Publications | Dario Bellicoso

Academic Publications

2025

Nonlinear trajectory optimization for robotic devices

C. Dario Bellicoso, Logan W. Tutt, Neil M. Neville, and Alexander D. Perkins

May 2025

US Patent App. 18/938,800

2024

Nonlinear trajectory optimization for robotic devices

C. Dario Bellicoso, Logan W. Tutt, Neil M. Neville, and Alexander D. Perkins

Dec 2024

US Patent 12,168,300
Object climbing by legged robots using training objects

Jared Di Carlo, Kevin Bergamin, C. Dario Bellicoso, and Scott Kuindersma

Jun 2024

US Patent App. 18/537,269

2023

Systems and methods for grasp planning for a robotic manipulator

Samuel Shaw, Logan W. Tutt, Shervin Talebi, C. Dario Bellicoso, Jennifer Barry, and Neil M. Neville

Jun 2023

US Patent App. 17/988,982

2020

Rolling in the Deep – Hybrid Locomotion for Wheeled-Legged Robots Using Online Trajectory Optimization

Marko Bjelonic, Prajish K. Sankar, C. Dario Bellicoso, Heike Vallery, and Marco Hutter

IEEE Robotics and Automation Letters, Jun 2020

DOI HTML Video

2019

Dynamic Locomotion on Slippery Ground

Fabian Jenelten, Jemin Hwangbo, Fabian Tresoldi, C. Dario Bellicoso, and Marco Hutter

IEEE Robotics and Automation Letters, Jun 2019

DOI Video
ALMA-Articulated Locomotion and Manipulation for a Torque-Controllable Robot

C. Dario Bellicoso, Koen Krämer, Markus Stäuble, Dhionis Sako, Fabian Jenelten, Marko Bjelonic, and Marco Hutter

In IEEE International Conference on Robotics and Automation (ICRA), Jun 2019

Abs PDF Video

The task of robotic mobile manipulation poses several scientific challenges that need to be addressed to execute complex manipulation tasks in unstructured environments, in which collaboration with humans might be required. Therefore, we present ALMA, a motion planning and control framework for a torque-controlled quadrupedal robot equipped with a six degrees of freedom robotic arm capable of performing dynamic locomotion while executing manipulation tasks. The online motion planning framework, together with a whole-body controller based on a hierarchical optimization algorithm, enables the system to walk, trot and pace while executing operational space end-effector control, reactive human-robot collaboration and torso posture optimization to increase the arm’s workspace. The torque control of the whole system enables the implementation of compliant behavior, allowing a user to safely interact with the robot. We verify our framework on the real robot by performing tasks such as opening a door and carrying a payload together with a human.
Keep Rollin’- Whole-Body Motion Control and Planning for Wheeled Quadrupedal Robots

Marko Bjelonic, C. Dario Bellicoso, Yvain Viragh, Dhionis Sako, F Dante Tresoldi, Fabian Jenelten, and Marco Hutter

IEEE Robotics and Automation Letters, Jun 2019

Abs DOI HTML PDF Video

We show dynamic locomotion strategies for wheeled quadrupedal robots, which combine the advantages of both walking and driving. The developed optimization framework tightly integrates the additional degrees of freedom introduced by the wheels. Our approach relies on a zero-moment point based motion optimization which continuously updates reference trajectories. The reference motions are tracked by a hierarchical whole-body controller which computes optimal generalized accelerations and contact forces by solving a sequence of prioritized tasks including the nonholonomic rolling constraints. Our approach has been tested on ANYmal, a quadrupedal robot that is fully torque-controlled including the non-steerable wheels attached to its legs. We conducted experiments on flat and inclined terrains as well as over steps, whereby we show that integrating the wheels into the motion control and planning framework results in intuitive motion trajectories, which enable more robust and dynamic locomotion compared to other wheeled-legged robots. Moreover, with a speed of 4 m/s and a reduction of the cost of transport by 83 % we prove the superiority of wheeled-legged robots compared to their legged counterparts.
Trajectory Optimization for Wheeled-Legged Quadrupedal Robots using Linearized ZMP Constraints

Yvain Viragh, Marko Bjelonic, C. Dario Bellicoso, Fabian Jenelten, and Marco Hutter

IEEE Robotics and Automation Letters, Jun 2019

Abs DOI HTML PDF Video

We present a trajectory optimizer for quadrupedal robots with actuated wheels. By solving for angular, vertical, and planar components of the base and feet trajectories in a cascaded fashion and by introducing a novel linear formulation of the zero-moment point (ZMP) balance criterion, we rely on quadratic programming only, thereby eliminating the need for nonlinear optimization routines. Yet, even for gaits containing full flight phases, we are able to generate trajectories for executing complex motions that involve simultaneous driving, walking, and turning. We verified our approach in simulations of the quadrupedal robot ANYmal equipped with wheels, where we are able to run the proposed trajectory optimizer at 50 Hz. To the best of our knowledge, this is the first time that such dynamic motions are demonstrated for wheeled-legged quadrupedal robots using an online motion planner.
Learning agile and dynamic motor skills for legged robots

