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 can be 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

Balancing experiments on a torque-controlled humanoid with hierarchical inverse dynamics

Recently several hierarchical inverse dynamics controllers based on cascades of quadratic programs have been proposed for application on torque controlled robots. They have important theoretical benefits but have never been implemented on a torque controlled robot where model inaccuracies and real-time computation requirements can be problematic. In this contribution we present an experimental evaluation of these algorithms in the context of balance control for a humanoid robot. The presented experiments demonstrate the applicability of the approach under real robot conditions (i.e. model uncertainty, estimation errors, etc). We propose a simplification of the optimization problem that allows us to decrease computation time enough to implement it in a fast torque control loop. We implement a momentum-based balance controller which shows robust performance in face of unknown disturbances, even when the robot is standing on only one foot. In a second experiment, a tracking task is evaluated to demonstrate the performance of the controller with more complicated hierarchies. Our results show that hierarchical inverse dynamics controllers can be used for feedback control of humanoid robots and that momentum-based balance control can be efficiently implemented on a real robot.Comment: appears in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 201

Momentum Control with Hierarchical Inverse Dynamics on a Torque-Controlled Humanoid

Hierarchical inverse dynamics based on cascades of quadratic programs have been proposed for the control of legged robots. They have important benefits but to the best of our knowledge have never been implemented on a torque controlled humanoid where model inaccuracies, sensor noise and real-time computation requirements can be problematic. Using a reformulation of existing algorithms, we propose a simplification of the problem that allows to achieve real-time control. Momentum-based control is integrated in the task hierarchy and a LQR design approach is used to compute the desired associated closed-loop behavior and improve performance. Extensive experiments on various balancing and tracking tasks show very robust performance in the face of unknown disturbances, even when the humanoid is standing on one foot. Our results demonstrate that hierarchical inverse dynamics together with momentum control can be efficiently used for feedback control under real robot conditions.Comment: 21 pages, 11 figures, 4 tables in Autonomous Robots (2015

Offline and Online Planning and Control Strategies for the Multi-Contact and Biped Locomotion of Humanoid Robots

In the past decades, the Research on humanoid robots made progress forward accomplishing exceptionally dynamic and agile motions. Starting from the DARPA Robotic Challenge in 2015, humanoid platforms have been successfully employed to perform more and more challenging tasks with the eventual aim of assisting or replacing humans in hazardous and stressful working situations. However, the deployment of these complex machines in realistic domestic and working environments still represents a high-level challenge for robotics. Such environments are characterized by unstructured and cluttered settings with continuously varying conditions due to the dynamic presence of humans and other mobile entities, which cannot only compromise the operation of the robotic system but can also pose severe risks both to the people and the robot itself due to unexpected interactions and impacts. The ability to react to these unexpected interactions is therefore a paramount requirement for enabling the robot to adapt its behavior to the task needs and the characteristics of the environment. Further, the capability to move in a complex and varying environment is an essential skill for a humanoid robot for the execution of any task. Indeed, human instructions may often require the robot to move and reach a desired location, e.g., for bringing an object or for inspecting a specific place of an infrastructure. In this context, a flexible and autonomous walking behavior is an essential skill, study of which represents one of the main topics of this Thesis, considering disturbances and unfeasibilities coming both from the environment and dynamic obstacles that populate realistic scenarios.  Locomotion planning strategies are still an open theme in the humanoids and legged robots research and can be classified in sample-based and optimization-based planning algorithms. The first, explore the configuration space, finding a feasible path between the start and goal robot’s configuration with different logic depending on the algorithm. They suffer of a high computational cost that often makes difficult, if not impossible, their online implementations but, compared to their counterparts, they do not need any environment or robot simplification to find a solution and they are probabilistic complete, meaning that a feasible solution can be certainly found if at least one exists. The goal of this thesis is to merge the two algorithms in a coupled offline-online planning framework to generate an offline global trajectory with a sample-based approach to cope with any kind of cluttered and complex environment, and online locally refine it during the execution, using a faster optimization-based algorithm that more suits an online implementation. The offline planner performances are improved by planning in the robot contact space instead of the whole-body robot configuration space, requiring an algorithm that maps the two state spaces.   The framework proposes a methodology to generate whole-body trajectories for the motion of humanoid and legged robots in realistic and dynamically changing environments.  This thesis focuses on the design and test of each component of this planning framework, whose validation is carried out on the real robotic platforms CENTAURO and COMAN+ in various loco-manipulation tasks scenarios. &nbsp

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