Learning dynamical systems with bifurcations

Trajectory planning through dynamical systems (DS) provides robust control for robots and has found numerous applications from locomotion to manipulation. However, to date, DS for controlling rhythmic patterns are distinct from DS used to control point to point motion and current approaches switch at run time across these to enable multiple behaviors. This switching can be brittle and subject to instabilities. We present an approach to embed cyclic and point to point dynamics in a single DS. We offer a method to learn the parameters of complete DS through a two-step optimization. By exploiting Hopf bifurcations, we can explicitly and smoothly transit across periodic and non-periodic phases, linear and nonlinear limit cycles, and non-periodic phases, in addition to changing the equilibrium's location and the limit cycle's amplitude. We use diffeomorphism and learn a mapping to modify the learned limit cycle to generate nonlinear limit cycles. The approach is validated with a real 7 DOF KUKA LWR 4+ manipulator to control wiping and with a humanoid robot in simulation.

On the dynamics of human locomotion and co-design of lower limb assistive devices

Jesse van den Kieboom

Recent developments in lower extremities wearable robotic devices for the assistance and rehabilitation of humans suffering from an impairment have led to several successes in the assistance of people who as a result regained a certain form of locomotive capability. Such devices are conventionally designed to be anthropomorphic. They follow the morphology of the human lower limbs. It has been shown previously that non-anthropomorphic designs can lead to increased comfort and better dynamical properties due to the fact that there is more morphological freedom in the design parameters of such a device. At the same time, exploitation of this freedom is not always intuitive and can be difficult to incorporate. In this work we strive towards a methodology aiding in the design of possible non-anthropomorphic structures for the task of human locomotion assistance by means of simulation and optimization. The simulation of such systems requires state of the art rigid body dynamics, contact dynamics and, importantly, closed loop dynamics. Through the course of our work, we first develop a novel, open and freely available, state of the art framework for the modeling and simulation of general coupled dynamical systems and show how such a framework enables the modeling of systems in a novel way. The resultant simulation environment is suitable for the evaluation of structural designs, with a specific focus on locomotion and wearable robots. To enable open-ended co-design of morphology and control, we employ population-based optimization methods to develop a novel Particle Swarm Optimization derivative specifically designed for the simultaneous optimization of solution structures (such as mechanical designs) as well as their continuous parameters. The optimizations that we aim to perform require large numbers of simulations to accommodate them and we develop another open and general framework to aid in large scale, population based optimizations in multi-user environments. Using the developed tools, we first explore the occurrence and underlying principles of natural human gait and apply our findings to the optimization of a bipedal gait of a humanoid robotic platform. Finally, we apply our developed methods to the co-design of a non-anthropomorphic, lower extremities, wearable robot in simulation, leading to an iterative co-design methodology aiding in the exploration of otherwise hard to realize morphological designs

EPFL2014

A Dynamical System Approach for Adaptive Grasping, Navigation and Co-Manipulation with Humanoid Robots

Aude Billard, Salman Faraji, Nadia Barbara Figueroa Fernandez, Mikhail Koptev

In this paper, we present an integrated approach that provides compliant control of an iCub humanoid robot and adaptive reaching, grasping, navigating and co-manipulating capabilities. We use state-dependent dynamical systems (DS) to (i) coordinate and drive the robots hands (in both position and orientation) to grasp an object using an intermediate virtual object, and (ii) drive the robot’s base while walking/navigating. The use of DS as motion generators allows us to adapt smoothly as the object moves and to re-plan on-line motion of the arms and body to reach the object’s new location. The desired motion generated by the DS are used in combination with a whole-body compliant control strategy that absorbs perturbations while walking and offers compliant behaviors for grasping and manipulation tasks. Further, the desired dynamics for the arm and body can be learned from demonstrations. By integrating these components, we achieve unprecedented adaptive behaviors for whole body manipulation. We showcase this in simulations and real-world experiments where iCub robots (i) walk-to-grasp objects, (ii) follow a human (or another iCub) through interaction and (iii) learn to navigate or co-manipulate an object from human guided demonstrations; whilst being robust to changing targets and perturbations.

IEEE2020

On the dynamics of human locomotion and co-design of lower limb assistive devices

Jesse van den Kieboom

EPFL2014