Jemin Hwangbo, Joonho Lee, Alexey Dosovitskiy, C. Dario Bellicoso, Vassilios Tsounis, Vladlen Koltun, and Marco Hutter

Science Robotics, Jun 2019

Abs DOI

Legged robots pose one of the greatest challenges in robotics. Dynamic and agile maneuvers of animals cannot be imitated by existing methods that are crafted by humans. A compelling alternative is reinforcement learning, which requires minimal craftsmanship and promotes the natural evolution of a control policy. However, so far, reinforcement learning research for legged robots is mainly limited to simulation, and only few and comparably simple examples have been deployed on real systems. The primary reason is that training with real robots, particularly with dynamically balancing systems, is complicated and expensive. In the present work, we introduce a method for training a neural network policy in simulation and transferring it to a state-of-the-art legged system, thereby leveraging fast, automated, and cost-effective data generation schemes. The approach is applied to the ANYmal robot, a sophisticated medium-dog–sized quadrupedal system. Using policies trained in simulation, the quadrupedal machine achieves locomotion skills that go beyond what had been achieved with prior methods: ANYmal is capable of precisely and energy-efficiently following high-level body velocity commands, running faster than before, and recovering from falling even in complex configurations.
Optimization-based planning and control for multi-limbed walking robots

C. Dario Bellicoso

ETH Zurich, Jun 2019

2018

Advances in Real-World Applications for Legged Robots

C. Dario Bellicoso, Marko Bjelonic, Lorenz Wellhausen, Dhionis Sako, Kai Holtmann, Fabian Guenther, Marco Tranzatto, Péter Fankhauser, and Marco Hutter

Journal of Field Robotics, Jun 2018

Abs DOI HTML PDF Video

This paper provides insight into the application of the quadrupedal robot ANYmal in outdoor missions of industrial inspection (ARGOS Challenge) and search and rescue (European Robotics League (ERL) Emergency Robots). In both competitions, the legged robot had to autonomously and semi-autonomously navigate in real-world scenarios to complete high-level tasks such as inspection and payload delivery. In the ARGOS competition, ANYmal used a rotating LiDAR sensor to localize on the industrial site and map the terrain and obstacles around the robot. In the ERL competition, additional Real-Time Kinematic (RTK)-Global Positioning System (GPS) was used to co-localize the legged robot with respect to a Micro Aerial Vehicle (MAV) that creates maps from the aerial view. The high mobility of legged robots allows overcoming large obstacles, e.g. steps and stairs, with statically and dynamically stable gaits. Moreover, the versatile machine can adapt its posture for inspection and payload delivery. The paper concludes with insight into the general learnings from the ARGOS and ERL challenges.
Real-Time Dance Generation to Music for a Legged Robot

Thomas Bi, Péter Fankhauser, C. Dario Bellicoso, and Marco Hutter

In 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Oct 2018

DOI
Skating with a force controlled quadrupedal robot

Marko Bjelonic, C. Dario Bellicoso, M Efe Tiryaki, and Marco Hutter

In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Oct 2018

Abs DOI HTML PDF Video

Traditional legged robots are capable of traversing challenging terrain, but lack of energy efficiency when compared to wheeled systems operating on flat environments. The combination of both locomotion domains overcomes the trade-off between mobility and efficiency. Therefore, this paper presents a novel motion planner and controller which together enable a legged robot equipped with skates to perform skating maneuvers. These are achieved by an appropriate combination of planned reaction forces and gliding motions. Our novel motion controller formulates a Virtual Model Controller and an optimal contact force distribution which takes into account the nonholonomic constraints introduced by the skates. This approach has been tested on the torque-controllable robot ANYmal equipped with passive wheels and ice skates as end-effectors. We conducted experiments on flat and inclined terrain, whereby we show that skating motions reduces the cost of transport by up to 80\,% with respect to traditional walking gaits.
Efficient Gait Selection for Quadrupedal Robots on the Moon and Mars

Hendrik Kolvenbach, C. Dario Bellicoso, Fabian Jenelten, Lorenz Wellhausen, and Marco Hutter

In 14th International Symposium on Artificial Intelligence, Robotics and Automation in Space (i-SAIRAS 2018), Oct 2018
Robust Rough-Terrain Locomotion with a Quadrupedal Robot

Péter Fankhauser, Marko Bjelonic, C. Dario Bellicoso, Takahiro Miki, and Marco Hutter

