Coupling-dependent convergence behavior of phase oscillators with tegotae-control

A bio-inspired way to model locomotion is using a network of coupled phase oscillators to create a Central Pattern Generator (CPG). The recently developed feedback control method tegotae includes exteroceptive force feedback into the governing phase update equations, leading to gait limit cycles. However, the oscillator coupling weights are often determined empirically. Here, we first investigate how the coupling coefficients influence the limit cycle convergence behavior on a 2- and 3-limbed structure in simulation. We find that the convergence with tegotae can be improved by introducing appropriate cross-couplings. This results in a smoother convergence and steady-state behavior where each individual oscillator drives the full network to a common convergence state in comparison to competing convergence states with ill-chosen cross-couplings. We then validate the findings in hardware and hypothesize how the appropriate couplings could be derived directly from the morphology, potentially eliminating the empiric determination.

Pattern Generation for Rough Terrain Locomotion with Quadrupedal Robots

Mostafa Ajallooeian

Animals are able to locomote on rough terrain without any apparent difficulty, but this does not mean that the locomotor system is simple. The locomotor system is actually a complex multi-input multi-output closed-loop control system. This thesis is dedicated to the design of controllers for rough terrain locomotion, for animal-like quadrupedal robots. We choose the problem of blind rough terrain locomotion as the target of experiments. Blind rough terrain locomotion requires continuous and momentary corrections of leg movements and body posture, and provides a proper testbed to observe the interaction of different mod- ules involved in locomotion control. As for the specific case of this thesis, we have to design rough terrain locomotion controllers that do not depend on the torque-control capability, have limited sensing, and have to be computationally light, all due to the properties of the robotics platform that we use. We propose that a robust locomotion controller, taking into account the aforementioned constraints, is constructed from at least three modules: 1) pattern generators providing the nominal patterns of locomotion; 2) A posture controller continuously adjusting the attitude of the body and keeping the robot upright; and 3) quick reflexes to react to unwanted momentary events like stumbling or an external force impulse. We introduce the framework of morphed oscillators to systematize the design of pattern gen- erators realized as coupled nonlinear oscillators. Morphed oscillators are nonlinear oscillators that can encode arbitrary limit cycle shapes and simultaneously have infinitely large basins of attraction. More importantly, they provide dynamical systems that can assume the role of feedforward locomotion controllers known as Central Pattern Generators (CPGs), and accept discontinuous sensory feedback without the risk of producing discontinuous output. On top of the CPG module, we add a kinematic model-based posture controller inspired by virtual model control (VMC), to control the body attitude. Virtual model control produces forces, and through the application of the Jacobian transpose method, generates torques which are added to the CPG torques. However, because our robots do not have a torque- control capability, we adapt the posture controller by producing task-space velocities instead of forces, thus generating joint-space velocity feedback signals. Since the CPG model used for locomotion generates joint velocities and accepts feedback without the fear of instability or discontinuity, the posture control feedback is easily integrated into the CPG dynamics. More- over, we introduce feedback signals for adjusting the posture by shifting the trunk positions, which directly update the limit cycle shape of the morphed oscillator nodes of the CPG. Reflexes are added, with minimal complexity, to react to momentary events. We implement simple impulse-based feedback mechanisms inspired by animals and successful rough terrain robots to 1) flex the leg if the robot is stumbling (stumbling correction reflex); 2) extend the leg if an expected contact is missing (leg extension reflex); or 3) initiate a lateral stepping sequence in response to a lateral external perturbation. CPG, posture controller, and reflexes are put together in a modular control architecture alongside additional modules that estimate inclination, control speed and direction, maintain timing of feedback signals, etc. [...]

EPFL2015

Locomotion Dynamics for Bio-inspired Robots with Soft Appendages: Application to Flapping Flight and Passive Swimming

Yannick Morel, Mathieu Porez

In animal locomotion, either in fish or flying insects, the use of flexible terminal organs or appendages greatly improves the performance of locomotion (thrust and lift). In this article, we propose a general unified framework for modeling and simulating the (bio-inspired) locomotion of robots using soft organs. The proposed approach is based on the model of Mobile Multibody Systems (MMS). The distributed flexibilities are modeled according to two major approaches: the Floating Frame Approach (FFA) and the Geometrically Exact Approach (GEA). Encompassing these two approaches in the Newton-Euler modeling formalism of robotics, this article proposes a unique modeling framework suited to the fast numerical integration of the dynamics of a MMS in both the FFA and the GEA. This general framework is applied on two illustrative examples drawn from bio-inspired locomotion: the passive swimming in von Karman Vortex Street, and the hovering flight with flexible flapping wings.

Springer2017

Pattern Generation for Rough Terrain Locomotion with Quadrupedal Robots

Mostafa Ajallooeian

EPFL2015