A Control and Optimization Framework for Robot Locomotion

Despite great efforts in designing legged robots, we are still far from the adaptivity, efficiency and robustness with which animals can move. Observations from successful biomimetic designs highlight the significant role of clever morphological design in achieving such performance. In addition, the important role of the controller in improving the locomotion performance is undoubtable. In fact, there is a complex link between morphology and motor control of locomoting systems. In animals’ locomotion, there is a large number of evidence showing the effective link between their morphology and functionality. Motivated by biological observations, similar questions can be posed from a robotics perspective: “what are the relative and complementary roles of robot control and morphology (similar to animal’s brain and body) in the generated locomotor behavior?”, and more pragmatically, “how can we take lessons from these observations to reduce the current gap between robots’ locomotion performance and what is observed in their biological counterparts?”. These are the fundamental questions that have motivated studies in this thesis. While empirical studies are essential to address aforementioned questions, they require simplifying contexts to yield insightful predictions and examinable theories. Both theoretical and physical models (i.e. simulations and robots) can significantly contribute in providing such insights. While robot experiments are essential to evaluate and explore the involved biological concept, they are usually time-consuming and costly. Hence, it would be advantageous if one could exploit the power of theoretical models for development of ideas and hypotheses before their implementation on the real robot. In this thesis, we aim at leveraging the strength of theoretical models to study the above-mentioned questions, namely, the relative role of control and morphology in improving the robot locomotion functionalities. To provide useful theoretical models, we take a step-wise approach, where we start from model-free methods and proceed with advancing the locomotion control by incorporating dynamics models at different levels of complexity. In particular, we develop a pool of robot models, starting from a simplified massless leg to a detailed dynamics model of the leg, to a 2D quadruped with spine joint and eventually to a 3D detailed dynamics model of a quadruped. Along with developing dynamics model of the robot, we devise a set of control and optimization techniques with the main goal of improving locomotion performance. There are several performance criteria to consider (such as energy efficiency, maneuverability, adaptivity to unknown terrains) and a key question is how to build the control architecture to hold a proper trade-off between these partially contradicting criteria. We take advantage of the developed dynamic models in both (i) improving the controller performance and (ii) implementing analytical tools to evaluate and compare different locomotion performance criteria. The central outcome of this thesis is a bio-inspired modeling, control, and optimization framework for legged robot locomotion, which is evaluated on a set of robots with different morphologies. In all cases, we explore how the locomotion performance can be improved by introducing new control techniques or be influenced by the morphological aspects (such as joint configuration and mass distribution). In particular, we show the effect of using more detailed dynamics model to improve the predictive performance of the simulations both for analyzing morphological factors and for robustness of the controller to internal (e.g. change in the inertial parameters) and external (e.g. walking on rough terrains) perturbations. The framework is generic and is used to model, control and analyze locomotion gaits for three compliant quadruped robots (Locomorph, Cheetah-Cub and Bobcat robots) and a modular robot (Roombots).

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

Co-evolution of Morphology and Control of Virtual Legged Robots for the Steering Task

Auke Ijspeert, Ken Larpin, Soha Pouya, Jesse van den Kieboom

Co-evolution of morphology and control is a powerful approach in robotics to study performance on a particular task, considering mechanical structure and control as a whole to accomplish a certain goal. Co-evolutionary methods have been used to study the effect of these two fundamental components, in particular when applied to locomotion and reaching tasks. The resulting robots are usually evolved in simulation for a particular static task, making it difficult to transfer the results to a real robotic system, where a certain controllability (beyond the scope of the particular task) is desired. In this work, we are interested in evolving a robot with an externally controllable behavior, in particular considering locomotion tasks. We investigate to what extent co-evolution can outperform the more traditional approach of evolving only the robot control. The locomotion behavior is evolved for a simulated quadruped robot, using a multi-objective evolutionary algorithm, considering speed and energy efficiency as the main objectives. Additionally, we introduce a third objective where we provide the robot with an external command indicating the robot locomotion direction, allowing us to steer the robot once it is evolved. The resulting quadrupedal robots show improved performance on the steering task when compared to robots where only control is evolved.

2011

Towards Robust Bipedal Locomotion

Salman Faraji

Thanks to better actuator technologies and control algorithms, humanoid robots to date can perform a wide range of locomotion activities outside lab environments. These robots face various control challenges like high dimensionality, contact switches during locomotion and a floating-base nature which makes them fall all the time. A rich set of sensory inputs and a high-bandwidth actuation are often needed to ensure fast and effective reactions to unforeseen conditions, e.g., terrain variations, external pushes, slippages, unknown payloads, etc. State of the art technologies today seem to provide such valuable hardware components. However, regarding software, there is plenty of room for improvement. Locomotion planning and control problems are often treated separately in conventional humanoid control algorithms. The control challenges mentioned above are probably the main reason for such separation. Here, planning refers to the process of finding consistent open-loop trajectories, which may take arbitrarily long computations off-line. Control, on the other hand, should be done very fast online to ensure stability. In this thesis, we want to link planning and control problems again and enable for online trajectory modification in a meaningful way. First, we propose a new way of describing robot geometries like molecules which breaks the complexity of conventional models. We use this technique and derive a planning algorithm that is fast enough to be used online for multi-contact motion planning. Similarly, we derive 3LP, a simplified linear three-mass model for bipedal walking, which offers orders of magnitude faster computations than full mechanical models. Next, we focus more on walking and use the 3LP model to formulate online control algorithms based on the foot-stepping strategy. The method is based on model predictive control, however, we also propose a faster controller with time-projection that demonstrates a close performance without numerical optimizations. We also deploy an efficient implementation of inverse dynamics together with advanced sensor fusion and actuator control algorithms to ensure a precise and compliant tracking of the simplified 3LP trajectories. Extensive simulations and hardware experiments on COMAN robot demonstrate effectiveness and strengths of our method. This thesis goes beyond humanoid walking applications. We further use the developed modeling tools to analyze and understand principles of human locomotion. Our 3LP model can describe the exchange of energy between human limbs in walking to some extent. We use this property to propose a metabolic-cost model of human walking which successfully describes trends in various conditions. The intrinsic power of the 3LP model to generate walking gaits in all these conditions makes it a handy solution for walking control and gait analysis, despite being yet a simplified model. To fill the reality gap, finally, we propose a kinematic conversion method that takes 3LP trajectories as input and generates more human-like postures. Using this method, the 3LP model, and the time-projecting controller, we introduce a graphical user interface in the end to simulate periodic and transient human-like walking conditions. We hope to use this combination in future to produce faster and more human-like walking gaits, possibly with more capable humanoid robots.