Intelligent Systems
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2023


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Stagewise Newton Method for Dynamic Game Control With Imperfect State Observation

Jordana, A., Hammoud, B., Carpentier, J., Righetti, L.

IEEE Control Systems Letters, 6, pages: 3241-3246, IEEE, Piscataway, NJ, USA, 2022 (article)

DOI [BibTex]

DOI [BibTex]

2021


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Robust walking based on MPC with viability guarantees

Yeganegi, M. H., Khadiv, M., Prete, A. D., Moosavian, S. A. A., Righetti, L.

IEEE Transactions on Robotics, October 2021 (article) Accepted

Abstract
Model predictive control (MPC) has shown great success for controlling complex systems such as legged robots. However, when closing the loop, the performance and feasibility of the finite horizon optimal control problem (OCP) solved at each control cycle is not guaranteed anymore. This is due to model discrepancies, the effect of low-level controllers, uncertainties and sensor noise. To address these issues, we propose a modified version of a standard MPC approach used in legged locomotion with viability (weak forward invariance) guarantees. In this approach, instead of adding a (conservative) terminal constraint to the problem, we propose to use the measured state projected to the viability kernel in the OCP solved at each control cycle. Moreover, we use past experimental data to find the best cost weights, which measure a combination of performance, constraint satisfaction robustness, or stability (invariance). These interpretable costs measure the trade off between robustness and performance. For this purpose, we use Bayesian optimization (BO) to systematically design experiments that help efficiently collect data to learn a cost function leading to robust performance. Our simulation results with different realistic disturbances (i.e. external pushes, unmodeled actuator dynamics and computational delay) show the effectiveness of our approach to create robust controllers for humanoid robots.

link (url) [BibTex]

2021

link (url) [BibTex]


The o80 C++ templated toolbox: Designing customized Python APIs for synchronizing realtime processes
The o80 C++ templated toolbox: Designing customized Python APIs for synchronizing realtime processes

Berenz, V., Naveau, M., Widmaier, F., Wüthrich, M., Passy, J., Guist, S., Büchler, D.

Journal of Open Source Software, 6(66):Article no. 2752, October 2021 (article)

Abstract
o80 (pronounced "oh-eighty") is software for synchronizing and organizing message exchange between (realtime) processes via simple customized Python APIs. Its target domain is robotics and machine learning. Our motivation for developing o80 is to ease the setup of robotics experiments (i.e., integration of various hardware and software) by machine learning scientists. Such setup typically requires time and technical effort, especially when realtime processes are involved. Ideally, scientists should have access to a simple Python API that hides the lower level communication details and simply allows the sending of actions and receiving of observations. o80 is a tool box for creating such API.

link (url) DOI [BibTex]


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Impedance Optimization for Uncertain Contact Interactions Through Risk Sensitive Optimal Control

Hammoud, B., Khadiv, M., Righetti, L.

IEEE Robotics and Automation Letters, Robotics and Automation Letters, Early Access(999):1-1, IEEE, ABC, March 2021 (article)

Abstract
This paper addresses the problem of computing optimal impedance schedules for legged locomotion tasks involving complex contact interactions. We formulate the problem of impedance regulation as a trade-off between disturbance rejection and measurement uncertainty. We extend a stochastic optimal control algorithm known as Risk Sensitive Control to take into account measurement uncertainty and propose a formal way to include such uncertainty for unknown contact locations. The approach can efficiently generate optimal state and control trajectories along with local feedback control gains, i.e. impedance schedules. Extensive simulations demonstrate the capabilities of the approach in generating meaningful stiffness and damping modulation patterns before and after contact interaction. For example, contact forces are reduced during early contacts, damping increases to anticipate a high impact event and tracking is automatically traded-off for increased stability. In particular, we show a significant improvement in performance during jumping and trotting tasks with a simulated quadruped robot.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Efficient Multi-Contact Pattern Generation with Sequential Convex Approximations of the Centroidal Dynamics

Ponton, B., Khadiv, M., Meduri, A., Righetti, L.

