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Safe Continuous Dynamic System Model Learning
Safe Continuous Dynamic System Model Learning
Paper Title
Active Sampling based Safe Identification of Dynamical Systems using Extreme Learning Machines and Barrier Certificates. pdf
Authors
Iman Salehi, Gang Yao, and Ashwin Dani
Date
May 2019
Published in
IEEE International Conference on Robotics and Automation (ICRA)
Experimental setup showing Baxter, the humanoid robot, in front of a safe operating region designated as an ellipse using Lego blocks.
Abstract: Learning the dynamical system (DS) model from data that preserves dynamical system properties is an important problem in many robot learning applications. Typically, the joint data coming from cyber-physical systems, such as robots have some underlying DS properties associated with it, e.g., convergence, invariance to a set, etc. In this paper, a model learning method is developed such that the trajectories of the DS are invariant in a given compact set. Such invariant DS models can be used to generate trajectories of the robot that will always remain in a prescribed set. In order to achieve invariance to a set, Barrier certificates are employed. The DS is approximated using Extreme Learning Machine (ELM), and a parameter learning problem subject to Barrier certificates enforced at all the points in the prescribed set is solved. To solve an infinite constraint problem for enforcing Barrier Certificates at every point in a given compact set, a modified constraint is developed that is sufficient to hold the Barrier certificates in the entire set. An active sampling strategy is formulated to minimize the number of constraints in learning. Simulation results of ELM learning with and without Barrier certificates are presented which show the invariance property being preserved in the ELM learning when learning procedure involves Barrier constraints. The method is validated using experiments conducted on a robot arm recreating invariant trajectories inside a prescribed set.
Robot Experiment and Simulation Results
Robot Experiment and Simulation Results
The video shows implementation of the learning dynamical systems algorithm that keeps the end effector generated trajectories in a confined space. Four experiments are carried out on the Baxter robot. The first experiment shows the Baxter robot following a trajectory generated from an unconstrained model to demonstrate the necessity of enforcing barrier constraints while learning the model. The second and third experiments showcase the ability of the learned model with barrier constraints to follow a trajectory without hitting the obstacles on the boundary regardless of the initial condition. The last experiment illustrates the learned model's ability to handle perturbations.
Ellipse and circle are used as smooth functions (black) to construct a barrier certificate that splits the state space into safe region (light gray) and unsafe region (dark gray). Illustration of the learned model's ability to handle perturbations.
The streamlines of the solutions of dynamical system models (in gray) are shown along with the demonstrated data (in solid red lines) and the reproductions (in dashed blue and green lines) for circular Barrier function (a) and elliptical Barrier function (b).
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