Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processes
- Resource Type
- Conference
- Authors
- Evangelisti, Giulio; Hirche, Sandra
- Source
- 2022 IEEE 61st Conference on Decision and Control (CDC) Decision and Control (CDC), 2022 IEEE 61st Conference on. :4078-4085 Dec, 2022
- Subject
- Robotics and Control Systems
Uncertainty
Gaussian processes
Numerical simulation
Probabilistic logic
Numerical models
Velocity measurement
Torque measurement
- Language
- ISSN
- 2576-2370
This paper proposes a physically consistent Gaussian Process (GP) enabling the data-driven modelling of uncertain Lagrangian systems. The function space is tailored according to the energy components of the Lagrangian and the differential equation structure, analytically guaranteeing properties such as energy conservation and quadratic form. The novel formulation of Cholesky decomposed matrix kernels allow the probabilistic preservation of positive definiteness. Only differential input-to-output measurements of the function map are required while Gaussian noise is permitted in torques, velocities, and accelerations. We demonstrate the effectiveness of the approach in numerical simulation.