Learning Dynamical System-Based Robot Motions from Demonstrations Via ODE-Driven Diffeomorphic Mappings
Haoyu Zhang, Long Cheng
AI summary
Problem
Existing dynamical system models rely on rigid diffeomorphic architectures that limit neural network expressiveness and increase computational overhead, hindering accurate learning of complex motions.
Approach
The framework replaces invertible network blocks with a Lipschitz-controlled neural flow, using bidirectional ODE integration for stability and a variational ODE for efficient Jacobian computation.
Key results
- 33.7% improvement in trajectory reproduction accuracy over baselines
- 20.8% reduction in Jacobian computation time via variational ODEs
- Guaranteed Lyapunov stability without restrictive invertible architectures
- Validated on LASA dataset and real-world 7-DOF Franka Emika arm
Why it matters
Expands the representational capacity of dynamical systems for robotics, enabling robust reproduction of complex motions while maintaining mathematical stability for real-time control.
Abstract
Learning from Demonstrations (LfD) has emerged as a prominent paradigm for imparting motion skills to robotic systems. Dynamical systems (DS) offer a potent mathematical framework for representing point-to-point motions, a critical requirement for numerous practical applications in robotics. While existing approaches typically construct DS models by employing diffeomorphic mappings to morph stable reference systems toward observed demonstrations, the requirement to preserve strict diffeomorphic properties introduces architec- tural constraints on neural network design, thereby constrain- ing their expressiveness. To address this limitation, we present a DS-based LfD formulation that relaxes traditional diffeo- morphism constraints. Our framework employs bidirectional temporal integration of ordinary differential equations (ODEs) to simultaneously satisfy stability guarantees and trajectory alignment objectives. A key innovation lies in a variational calculus framework for Jacobian estimation, enabling efficient computation of DS vector fields while maintaining numeri- cal stability. Comprehensive evaluations demonstrate that our method achieves 33.7% improvement in trajectory reproduction accuracy compared to state-of-the-art baselines while preserv- ing Lyapunov stability. The proposed methodology significantly expands the representational capacity of DS-based learning sys- tems, enabling robust reproduction of complex motion patterns.