alex.bin — bash — 80x24
$

Research

Robotics Motion and Path Planning Legged Locomotion Trajectory Optimization Nonlinear Programming Optimal Control

To make a robot move, it needs a motion-plan to follow. Traditionally an engineer has to look at the terrain and the proposed task, and then hand-design how the robot should move. This is tedious, since it requires a custom motion for each situation. I want to automate this by representing the the laws of physics through one universal mathematical optimization problem. Off-the-shelf solvers then automatically generate the solution motion-plan. Each solution obeys the encoded laws of physics, regardless of the specific goal position or terrain. These optimized plans can then be executed on the robot.... show intro»

Main contribution   RA-L 2018 paper

3 min overview.

30 minute in-depth explanation.

Background knowledge  PhD Thesis

Optimization-based motion-planning for legged robots connects a lot of different research topics.

Card image cap
Why walking is difficult

3 min read  ·  Chapter 1.3

We're used to seeing cars drive around and drones flying over our heads. So why is it is so much more difficult to have machines that walk?

Card image cap
Models for legged robots

30 min read  ·  Chapter 1.2

To represent the physics of legged robots mathematically, there exists a variety of models (RBD, Centroidal, SRBD, LIPM). Here we explain their differences and underlying assumptions.

Card image cap
Trajectory Optimization

10 min read  ·  Chapter 1.4

To produce a general formulation, we work on a high abstraction layer, defining physical laws in terms of mathematical equations. Existing optimization solvers then solve this problem to produce the motion-plans. Here we present an overview of this type of approach.

Vertex-based ZMP constraints  RA-L 2017 paper

If you use the LIP model, you might be interested in this formulation of ZMP constraints. Traditionally, support areas where necessary, whereas with this formulation support-lines and support-points work as well, allowing e.g. quadruped trotting, or biped point-feet running.


All other publications, videos, slides can be downloaded here.

Sftware

The approach described in the above paper is implemented by towr. This code uses the convenient NLP solver interface ifopt to formulate the problem independent of the solver. The ROS package xpp is used to visualize the produced motions.

Light-weight and extensible C++ library for trajectory optimization for legged robots.

Star Download

Eigen-based, light-weight C++ Interface to NLP Solvers (Ipopt, Snopt).

Star Download

Visualization of legged robots, forces, support areas, ZMP, CoM etc. in ROS rviz.

Star Download

Publication List

Download pdfs, videos, slides, bibtex info and more. See also Google Scholar.

Optimization-based motion planning for legged robots. Winkler, A. W Ph.D. Thesis, ETH Zurich. 2018
Optimization-based motion planning for legged robots [pdf] pdf   Optimization-based motion planning for legged robots [link] slides   Optimization-based motion planning for legged robots [link] link   doi   bibtex   abstract
@phdthesis{winkler18_phd,
  author    = {Winkler, Alexander W},
  title     = {Optimization-based motion planning for legged robots},
  publisher = {ETH Zurich},
  year      = {2018},
  school    = {ETH Zurich},
  doi       = {10.3929/ethz-b-000272432},
  abstract  = {What are the most prominent physical restrictions that make legged locomotion difficult? 
               Which dynamic models (RBD, Centroidal, SRBD, LIPM) can be used to
               capture the physics of legged locomotion and what is the trade-off between them?
               How can Trajectory Optimization help to generate universal solutions? 
               What criteria can be used to compare motion planning algorithms?  
               How to use the SRBD to optimize for the full 6D-base, end-effectors and gait
               in milliseconds?.}
}



What are the most prominent physical restrictions that make legged locomotion difficult? Which dynamic models (RBD, Centroidal, SRBD, LIPM) can be used to capture the physics of legged locomotion and what is the trade-off between them? How can Trajectory Optimization help to generate universal solutions? What criteria can be used to compare motion planning algorithms? How to use the SRBD to optimize for the full 6D-base, end-effectors and gait in milliseconds?.
Gait and Trajectory Optimization for Legged Systems through Phase-based End-Effector Parameterization. Winkler, A. W; Bellicoso, D. C; Hutter, M.; and Buchli, J. IEEE Robotics and Automation Letters (RA-L). 2018
Gait and Trajectory Optimization for Legged Systems through Phase-based End-Effector Parameterization [pdf] pdf   Gait and Trajectory Optimization for Legged Systems through Phase-based End-Effector Parameterization [link] video   Gait and Trajectory Optimization for Legged Systems through Phase-based End-Effector Parameterization [link] tutorial   Gait and Trajectory Optimization for Legged Systems through Phase-based End-Effector Parameterization [link] slides   Gait and Trajectory Optimization for Legged Systems through Phase-based End-Effector Parameterization [link] link   doi   bibtex   abstract
@article{winkler18,
  author    = {Winkler, Alexander W and 
               Bellicoso, Dario C and 
               Hutter, Marco and
               Buchli, Jonas},
  title     = {Gait and Trajectory Optimization for Legged Systems 
               through Phase-based End-Effector Parameterization},
  journal   = {IEEE Robotics and Automation Letters (RA-L)},
  year      = {2018},
  month     = {July},
  pages     = {1560-1567},
  doi       = {10.1109/LRA.2018.2798285},
  volume    = {3},
  abstract  = {We present a single Trajectory Optimization formulation
               for legged locomotion that automatically determines
               the gait-sequence, step-timings, footholds, swing-leg motions and
               6D body motion over non-flat 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
               NLP 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
               used to generate these motions is made freely available.},
  keywords  = {legged locomotion, trajectory optimization}
}