In IEEE International Conference on Robotics and Automation (ICRA), Oct 2018

Abs DOI HTML Video

Robots working in natural, urban, and industrial settings need to be able to navigate challenging environments. In this paper, we present a motion planner for the perceptive rough-terrain locomotion with quadrupedal robots. The planner finds safe footholds along with collision-free swing-leg motions by leveraging an acquired terrain map. To this end, we present a novel pose optimization approach that enables the robot to climb over significant obstacles. We experimentally validate our approach with the quadrupedal robot ANYmal by autonomously traversing obstacles such steps, inclines, and stairs. The locomotion planner re-plans the motion at every step to cope with disturbances and dynamic environments. The robot has no prior knowledge of the scene, and all mapping, state estimation, control, and planning is performed in real-time onboard the robot.
Gait and trajectory optimization for legged systems through phase-based end-effector parameterization

Alexander W Winkler, C. Dario Bellicoso, Marco Hutter, and Jonas Buchli

IEEE Robotics and Automation Letters, Oct 2018

Abs

We present a single trajectory optimization formulation for legged locomotion that automatically determines the gait sequence, step timings, footholds, swing-leg motions, and six-dimensional body motion over nonflat terrain, without any additional modules. Our phase-based parameterization of feet motion and forces allows to optimize over the discrete gait sequence using only continuous decision variables. The system is represented using a simplified centroidal dynamics model that is influenced by the feet’s location and forces. We explicitly enforce friction cone constraints, depending on the shape of the terrain. The nonlinear programming problem solver generates highly dynamic motion plans with full flight phases for a variety of legged systems with arbitrary morphologies in an efficient manner. We validate the feasibility of the generated plans in simulation and on the real quadruped robot ANYmal. Additionally, the entire solver software TOWR, which used to generate these motions is made freely available.
Whole-body nonlinear model predictive control through contacts for quadrupeds

Michael Neunert, Markus Stäuble, Markus Giftthaler, C. Dario Bellicoso, Jan Carius, Christian Gehring, Marco Hutter, and Jonas Buchli

IEEE Robotics and Automation Letters, Jan 2018

Abs

In this letter, we present a whole-body nonlinear model predictive control approach for rigid body systems subject to contacts. We use a full-dynamic system model which also includes explicit contact dynamics. Therefore, contact locations, sequences, and timings are not prespecified but optimized by the solver. Yet, using numerical and software engineering allows for running the nonlinear Optimal Control solver at rates up to 190 Hz on a quadruped for a time horizon of half a second. This outperforms the state-of-the-art by at least one order of magnitude. Hardware experiments in the form of periodic and nonperiodic tasks are applied to two quadrupeds with different actuation systems. The obtained results underline the performance, transferability, and robustness of the approach.
Dynamic Locomotion Through Online Nonlinear Motion Optimization for Quadrupedal Robots

C. Dario Bellicoso, Fabian Jenelten, Christian Gehring, and Marco Hutter

IEEE Robotics and Automation Letters, Jan 2018

Abs

This letter presents a realtime motion planning and control method that enables a quadrupedal robot to execute dynamic gaits including trot, pace, and dynamic lateral walk, as well as gaits with full flight phases such as jumping, pronking, and running trot. The proposed method also enables smooth transitions between these gaits. Our approach relies on an online zero-moment point based motion planner which continuously updates the reference motion trajectory as a function of the contact schedule and the state of the robot. The reference footholds for each leg are obtained by solving a separate optimization problem. The resulting optimized motion plans are tracked by a hierarchical whole-body controller. Our framework has been tested in simulation and on ANYmal, a fully torque-controllable quadrupedal robot, both in simulation and on the actual robot.

2017

Dynamic locomotion and whole-body control for quadrupedal robots

C. Dario Bellicoso, Fabian Jenelten, Péter Fankhauser, Christian Gehring, Jemin Hwangbo, and Marco Hutter

In International Conference on Intelligent Robots and Systems (IROS), 2017 IEEE/RSJ, Jan 2017

Video
ANYmal-toward legged robots for harsh environments

Marco Hutter, Christian Gehring, Andreas Lauber, F Gunther, C. Dario Bellicoso, Vassilios Tsounis, Péter Fankhauser, Remo Diethelm, Samuel Bachmann, Michael Blösch, Hendrik Kolvenbach, Marko Bjelonic, and others

