on achieving robust and safe control requires solving second-order cone programs (SOCP). Unfortunately, existing general purpose SOCP methods are often infeasible for real-time robotic tasks due to high memory and computational requirements imposed by existing general optimization methods. The key contribution of this paper is a fast and memory-efficient algorithm for SOCP that would enable robust and safe mission planning on-board robots in real-time. Our algorithm does not have any external dependency, can efficiently utilize warm start provided in safe planning settings, and in fact leads to significant speed up over standard optimization packages (like SDPT3) for even standard SOCP problems. For example, for a standard quadrotor problem, our method leads to speedup of 1000x over SDPT3 without any deterioration in the solution quality. Our method is based on two insights: a) SOCPs can be interpreted as optimizing a function over a polytope with infinite sides, b) a linear function can be efficiently optimized over this polytope. We combine the above observations with a novel utilization of Wolfe's algorithm to obtain an efficient optimization method that can be easily implemented on small embedded devices. In addition to the above mentioned algorithm, we also design a two-level sensing method based on Gaussian Process for complex obstacles with non-linear boundaries such as a cylinder

Synthesizing Manipulation Sequences for Under-Specified Tasks using Unrolled Markov Random Fields

Abstract — Many tasks in human environments require performing a sequence of navigation and manipulation steps involving objects. In unstructured human environments, the location and configuration of the objects involved often change in unpredictable ways. This requires a high-level planning strategy that is robust and flexible in an uncertain environment. We propose a novel dynamic planning strategy, which can be trained from a set of example sequences. High level tasks are expressed as a sequence of primitive actions or controllers (with appropriate parameters). Our score function, based on Markov Random Field (MRF), captures the relations between environment, controllers, and their arguments. By expressing the environment using sets of attributes, the approach generalizes well to unseen scenarios. We train the parameters of our MRF using a maximum margin learning method. We provide a detailed empirical validation of our overall framework demonstrating successful plan strategies for a variety of tasks. 1 I

Unified Robust Path Planning and Optimal Trajectory Generation for Efficient 3D Area Coverage of Quadrotor UAVs

Area coverage is an important problem in robotics applications, which has been widely used in search and rescue, offshore industrial inspection, and smart agriculture. This paper demonstrates a novel unified robust path planning, optimal trajectory generation, and control architecture for a quadrotor coverage mission. To achieve safe navigation in uncertain working environments containing obstacles, the proposed algorithm applies a modified probabilistic roadmap to generating a connected search graph considering the risk of collision with the obstacles. Furthermore, a recursive node and link generation scheme determines a more efficient search graph without extra complexity to reduce the computational burden during the planning procedure. An optimal three-dimensional trajectory generation is then suggested to connect the optimal discrete path generated by the planning algorithm, and the robust control policy is designed based on the cascade NLH∞ framework. The integrated framework is capable of compensating for the effects of uncertainties and disturbances while accomplishing the area coverage mission. The feasibility, robustness and performance of the proposed framework are evaluated through Monte Carlo simulations, PX4 Software-In-the-Loop test facility, and real-world experiments