IEEE Transactions on Robotics, Early access, pages: 1-19, IEEE, February 2021 (article)

Abstract
This article investigates the problem of efficient computation of physically consistent multicontact behaviors. Recent work showed that under mild assumptions, the problem could be decomposed into simpler kinematic and centroidal dynamic optimization problems. Based on this approach, we propose a general convex relaxation of the centroidal dynamics leading to two computationally efficient algorithms based on iterative resolutions of second-order cone programs. They optimize centroidal trajectories, contact forces, and importantly the timing of the motions. We include the approach in a kinodynamic optimization method to generate full-body movements. Finally, the approach is embedded in a mixed-integer solver to further find dynamically consistent contact sequences. Extensive numerical experiments demonstrate the computational efficiency of the approach, suggesting that it could be used in a fast receding horizon control loop. Executions of the planned motions on simulated humanoids and quadrupeds and on a real quadruped robot further show the quality of the optimized motions.

link (url) DOI [BibTex]


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Robot Learning with Crash Constraints

Marco, A., Baumann, D., Khadiv, M., Hennig, P., Righetti, L., Trimpe, S.

IEEE Robotics and Automation Letters, 6(2):1439-1446, IEEE, February 2021 (article)

Abstract
In the past decade, numerous machine learning algorithms have been shown to successfully learn optimal policies to control real robotic systems. However, it is common to encounter failing behaviors as the learning loop progresses. Specifically, in robot applications where failing is undesired but not catastrophic, many algorithms struggle with leveraging data obtained from failures. This is usually caused by (i) the failed experiment ending prematurely, or (ii) the acquired data being scarce or corrupted. Both complicate the design of proper reward functions to penalize failures. In this paper, we propose a framework that addresses those issues. We consider failing behaviors as those that violate a constraint and address the problem of learning with crash constraints, where no data is obtained upon constraint violation. The no-data case is addressed by a novel GP model (GPCR) for the constraint that combines discrete events (failure/success) with continuous observations (only obtained upon success). We demonstrate the effectiveness of our framework on simulated benchmarks and on a real jumping quadruped, where the constraint threshold is unknown a priori. Experimental data is collected, by means of constrained Bayesian optimization, directly on the real robot. Our results outperform manual tuning and GPCR proves useful on estimating the constraint threshold.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Variable Horizon MPC with Swing Foot Dynamics for Bipedal Walking Control

Daneshmand, E., Khadiv, M., Grimminger, F., Righetti, L.

IEEE Robotics and Automation Letters, 6, pages: 2349-2356, February 2021 (article)

Abstract
In this paper, we present a novel two-level variable Horizon Model Predictive Control (VH-MPC) framework for bipedal locomotion. In this framework, the higher level computes the landing location and timing (horizon length) of the swing foot to stabilize the unstable part of the center of mass (CoM) dynamics, using feedback from the CoM states. The lower level takes into account the swing foot dynamics and generates dynamically consistent trajectories for landing at the desired time as close as possible to the desired location. To do that, we use a simplified model of the robot dynamics projected in swing foot space that takes into account joint torque constraints as well as the friction cone constraints of the stance foot. We show the effectiveness of our proposed control framework by implementing robust walking patterns on our torque-controlled and open-source biped robot, Bolt. We report extensive simulations and real robot experiments in the presence of various disturbances and uncertainties.

DOI [BibTex]

DOI [BibTex]


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Reactive Balance Control for Legged Robots under Visco-Elastic Contacts

Flayols, T., Prete, A. D., Khadiv, M., Mansard, N., Righetti, L.

Applied Sciences, 11(1)(1):353, MDPI, January 2021 (article)

Abstract
Contacts between robots and environment are often assumed to be rigid for control purposes. This assumption can lead to poor performance when contacts are soft and/or underdamped. However, the problem of balancing on soft contacts has not received much attention in the literature. This paper presents two novel approaches to control a legged robot balancing on visco-elastic contacts, and compares them to other two state-of-the-art methods. Our simulation results show that performance heavily depends on the contact stiffness and the noises/uncertainties introduced in the simulation. Briefly, the two novel controllers performed best for soft/medium contacts, whereas “inverse-dynamics control under rigid-contact assumptions” was the best one for stiff contacts. Admittance control was instead the most robust, but suffered in terms of performance. These results shed light on this challenging problem, while pointing out interesting directions for future investigation.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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On the use of simulation in robotics: Opportunities challenges, and suggestions for moving forward

Choi, H., Crump, C., Duriez, C., Elmquist, A., Hager, G., Han, D., Hearl, F., Hodgins, J., Jain, A., Leve, F., Li, C., Meier, F., Negrut, D., Righetti, L., Rodriguez, A., Tan, J., Trinkle, J.

