Closed-Loop Motion Planning for Differentially Flat Systems: A Time-Varying Optimization Framework
Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to follow, and an online/closed-loop stage, tracking, that corrects for unmodeled dynamics and disturbances. Such an approach generally introduces conservativeness into the planning stage, which becomes difficult to overcome as the model complexity increases and real-time decisions need to be made in a changing environment. This work addresses these challenges for the class of differentially flat nonlinear systems by integrating planning and control into a cohesive closed-loop task. Precisely, we develop an optimization-based framework that aims to steer a differentially flat system to a trajectory implicitly defined via a constrained time-varying optimization problem. To that end, we generalize the notion of feedback linearization, which makes non-linear systems behave as linear systems, and develop controllers that effectively transform a differentially flat system into an optimization algorithm that seeks to find the optimal solution of a (possibly time-varying) optimization problem. Under sufficient regularity assumptions, we prove global asymptotic convergence for the optimization dynamics to the minimizer of the time-varying optimization problem. We illustrate the effectiveness of our method with two numerical examples: a multi-robot tracking problem and a robot obstacle avoidance problem.
Code (0)
등록된 구현이 없습니다.
Tasks
Motion PlanningSimilar Papers 제목 키워드 기반
Ultrafast Sampling-based Kinodynamic Planning via Differential Flatness
Motion planning under dynamics constraints, i.e, kinodynamic planning, enables safe robot operation by generating dynamically feasible trajectories that the robot can accurately track. For high-DOF robots such as manipul…
Motion PlanningNuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles
In this work, we propose the world's first closed-loop ML-based planning benchmark for autonomous driving. While there is a growing body of ML-based motion planners, the lack of established datasets and metrics has limit…
Autonomous DrivingAutonomous VehiclesMotion ForecastingMotion Planning+1SENSE-STEP: Learning Sim-to-Real Locomotion for a Sensory-Enabled Soft Quadruped Robot
Robust closed-loop locomotion remains challenging for soft quadruped robots due to high-dimensional dynamics, actuator hysteresis, and difficult-to-model contact interactions, while conventional proprioception provides l…
ReactiveBFM: Reactive Closed-Loop Motion Planning Towards Universal Humanoid Whole-Body Control
While current Behavior Foundation Models (BFMs) provide robust control priors for humanoids, they only execute pre-defined reference motions. As a result, they are vulnerable to environmental shifts and incapable of reac…
Motion PlanningAdv3D: Generating Safety-Critical 3D Objects through Closed-Loop Simulation
Self-driving vehicles (SDVs) must be rigorously tested on a wide range of scenarios to ensure safe deployment. The industry typically relies on closed-loop simulation to evaluate how the SDV interacts on a corpus of synt…
Motion Planning