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

Dominique Bonvin, Timm Faulwasser, Alejandro Gabriel Marchetti, Predrag Milosavljevic
Ieee, 2016
Article de conférence

Résumé

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.

Official source

https://infoscience.epfl.ch/record/217554?ln=fr

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Frequency-Aware Model Predictive Control

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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.

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Legged machines have the potential to traverse terrain that wheeled robots cannot. These capabilities are useful in scenarios such as stairs in homes or debris-filled disaster scenes, such as earthquake areas. This thesis develops one of the algorithms necessary to achieve such a task, a motion-planner, which translates a high-level task into a desired motion-plan for a legged robot to execute. A core difficulty in legged locomotion is that a forward body movement cannot be directly generated, but results from contact forces between the end-effectors and the environment. Furthermore, there are various physical restrictions on the contact forces that can be generated. These can make hand-crafting valid motions for all the interdependent quantities such as body motion, end-effector motion and contact forces tedious and even infeasible for complex tasks. Alternatively, Trajectory Optimization can be utilized to generate motions in a more general, automated way. Only a high-level task is specified, while the algorithm determines the motions and forces taking into account the physical restrictions of legged locomotion. This approach is attractive because once the problem has been properly modeled, the algorithm would, in an ideal case, produce motions for any high-level task, solving legged locomotion planning on a general level. This thesis presents approaches to transcribe, using e.g. collocation, the legged locomotion problem into a mathematical optimization problem, then solvable by off-the-shelf software. The three developed motion-planning algorithms generate motion-plans for increasingly complex terrains and tasks. Simulation and experiments on the quadruped robots HyQ and ANYmal verify the physical correctness of the motion-plans. The final formulation and main contribution of this thesis holistically determines the gait- sequence, step-timings, footholds, contact forces, swing-leg motions and 6-dimensional body motion, given a desired goal state and 2.5D height map of the non-flat terrain. We model the robot as a single rigid body (SRBD) controlled by the contact forces at the end- effectors. Our novel phase-based parameterization of end-effector motion and forces allows optimizing over the discrete gait sequence using only continuous decision variables. The algorithm efficiently generates highly dynamic motion-plans with flight-phases for legged systems, such as monopeds, bipeds, and quadrupeds.

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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.

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EPFL2022