PNAS, 118(1):e1907856118, January 2021 (article)

DOI [BibTex]

DOI [BibTex]


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Jerk Control of Floating Base Systems With Contact-Stable Parameterized Force Feedback

Gazar, A., Nava, G., Chavez, F. J. A., Pucci, D.

IEEE Transactions on Robotics, 37(1):1-15, IEEE, 2021 (article)

DOI [BibTex]

DOI [BibTex]

2020


Learning Variable Impedance Control for Contact Sensitive Tasks
Learning Variable Impedance Control for Contact Sensitive Tasks

Bogdanovic, M., Khadiv, M., Righetti, L.

IEEE Robotics and Automation Letters, 5(4), IEEE, July 2020 (article)

Abstract
Reinforcement learning algorithms have shown great success in solving different problems ranging from playing video games to robotics. However, they struggle to solve delicate robotic problems, especially those involving contact interactions. Though in principle a policy outputting joint torques should be able to learn these tasks, in practice we see that they have difficulty to robustly solve the problem without any structure in the action space. In this paper, we investigate how the choice of action space can give robust performance in presence of contact uncertainties. We propose to learn a policy that outputs impedance and desired position in joint space as a function of system states without imposing any other structure to the problem. We compare the performance of this approach to torque and position control policies under different contact uncertainties. Extensive simulation results on two different systems, a hopper (floating-base) with intermittent contacts and a manipulator (fixed-base) wiping a table, show that our proposed approach outperforms policies outputting torque or position in terms of both learning rate and robustness to environment uncertainty.

DOI [BibTex]

2020

DOI [BibTex]


Walking Control Based on Step Timing Adaptation
Walking Control Based on Step Timing Adaptation

Khadiv, M., Herzog, A., Moosavian, S. A. A., Righetti, L.

IEEE Transactions on Robotics, 36, pages: 629 - 643, IEEE, June 2020 (article)

Abstract
Step adjustment can improve the gait robustness of biped robots; however, the adaptation of step timing is often neglected as it gives rise to nonconvex problems when optimized over several footsteps. In this article, we argue that it is not necessary to optimize walking over several steps to ensure gait viability and show that it is sufficient to merely select the next step timing and location. Using this insight, we propose a novel walking pattern generator that optimally selects step location and timing at every control cycle. Our approach is computationally simple compared to standard approaches in the literature, yet guarantees that any viable state will remain viable in the future. We propose a swing foot adaptation strategy and integrate the pattern generator with an inverse dynamics controller that does not explicitly control the center of mass nor the foot center of pressure. This is particularly useful for biped robots with limited control authority over their foot center of pressure, such as robots with point feet or passive ankles. Extensive simulations on a humanoid robot with passive ankles demonstrate the capabilities of the approach in various walking situations, including external pushes and foot slippage, and emphasize the importance of step timing adaptation to stabilize walking.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Robust Humanoid Contact Planning with Learned Zero-and One-Step Capturability Prediction

Lin, Y., Righetti, L., Berenson, D.

IEEE Robotics and Automation Letters, Robotics and Automation Letters, 5, pages: 2451-2458, IEEE, February 2020 (article)

Abstract
Humanoid robots maintain balance and navigate by controlling the contact wrenches applied to the environ- ment. While it is possible to plan dynamically-feasible motion that applies appropriate wrenches using existing methods, a humanoid may also be affected by external disturbances. Existing systems typically rely on controllers to reactively recover from disturbances. However, such controllers may fail when the robot cannot reach contacts capable of rejecting a given disturbance. In this paper, we propose a search-based footstep planner which aims to maximize the probability of the robot successfully reaching the goal without falling as a result of a disturbance. The planner considers not only the poses of the planned contact sequence, but also alternative contacts near the planned contact sequence that can be used to recover from external disturbances. Although this additional consideration significantly increases the computation load, we train neural networks to efficiently predict multi-contact zero- step and one-step capturability, which allows the planner to generate robust contact sequences efficiently. Our results show that our approach generates footstep sequences that are more robust to external disturbances than a conventional footstep planner in four challenging scenarios.

[BibTex]

[BibTex]

2019


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Epstein, Project Maven, and Some Reasons to Think About Where We Get Our Funding [Ethical, Legal, and Societal Issues]

Bretl, T., Righetti, L., Madhavan, R.

IEEE Robotics & Automation Magazine, 26, December 2019 (article)

[BibTex]

2019

[BibTex]


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Unintended Consequences of Biased Robotic and Artificial Intelligence Systems [Ethical, Legal, and Societal Issues]

Righetti, L., Madhavan, R., Chatila, R.

