Frequency-Aware Model Predictive Control

Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors cannot be only a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highly compliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance.

Time-Optimal Path-Following Operation in the Presence of Uncertainty

Dominique Bonvin, Timm Faulwasser, Alejandro Gabriel Marchetti, Predrag Milosavljevic

Path-following tasks, which refer to dynamic motion planning along pre-specified geometric references, are frequently encountered in applications such as milling, robot-supported measurements, and trajectory planning for autonomous vehicles. Different convex and non-convex optimal control formulations have been proposed to tackle these problems for the case of perfect models. This paper analyzes path-following problems in the presence of plant-model mismatch. The proposed adaptation strategies rely on concepts that are well known in the field of real-time optimization. We present conditions guaranteeing that, upon convergence, a minimum-time solution is attained despite the presence of plant-model mismatch. We draw upon a simulated robotic example to illustrate our results.

Ieee2016

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.

EPFL2018

Memory of Motion for Initializing Optimization in Robotics

Teguh Santoso Lembono

Many robotics problems are formulated as optimization problems. However, most optimization solvers in robotics are locally optimal and the performance depends a lot on the initial guess. For challenging problems, the solver will often get stuck at poor local optima without a good initialization. In this thesis, we consider various techniques to provide a good initial guess to the solver based on previous experience. We use the term memory of motion to collectively refer to these techniques. The key idea is to use the existing system models, cost functions, and simulation tools to generate a database of solutions, and then construct a memory of motion model. During online execution, we can then query the initial guess of a given task from the memory of motion. We show that it improves the solver performance in terms of the solution quality, the success rates, and the computation time. We consider two different formulations, i.e., supervised learning and probability density estimation. In the first part, we formulate a regression problem to find the mapping between the task parameters and the solutions. Such a formulation is convenient, as there are a lot of function approximations available, but using them as a black box tool may result in poor predictions. It is especially the case for multimodal problems where there can be several different solutions for a given task and standard function approximators will simply average the different modes. We first propose an ensemble of function approximators that can handle multimodal problems to initialize an optimization-based motion planner. We then investigate the problem of initializing an optimal control solver for legged robot locomotion, where we need to also provide the initial guess of the control sequence. We evaluate the effect of different initialization components on the optimal control solver performance. In the second part, we consider another formulation by first transforming the cost function into an unnormalized Probability Density Function (PDF) and approximating it using various models. This formulation addresses several shortcomings of the supervised learning approaches by using the cost function itself to train or construct the predictive model. It allows us to generate initial guesses that have high probabilities of having low-cost values instead of simply imitating the dataset. We first show that we can obtain a trajectory distribution of an iLQR problem as a Gaussian distribution, and tracking this distribution results in a cost-efficient and robust controller. We then propose a generative adversarial framework to learn the distribution of robot configurations under constraints. Finally, we use tensor methods to approximate the unnormalized PDF. Since it does not rely on gradient information, the method is quite robust in finding the (possibly multiple) global optima or at least the good local optima of various challenging problems including some benchmark optimization functions, inverse kinematics, and motion planning.