Advanced Robotics, Jan 2017

Abs DOI HTML PDF

This paper provides a system overview about ANYmal, a quadrupedal robot developed for operation in harsh environments. The 30 kg, 0.5 m tall robotic dog was built in a modular way for simple maintenance and user-friendly handling, while focusing on high mobility and dynamic motion capability. The system is tightly sealed to reach IP67 standard and protected to survive falls. Rotating lidar sensors in the front and back are used for localization and terrain mapping and compact force sensors in the feet provide accurate measurements about the contact situations. The variable payload, such as a modular pan-tilt head with a variety of inspection sensors, can be exchanged depending on the application. Thanks to novel, compliant joint modules with integrated electronics, ANYmal is precisely torque controllable and very robust against impulsive loads during running or jumping. In a series of experiments we demonstrate that ANYmal can execute various climbing maneuvers, walking gaits, as well as a dynamic trot and jump. As special feature, the joints can be fully rotated to switch between X- and O-type kinematic configurations. Detailed measurements unveil a low energy consumption of 280 W during locomotion, which results in an autonomy of more than 2 h.
Quadrupedal locomotion using trajectory optimization and hierarchical whole body control

Christian Gehring, C. Dario Bellicoso, Péter Fankhauser, Stelian Coros, and Marco Hutter

In International Conference on Robotics and Automation (ICRA), 2017 IEEE, Jan 2017

2016

Perception-less terrain adaptation through whole body control and hierarchical optimization

C. Dario Bellicoso, Christian Gehring, Jemin Hwangbo, Péter Fankhauser, and Marco Hutter

In 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), Jan 2016

DOI Video
Free gait—An architecture for the versatile control of legged robots

Péter Fankhauser, C. Dario Bellicoso, Christian Gehring, Renaud Dubé, Abel Gawel, and Marco Hutter

In International Conference on Humanoid Robots (Humanoids), 2016 IEEE-RAS 16th, Jan 2016
ANYpulator: Design and control of a safe robotic arm

Karen Bodie, C. Dario Bellicoso, and Marco Hutter

In Intelligent Robots and Systems (IROS), 2016 IEEE/RSJ International Conference on, Jan 2016
Probabilistic foot contact estimation by fusing information from dynamics and differential/forward kinematics

Jemin Hwangbo, C. Dario Bellicoso, Péter Fankhauser, and Marco Hutter

In International Conference on Intelligent Robots and Systems (IROS), 2016 IEEE/RSJ, Jan 2016
Anymal-a highly mobile and dynamic quadrupedal robot

Marco Hutter, Christian Gehring, Dominic Jud, Andreas Lauber, C. Dario Bellicoso, Vassilios Tsounis, Jemin Hwangbo, Karen Bodie, Peter Fankhauser, Michael Bloesch, and others

In 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Jan 2016
A Primer on the Differential Calculus of 3D Orientations

Michael Bloesch, Hannes Sommer, Tristan Laidlow, Michael Burri, Gabriel Nützi, Peter Fankhauser, C. Dario Bellicoso, Christian Gehring, Stefan Leutenegger, Marco Hutter, and Roland Siegwart

CoRR, Jan 2016
Practice makes perfect: An optimization-based approach to controlling agile motions for a quadruped robot

Christian Gehring, Stelian Coros, Marco Hutter, C. Dario Bellicoso, Huub Heijnen, Remo Diethelm, Michael Bloesch, Péter Fankhauser, Jemin Hwangbo, Mark Hoepflinger, and others

IEEE Robotics & Automation Magazine, Jan 2016

2015

Direct state-to-action mapping for high DOF robots using ELM

Jemin Hwangbo, Christian Gehring, Dario Bellicoso, Péter Fankhauser, Roland Siegwart, and Marco Hutter

In 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Jan 2015

DOI
Dynamic trotting on slopes for quadrupedal robots

Christian Gehring, C. Dario Bellicoso, Stelian Coros, Michael Bloesch, Péter Fankhauser, Marco Hutter, and Roland Siegwart

In 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Jan 2015

DOI Video
Design, modeling and control of a 5-DoF light-weight robot arm for aerial manipulation

C. Dario Bellicoso, Luca Rosario Buonocore, Vincenzo Lippiello, and Bruno Siciliano

In 2015 23rd Mediterranean Conference on Control and Automation (MED), Jan 2015

DOI PDF

Patents

2025

Nonlinear trajectory optimization for robotic devices

C. Dario Bellicoso, Logan W. Tutt, Neil M. Neville, and Alexander D. Perkins

May 2025

US Patent App. 18/938,800

2024

Nonlinear trajectory optimization for robotic devices

C. Dario Bellicoso, Logan W. Tutt, Neil M. Neville, and Alexander D. Perkins

Dec 2024

US Patent 12,168,300
Object climbing by legged robots using training objects

Jared Di Carlo, Kevin Bergamin, C. Dario Bellicoso, and Scott Kuindersma

Jun 2024

US Patent App. 18/537,269

2023

Systems and methods for grasp planning for a robotic manipulator

Samuel Shaw, Logan W. Tutt, Shervin Talebi, C. Dario Bellicoso, Jennifer Barry, and Neil M. Neville

Jun 2023

US Patent App. 17/988,982