3LP: a linear 3D-walking model including torso and swing dynamics

In this paper, we present a new model of biped locomotion which is composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to double support, this model has different actuation possibilities in the swing hip and stance ankle which could be widely used to produce different walking gaits. Without the need for numerical time-integration, closed-form solutions help finding periodic gaits which could be simply scaled in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can provide a computationally fast platform for model predictive controllers to predict the future and consider meaningful inequality constraints to ensure feasibility of the motion. Such property is coming from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract high level template space. The proposed model produces human-like torque and ground reaction force profiles and thus, compared to point-mass models, it is more promising for precise control of humanoid robots. Despite being linear and lacking many other features of human walking like CoM excursion, knee flexion and ground clearance, we show that the proposed model can predict one of the main optimality trends in human walking, i.e. nonlinear speed-frequency relationship. In this paper, we mainly focus on describing the model and its capabilities, comparing it with human data and calculating optimal human gait variables. Setting up control problems and advanced biomechanical analysis still remain for future works.Comment: Journal paper under revie

Design of artificial neural oscillatory circuits for the control of lamprey- and salamander-like locomotion using evolutionary algorithms

This dissertation investigates the evolutionary design of oscillatory artificial neural networks for the control of animal-like locomotion. It is inspired by the neural organ¬ isation of locomotor circuitries in vertebrates, and explores in particular the control of undulatory swimming and walking. The difficulty with designing such controllers is to find mechanisms which can transform commands concerning the direction and the speed of motion into the multiple rhythmic signals sent to the multiple actuators typically involved in animal-like locomotion. In vertebrates, such control mechanisms are provided by central pattern generators which are neural circuits capable of pro¬ ducing the patterns of oscillations necessary for locomotion without oscillatory input from higher control centres or from sensory feedback. This thesis explores the space of possible neural configurations for the control of undulatory locomotion, and addresses the problem of how biologically plausible neural controllers can be automatically generated.Evolutionary algorithms are used to design connectionist models of central pattern generators for the motion of simulated lampreys and salamanders. This work is inspired by Ekeberg's neuronal and mechanical simulation of the lamprey [Ekeberg 93]. The first part of the thesis consists of developing alternative neural controllers for a similar mechanical simulation. Using a genetic algorithm and an incremental approach, a variety of controllers other than the biological configuration are successfully developed which can control swimming with at least the same efficiency. The same method is then used to generate synaptic weights for a controller which has the observed biological connectivity in order to illustrate how the genetic algorithm could be used for developing neurobiological models. Biologically plausible controllers are evolved which better fit physiological observations than Ekeberg's hand-crafted model. Finally, in collaboration with Jerome Kodjabachian, swimming controllers are designed using a developmental encoding scheme, in which developmental programs are evolved which determine how neurons divide and get connected to each other on a two-dimensional substrate.The second part of this dissertation examines the control of salamander-like swimming and trotting. Salamanders swim like lampreys but, on the ground, they switch to a trotting gait in which the trunk performs a standing wave with the nodes at the girdles. Little is known about the locomotion circuitry of the salamander, but neurobiologists have hypothesised that it is based on a lamprey-like organisation. A mechanical sim¬ ulation of a salamander-like animat is developed, and neural controllers capable of exhibiting the two types of gaits are evolved. The controllers are made of two neural oscillators projecting to the limb motoneurons and to lamprey-like trunk circuitry. By modulating the tonic input applied to the networks, the type of gait, the speed and the direction of motion can be varied.By developing neural controllers for lamprey- and salamander-like locomotion, this thesis provides insights into the biological control of undulatory swimming and walking, and shows how evolutionary algorithms can be used for developing neurobiological models and for generating neural controllers for locomotion. Such a method could potentially be used for designing controllers for swimming or walking robots, for instance

Imprecise dynamic walking with time-projection control

We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rules to account for swing dynamics and leg-retraction. We apply it to a simulated Atlas robot in position-control, always commanded to perform in-place walking. The stance hip joint in our robot keeps the torso upright to let the robot naturally fall, and the swing hip joint tracks the desired footstep location. Combined with simple Center of Pressure (CoP) damping rules in the low-level controller, our foot-placement enables the robot to recover from strong pushes and produce periodic walking gaits when subject to persistent sources of disturbance, externally or internally. These gaits are imprecise, i.e., emergent from asymmetry sources rather than precisely imposing a desired velocity to the robot. Also in extreme conditions, restricting linearity assumptions of the 3LP model are often violated, but the system remains robust in our simulations. An extensive analysis of closed-loop eigenvalues, viable regions and sensitivity to push timings further demonstrate the strengths of our simple controller