IEEE Robotics & Automation Magazine, 26, September 2019 (article)

[BibTex]

[BibTex]


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Optimal Stair Climbing Pattern Generation for Humanoids Using Virtual Slope and Distributed Mass Model

Shahrokhshahi, A., Yousefi-Koma, A., Khadiv, M., Mansouri, S., Mohtasebi, S. S.

Journal of Intelligent and Robotics Systems, 94:1, pages: 43-59, April 2019 (article)

DOI [BibTex]

DOI [BibTex]


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A Robustness Analysis of Inverse Optimal Control of Bipedal Walking

Rebula, J. R., Schaal, S., Finley, J., Righetti, L.

IEEE Robotics and Automation Letters, 4(4):4531-4538, 2019 (article)

DOI [BibTex]

DOI [BibTex]


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Rigid vs compliant contact: an experimental study on biped walking

Khadiv, M., Moosavian, S. A. A., Yousefi-Koma, A., Sadedel, M., Ehsani-Seresht, A., Mansouri, S.

Multibody System Dynamics, 45(4):379-401, 2019 (article)

DOI [BibTex]

DOI [BibTex]


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Birch tar production does not prove Neanderthal behavioral complexity

Schmidt, P., Blessing, M., Rageot, M., Iovita, R., Pfleging, J., Nickel, K. G., Righetti, L., Tennie, C.

Proceedings of the National Academy of Sciences (PNAS), 116(36):17707-17711, 2019 (article)

DOI [BibTex]

DOI [BibTex]

2018


Robust Physics-based Motion Retargeting with Realistic Body Shapes
Robust Physics-based Motion Retargeting with Realistic Body Shapes

Borno, M. A., Righetti, L., Black, M. J., Delp, S. L., Fiume, E., Romero, J.

Computer Graphics Forum, 37, pages: 6:1-12, July 2018 (article)

Abstract
Motion capture is often retargeted to new, and sometimes drastically different, characters. When the characters take on realistic human shapes, however, we become more sensitive to the motion looking right. This means adapting it to be consistent with the physical constraints imposed by different body shapes. We show how to take realistic 3D human shapes, approximate them using a simplified representation, and animate them so that they move realistically using physically-based retargeting. We develop a novel spacetime optimization approach that learns and robustly adapts physical controllers to new bodies and constraints. The approach automatically adapts the motion of the mocap subject to the body shape of a target subject. This motion respects the physical properties of the new body and every body shape results in a different and appropriate movement. This makes it easy to create a varied set of motions from a single mocap sequence by simply varying the characters. In an interactive environment, successful retargeting requires adapting the motion to unexpected external forces. We achieve robustness to such forces using a novel LQR-tree formulation. We show that the simulated motions look appropriate to each character’s anatomy and their actions are robust to perturbations.

pdf video Project Page [BibTex]

2018

pdf video Project Page [BibTex]


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Learning a Structured Neural Network Policy for a Hopping Task.

Viereck, J., Kozolinsky, J., Herzog, A., Righetti, L.

IEEE Robotics and Automation Letters, 3(4):4092-4099, October 2018 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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The Impact of Robotics and Automation on Working Conditions and Employment [Ethical, Legal, and Societal Issues]

Pham, Q., Madhavan, R., Righetti, L., Smart, W., Chatila, R.

IEEE Robotics and Automation Magazine, 25(2):126-128, June 2018 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Lethal Autonomous Weapon Systems [Ethical, Legal, and Societal Issues]

Righetti, L., Pham, Q., Madhavan, R., Chatila, R.

IEEE Robotics \& Automation Magazine, 25(1):123-126, March 2018 (article)

Abstract
The topic of lethal autonomous weapon systems has recently caught public attention due to extensive news coverage and apocalyptic declarations from famous scientists and technologists. Weapon systems with increasing autonomy are being developed due to fast improvements in machine learning, robotics, and automation in general. These developments raise important and complex security, legal, ethical, societal, and technological issues that are being extensively discussed by scholars, nongovernmental organizations (NGOs), militaries, governments, and the international community. Unfortunately, the robotics community has stayed out of the debate, for the most part, despite being the main provider of autonomous technologies. In this column, we review the main issues raised by the increase of autonomy in weapon systems and the state of the international discussion. We argue that the robotics community has a fundamental role to play in these discussions, for its own sake, to provide the often-missing technical expertise necessary to frame the debate and promote technological development in line with the IEEE Robotics and Automation Society (RAS) objective of advancing technology to benefit humanity.

link (url) DOI [BibTex]

link (url) DOI [BibTex]

2016


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

Herzog, A., Rotella, N., Mason, S., Grimminger, F., Schaal, S., Righetti, L.

