Bridging the gap between safety and real-time performance in receding-horizon trajectory design for mobile robots

Abstract

To operate with limited sensor horizons in unpredictable environments, autonomous robots use a receding-horizon strategy to plan trajectories, wherein they execute a short plan while creating the next plan. However, creating safe, dynamically feasible trajectories in real time is challenging, and planners must ensure persistent feasibility, meaning a new trajectory is always available before the previous one has finished executing. Existing approaches make a tradeoff between model complexity and planning speed, which can require sacrificing guarantees of safety and dynamic feasibility. This work presents the Reachability-based Trajectory Design (RTD) method for trajectory planning. RTD begins with an offline forward reachable set (FRS) computation of a robot’s motion when tracking parameterized trajectories; the FRS provably bounds tracking error. At runtime, the FRS is used to map obstacles to parameterized trajectories, allowing RTD to select a safe trajectory at every planning iteration. RTD prescribes an obstacle representation to ensure that obstacle constraints can be created and evaluated in real time while maintaining safety. Persistent feasibility is achieved by prescribing a minimum sensor horizon and a minimum duration for the planned trajectories. A system decomposition approach is used to improve the tractability of computing the FRS, allowing RTD to create more complex plans at runtime. RTD is compared in simulation with rapidly-exploring random trees and nonlinear model-predictive control. RTD is also demonstrated in randomly crafted environments on two hardware platforms: a differential-drive Segway and a car-like Rover. The proposed method is safe and persistently feasible across thousands of simulations and dozens of real-world hardware demos.

Reachability-based Trajectory Safeguard (RTS): A Safe and Fast Reinforcement Learning Safety Layer for Continuous Control

“…We fix ṗplan (t fin , •) = 0 so all plans end with a braking failsafe maneuver. If the robot fails to find a safe plan in a planning iteration, it can continue a previouslyfound safe plan, enabling persistent safety [12,Thm. 39].…”

“…The present work develops a safety layer using a trajectory-parameterized reachable set, computed offline, over a continuous action space, to ensure safe learning online in real-time. This approach is motivated by Reachabilitybased Trajectory Design (RTD), a recent approch to safe robot motion planning, which uses an offline reachability computation and online receding horizon planning [12]. RTD uses a simplified, parameterized model to generate reference trajectories, or plans, and upper bounds the tracking error between the robot and planning model.…”

Eyes-Closed Safety Kernels: Safety for Autonomous Systems Under Loss of Observability

“…This allows for planning trajectories that are guaranteed to be trackable by the high-fidelity model. These works are extended in [18] and [19], allowing for limited sensing radii. Meanwhile, [20] leverages a similar idea to generate trajectories that incorporate system tracking error and will not have any at-fault collisions in unforeseen environments with limited sensing radius.…”

Safe-by-Design Planner-Tracker Synthesis

“…Designing controllers that meet such requirements in realtime may be computationally intractable, e.g., due to large system dimension or nonlinearities in a high-fidelity dynamical model of the system. The planner-tracker framework [30,9,28,15,27,29,25] addresses this challenge with a layered architecture where a lower-fidelity "planning" model is employed for online planning and a "tracking" controller, synthesized offline, keeps the tracking error between the high-fidelity ("tracking") model and the planning model within a bounded set. System safety is then guaranteed if the planner constraints, when augmented by the tracking error bound, lie within the safety constraints.…”