Self-organized adaptive legged locomotion in a compliant quadruped robot

In this contribution we present experiments of an adaptive locomotion controller on a compliant quadruped robot. The adaptive controller consists of adaptive frequency oscillators in different configurations and produces dynamic gaits such as bounding and jumping. We show two main results: (1)The adaptive controller is able to track the resonant frequency of the robot which is a function of different body parameters (2)controllers based on dynamical systems as we present are able to "recognize” mechanically intrinsic modes of locomotion, adapt to them and enforce them. More specifically the main results are supported by several experiments, showing first that the adaptive controller is constantly tracking body properties and readjusting to them. Second, that important gait parameters are dependent on the geometry and movement of the robot and the controller can account for that. Third, that local control is sufficient and the adaptive controller can adapt to the different mechanical modes. And finally, that key properties of the gaits are not only depending on properties of the body but also the actual mode of movement that the body is operating in. We show that even if we specify the gait pattern on the level of the CPG the chosen gait pattern does not necessarily correspond to the CPG's pattern. Furthermore, we present the analytical treatment of adaptive frequency oscillators in closed feedback loops, and compare the results to the data from the robot experiment

Push recovery with stepping strategy based on time-projection control

In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.Comment: 20 pages journal pape

A macroscopic analytical model of collaboration in distributed robotic systems

In this article, we present a macroscopic analytical model of collaboration in a group of reactive robots. The model consists of a series of coupled differential equations that describe the dynamics of group behavior. After presenting the general model, we analyze in detail a case study of collaboration, the stick-pulling experiment, studied experimentally and in simulation by Ijspeert et al. [Autonomous Robots, 11, 149-171]. The robots' task is to pull sticks out of their holes, and it can be successfully achieved only through the collaboration of two robots. There is no explicit communication or coordination between the robots. Unlike microscopic simulations (sensor-based or using a probabilistic numerical model), in which computational time scales with the robot group size, the macroscopic model is computationally efficient, because its solutions are independent of robot group size. Analysis reproduces several qualitative conclusions of Ijspeert et al.: namely, the different dynamical regimes for different values of the ratio of robots to sticks, the existence of optimal control parameters that maximize system performance as a function of group size, and the transition from superlinear to sublinear performance as the number of robots is increased

Modeling discrete and rhythmic movements through motor primitives: a review

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the wor

CPG-RL: Learning Central Pattern Generators for Quadruped Locomotion

In this letter, we present a method for integrating central pattern generators (CPGs), i.e. systems of coupled oscillators, into the deep reinforcement learning (DRL) framework to produce robust and omnidirectional quadruped locomotion. The agent learns to directly modulate the intrinsic oscillator setpoints (amplitude and frequency) and coordinate rhythmic behavior among different oscillators. This approach also allows the use of DRL to explore questions related to neuroscience, namely the role of descending pathways, interoscillator couplings, and sensory feedback in gait generation. We train our policies in simulation and perform a sim-to-real transfer to the Unitree A1 quadruped, where we observe robust behavior to disturbances unseen during training, most notably to a dynamically added 13.75 kg load representing 115% of the nominal quadruped mass. We test several different observation spaces based on proprioceptive sensing and show that our framework is deployable with no domain randomization and very little feedback, where along with the oscillator states, it is possible to provide only contact booleans in the observation space. Video results can be found at https://youtu.be/xqXHLzLsEV4.Comment: Accepted for IEEE Robotics and Automation Letters, September 202

Biorobotics: Using robots to emulate and investigate agile animal locomotion

The graceful and agile movements of animals are difficult to analyze and emulate because locomotion is the result of a complex interplay of many components: the central and peripheral nervous systems, the musculoskeletal system, and the environment. The goals of biorobotics are to take inspiration from biological principles to design robots that match the agility of animals, and to use robots as scientific tools to investigate animal adaptive behavior. Used as physical models, biorobots contribute to hypothesis testing in fields such as hydrodynamics, biomechanics, neuroscience, and prosthetics. Their use may contribute to the design of prosthetic devices that more closely take human locomotion principles into account