Autonomous Robots, 40(3):473-491, 2016 (article)

Abstract
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.

link (url) DOI [BibTex]

2015


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Kinematic and gait similarities between crawling human infants and other quadruped mammals

Righetti, L., Nylen, A., Rosander, K., Ijspeert, A.

Frontiers in Neurology, 6(17), February 2015 (article)

Abstract
Crawling on hands and knees is an early pattern of human infant locomotion, which offers an interesting way of studying quadrupedalism in one of its simplest form. We investigate how crawling human infants compare to other quadruped mammals, especially primates. We present quantitative data on both the gait and kinematics of seven 10-month-old crawling infants. Body movements were measured with an optoelectronic system giving precise data on 3-dimensional limb movements. Crawling on hands and knees is very similar to the locomotion of non-human primates in terms of the quite protracted arm at touch-down, the coordination between the spine movements in the lateral plane and the limbs, the relatively extended limbs during locomotion and the strong correlation between stance duration and speed of locomotion. However, there are important differences compared to primates, such as the choice of a lateral-sequence walking gait, which is similar to most non-primate mammals and the relatively stiff elbows during stance as opposed to the quite compliant gaits of primates. These finding raise the question of the role of both the mechanical structure of the body and neural control on the determination of these characteristics.

link (url) DOI [BibTex]

2015

link (url) DOI [BibTex]

2014


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An autonomous manipulation system based on force control and optimization

Righetti, L., Kalakrishnan, M., Pastor, P., Binney, J., Kelly, J., Voorhies, R. C., Sukhatme, G. S., Schaal, S.

Autonomous Robots, 36(1-2):11-30, January 2014 (article)

Abstract
In this paper we present an architecture for autonomous manipulation. Our approach is based on the belief that contact interactions during manipulation should be exploited to improve dexterity and that optimizing motion plans is useful to create more robust and repeatable manipulation behaviors. We therefore propose an architecture where state of the art force/torque control and optimization-based motion planning are the core components of the system. We give a detailed description of the modules that constitute the complete system and discuss the challenges inherent to creating such a system. We present experimental results for several grasping and manipulation tasks to demonstrate the performance and robustness of our approach.

link (url) DOI [BibTex]

2014

link (url) DOI [BibTex]


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Learning of grasp selection based on shape-templates

Herzog, A., Pastor, P., Kalakrishnan, M., Righetti, L., Bohg, J., Asfour, T., Schaal, S.

Autonomous Robots, 36(1-2):51-65, January 2014 (article)

Abstract
The ability to grasp unknown objects still remains an unsolved problem in the robotics community. One of the challenges is to choose an appropriate grasp configuration, i.e., the 6D pose of the hand relative to the object and its finger configuration. In this paper, we introduce an algorithm that is based on the assumption that similarly shaped objects can be grasped in a similar way. It is able to synthesize good grasp poses for unknown objects by finding the best matching object shape templates associated with previously demonstrated grasps. The grasp selection algorithm is able to improve over time by using the information of previous grasp attempts to adapt the ranking of the templates to new situations. We tested our approach on two different platforms, the Willow Garage PR2 and the Barrett WAM robot, which have very different hand kinematics. Furthermore, we compared our algorithm with other grasp planners and demonstrated its superior performance. The results presented in this paper show that the algorithm is able to find good grasp configurations for a large set of unknown objects from a relatively small set of demonstrations, and does improve its performance over time.

link (url) DOI [BibTex]

2013


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Optimal distribution of contact forces with inverse-dynamics control

Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., Schaal, S.

