Dynamic Movement Primitives with Control Barrier Functions for Constrained Trajectory Planning
Federico Vesentini, Daniele Meli, Nicola Sansonetto, Luca Di Persio, Riccardo Muradore
AI summary
Problem
Dynamic Movement Primitives (DMPs) excel at trajectory imitation but lack formal guarantees for satisfying complex nonlinear kinodynamic and safety constraints during execution, limiting their use in critical robotic applications.
Approach
The authors reformulate DMPs in control-affine form and directly combine them with the closed-form safety input from Control Barrier Functions (CBFs), enabling real-time constraint enforcement without iterative optimization.
Key results
- Formulation of Constrained Movement Primitives (CMPs) integrating DMPs and CBFs
- Theoretical proof of safe goal convergence under nonlinear constraints
- Simulation and real-robot validation for velocity limits, dynamic obstacle avoidance, and centrifugal acceleration
- Closed-form, computationally efficient constraint enforcement bypassing iterative optimization
Why it matters
Provides a computationally efficient, provably safe planning method for mobile robots and dynamic systems operating in cluttered or kinodynamically constrained environments.
Abstract
Dynamic Movement Primitives (DMPs) form a robust framework for trajectory generation based on imitation learn- ing, aiming to replicate the shape of reference trajectories from demonstrations closely. DMPs have been extensively employed for trajectory planning in robotic systems. However, they cannot safely guarantee complex nonlinear constraints, which is essential at the control level. On the other hand, Control Barrier Functions (CBFs) are used to modulate the input of control-affine dynamic systems subject to state-dependent constraints, guaranteeing that the system remains within predefined safe sets while converging towards target states. This letter proposes Constrained Movement Primitives (CMPs), a novel framework that integrates DMPs with CBFs to generate safe-by-construction trajectories subject to non- linear constraints. We represent DMPs in control-affine form and combine them with the closed-form input provided by CBFs, over- comingthelimitationsofexistingiterativeoptimisationmethodsfor constrained DMPs. We demonstrate that CBFs preserve the goal convergence guarantees of DMPs. Moreover, we validate our ap- proach in simulation and on a real mobile robot subject to nonlinear kinodynamic constraints, concerning maximum Cartesian velocity, obstacle avoidance, and maximum centrifugal acceleration to avoid slippery over curved trajectories.