Learning Contracting Nonlinear Dynamics From Human Demonstration for Robot Motion Planning

In this paper, we present an algorithm to learn the dynamics of human arm motion from the data collected from human actions. Learning the motion plans from human demonstrations is essential in making robot programming possible by nonexpert programmers as well as realizing human-robot collaboration. The highly complex human reaching motion is generated by a stable closed-loop dynamical system. To capture the complexity a neural network (NN) is used to represent the dynamics of the human motion states. The trajectories of arm generated by humans for reaching to a place are contracting towards the goal location from various initial conditions with built in obstacle avoidance. To take into consideration the contracting nature of the human motion dynamics the unknown motion model is learned using a NN subject to contraction analysis constraints. To learn the NN parameters an optimization problem is formulated by relaxing the non-convex contraction constraints to Linear matrix inequality (LMI) constraints. Sequential Quadratic Programming (SQP) is used to solve the optimization problem subject to the LMI constraints. For obstacle avoidance a negative gradient of the repulsive potential function is added to the learned contracting NN model. Experiments are conducted on Baxter robot platform to show that the robot can generate reaching paths from the contracting NN dynamics learned from human demonstrated data recorded using Microsoft Kinect sensor. The algorithm is able to adapt to situations for which the demonstrations are not available, e.g., an obstacle placed in the path.