The International Journal of Robotics Research, 32(3):280-298, March 2013 (article)

Abstract
The development of legged robots for complex environments requires controllers that guarantee both high tracking performance and compliance with the environment. More specifically the control of the contact interaction with the environment is of crucial importance to ensure stable, robust and safe motions. In this contribution we develop an inverse-dynamics controller for floating-base robots under contact constraints that can minimize any combination of linear and quadratic costs in the contact constraints and the commands. Our main result is the exact analytical derivation of the controller. Such a result is particularly relevant for legged robots as it allows us to use torque redundancy to directly optimize contact interactions. For example, given a desired locomotion behavior, we can guarantee the minimization of contact forces to reduce slipping on difficult terrains while ensuring high tracking performance of the desired motion. The main advantages of the controller are its simplicity, computational efficiency and robustness to model inaccuracies. We present detailed experimental results on simulated humanoid and quadruped robots as well as a real quadruped robot. The experiments demonstrate that the controller can greatly improve the robustness of locomotion of the robots.1

link (url) DOI [BibTex]

2013

link (url) DOI [BibTex]


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Controlled Reduction with Unactuated Cyclic Variables: Application to 3D Bipedal Walking with Passive Yaw Rotation

Gregg, R., Righetti, L.

IEEE Transactions on Automatic Control, 58(10):2679-2685, October 2013 (article)

Abstract
This technical note shows that viscous damping can shape momentum conservation laws in a manner that stabilizes yaw rotation and enables steering for underactuated 3D walking. We first show that unactuated cyclic variables can be controlled by passively shaped conservation laws given a stabilizing controller in the actuated coordinates. We then exploit this result to realize controlled geometric reduction with multiple unactuated cyclic variables. We apply this underactuated control strategy to a five-link 3D biped to produce exponentially stable straight-ahead walking and steering in the presence of passive yawing.

link (url) DOI [BibTex]

2011


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Toward simple control for complex, autonomous robotic applications: combining discrete and rhythmic motor primitives

Degallier, S., Righetti, L., Gay, S., Ijspeert, A.

Autonomous Robots, 31(2-3):155-181, October 2011 (article)

Abstract
Vertebrates are able to quickly adapt to new environments in a very robust, seemingly effortless way. To explain both this adaptivity and robustness, a very promising perspective in neurosciences is the modular approach to movement generation: Movements results from combinations of a finite set of stable motor primitives organized at the spinal level. In this article we apply this concept of modular generation of movements to the control of robots with a high number of degrees of freedom, an issue that is challenging notably because planning complex, multidimensional trajectories in time-varying environments is a laborious and costly process. We thus propose to decrease the complexity of the planning phase through the use of a combination of discrete and rhythmic motor primitives, leading to the decoupling of the planning phase (i.e. the choice of behavior) and the actual trajectory generation. Such implementation eases the control of, and the switch between, different behaviors by reducing the dimensionality of the high-level commands. Moreover, since the motor primitives are generated by dynamical systems, the trajectories can be smoothly modulated, either by high-level commands to change the current behavior or by sensory feedback information to adapt to environmental constraints. In order to show the generality of our approach, we apply the framework to interactive drumming and infant crawling in a humanoid robot. These experiments illustrate the simplicity of the control architecture in terms of planning, the integration of different types of feedback (vision and contact) and the capacity of autonomously switching between different behaviors (crawling and simple reaching).

link (url) DOI [BibTex]

2011

link (url) DOI [BibTex]

2009


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Adaptive Frequency Oscillators and Applications

Righetti, L., Buchli, J., Ijspeert, A.

The Open Cybernetics \& Systemics Journal, 3, pages: 64-69, 2009 (article)

Abstract
In this contribution we present a generic mechanism to transform an oscillator into an adaptive frequency oscillator, which can then dynamically adapt its parameters to learn the frequency of any periodic driving signal. Adaptation is done in a dynamic way: it is part of the dynamical system and not an offline process. This mechanism goes beyond entrainment since it works for any initial frequencies and the learned frequency stays encoded in the system even if the driving signal disappears. Interestingly, this mechanism can easily be applied to a large class of oscillators from harmonic oscillators to relaxation types and strange attractors. Several practical applications of this mechanism are then presented, ranging from adaptive control of compliant robots to frequency analysis of signals and construction of limit cycles of arbitrary shape.

link (url) [BibTex]

2009

link (url) [BibTex]

2008


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Frequency analysis with coupled nonlinear oscillators

Buchli, J., Righetti, L., Ijspeert, A.

Physica D: Nonlinear Phenomena, 237(13):1705-1718, August 2008 (article)

Abstract
We present a method to obtain the frequency spectrum of a signal with a nonlinear dynamical system. The dynamical system is composed of a pool of adaptive frequency oscillators with negative mean-field coupling. For the frequency analysis, the synchronization and adaptation properties of the component oscillators are exploited. The frequency spectrum of the signal is reflected in the statistics of the intrinsic frequencies of the oscillators. The frequency analysis is completely embedded in the dynamics of the system. Thus, no pre-processing or additional parameters, such as time windows, are needed. Representative results of the numerical integration of the system are presented. It is shown, that the oscillators tune to the correct frequencies for both discrete and continuous spectra. Due to its dynamic nature the system is also capable to track non-stationary spectra. Further, we show that the system can be modeled in a probabilistic manner by means of a nonlinear Fokker–Planck equation. The probabilistic treatment is in good agreement with the numerical results, and provides a useful tool to understand the underlying mechanisms leading to convergence.

link (url) DOI [BibTex]

2008

link (url) DOI [BibTex]

2007


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iCub - The Design and Realization of an Open Humanoid Platform for Cognitive and Neuroscience Research

Tsagarakis, N., Metta, G., Sandini, G., Vernon, D., Beira, R., Becchi, F., Righetti, L., Santos-Victor, J., Ijspeert, A., Carrozza, M., Caldwell, D.

Advanced Robotics, 21(10):1151-1175, 2007 (article)

Abstract
The development of robotic cognition and the advancement of understanding of human cognition form two of the current greatest challenges in robotics and neuroscience, respectively. The RobotCub project aims to develop an embodied robotic child (iCub) with the physical (height 90 cm and mass less than 23 kg) and ultimately cognitive abilities of a 2.5-year-old human child. The iCub will be a freely available open system which can be used by scientists in all cognate disciplines from developmental psychology to epigenetic robotics to enhance understanding of cognitive systems through the study of cognitive development. The iCub will be open both in software, but more importantly in all aspects of the hardware and mechanical design. In this paper the design of the mechanisms and structures forming the basic 'body' of the iCub are described. The papers considers kinematic structures dynamic design criteria, actuator specification and selection, and detailed mechanical and electronic design. The paper concludes with tests of the performance of sample joints, and comparison of these results with the design requirements and simulation projects.

link (url) DOI [BibTex]

2007

link (url) DOI [BibTex]

2006


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Dynamic Hebbian learning in adaptive frequency oscillators

Righetti, L., Buchli, J., Ijspeert, A.

Physica D: Nonlinear Phenomena, 216(2):269-281, 2006 (article)

Abstract
Nonlinear oscillators are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for oscillators which adapts their frequency to the frequency of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of oscillators, from phase oscillators to relaxation oscillators and strange attractors with a generic learning rule. One major feature of our learning rule is that the oscillators constructed can adapt their frequency without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive oscillator. The convergence of the learning is proved for the Hopf oscillator, then numerical experiments are carried out to explore the learning capabilities of the system. Finally, we generalize the learning rule to non-harmonic oscillators like relaxation oscillators and strange attractors.

link (url) DOI [BibTex]

2006

link (url) DOI [BibTex]


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Engineering Entrainment and Adaptation in Limit Cycle Systems – From biological inspiration to applications in robotics

Buchli, J., Righetti, L., Ijspeert, A.

Biological Cybernetics, 95(6):645-664, December 2006 (article)

Abstract
Periodic behavior is key to life and is observed in multiple instances and at multiple time scales in our metabolism, our natural environment, and our engineered environment. A natural way of modeling or generating periodic behavior is done by using oscillators, i.e., dynamical systems that exhibit limit cycle behavior. While there is extensive literature on methods to analyze such dynamical systems, much less work has been done on methods to synthesize an oscillator to exhibit some specific desired characteristics. The goal of this article is twofold: (1) to provide a framework for characterizing and designing oscillators and (2) to review how classes of well-known oscillators can be understood and related to this framework. The basis of the framework is to characterize oscillators in terms of their fundamental temporal and spatial behavior and in terms of properties that these two behaviors can be designed to exhibit. This focus on fundamental properties is important because it allows us to systematically compare a large variety of oscillators that might at first sight appear very different from each other. We identify several specifications that are useful for design, such as frequency-locking behavior, phase-locking behavior, and specific output signal shape. We also identify two classes of design methods by which these specifications can be met, namely offline methods and online methods. By relating these specifications to our framework and by presenting several examples of how oscillators have been designed in the literature, this article provides a useful methodology and toolbox for designing oscillators for a wide range of purposes. In particular, the focus on synthesis of limit cycle dynamical systems should be useful both for engineering and for computational modeling of physical or biological phenomena.

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