We present a single Trajectory Optimization formulation for legged locomotion that automatically determines the gait-sequence, step-timings, footholds, swing-leg motions and 6D body motion over non-flat 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 NLP 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 used to generate these motions is made freely available.
Fast Trajectory Optimization for Legged Robots using Vertex-based ZMP Constraints. Winkler, A. W; Farshidian, F.; Pardo, D.; Neunert, M.; and Buchli, J. IEEE Robotics and Automation Letters (RA-L). 2017
Fast Trajectory Optimization for Legged Robots using Vertex-based ZMP Constraints [pdf] pdf   Fast Trajectory Optimization for Legged Robots using Vertex-based ZMP Constraints [link] video   Fast Trajectory Optimization for Legged Robots using Vertex-based ZMP Constraints [link] slides   Fast Trajectory Optimization for Legged Robots using Vertex-based ZMP Constraints [link] link   doi   bibtex   abstract
@article{winkler17b,
  author    = {Winkler, Alexander W and 
               Farshidian, Farbod and 
               Pardo, Diego and 
               Neunert, Michael and 
               Buchli, Jonas},
  title     = {Fast Trajectory Optimization for Legged Robots 
               using Vertex-based ZMP Constraints},
  journal   = {IEEE Robotics and Automation Letters (RA-L)},
  year      = {2017},
  month     = {oct},
  pages     = {2201-2208},
  doi       = {10.1109/LRA.2017.2723931},
  volume    = {2},
  abstract  = {This paper combines the fast Zero-Moment-Point (ZMP) approaches 
               that work well in practice with the broader range of capabilities
               of a Trajectory Optimization formulation, by optimizing over body
               motion, footholds and Center of Pressure simultaneously. We 
               introduce a vertex-based representation of the support-area 
               constraint, which can treat arbitrarily oriented point-, line-, 
               and area-contacts uniformly. This generalization allows us to 
               create motions such quadrupedal walking, trotting, bounding, 
               pacing, combinations and transitions between these, limping, 
               bipedal walking and push-recovery all with the same approach. 
               This formulation constitutes a minimal representation of the 
               physical laws (unilateral contact forces) and kinematic 
               restrictions (range of motion) in legged locomotion, which allows
               us to generate various motion in less than a second. We 
               demonstrate the feasibility of the generated motions on a real 
               quadruped robot.},
  keywords  = {legged locomotion, trajectory optimization}
}

This paper combines the fast Zero-Moment-Point (ZMP) approaches that work well in practice with the broader range of capabilities of a Trajectory Optimization formulation, by optimizing over body motion, footholds and Center of Pressure simultaneously. We introduce a vertex-based representation of the support-area constraint, which can treat arbitrarily oriented point-, line-, and area-contacts uniformly. This generalization allows us to create motions such quadrupedal walking, trotting, bounding, pacing, combinations and transitions between these, limping, bipedal walking and push-recovery all with the same approach. This formulation constitutes a minimal representation of the physical laws (unilateral contact forces) and kinematic restrictions (range of motion) in legged locomotion, which allows us to generate various motion in less than a second. We demonstrate the feasibility of the generated motions on a real quadruped robot.
show all  
Robust Whole-Body Motion Control of Legged Robots. Farshidian, F.; Jelavic, E.; Winkler, A. W; and Buchli, J. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). 2017
Robust Whole-Body Motion Control of Legged Robots [pdf] pdf   Robust Whole-Body Motion Control of Legged Robots [link] video   bibtex   abstract
@inproceedings{farshidian17b,
  author    = {Farshidian, Farbod and 
               Jelavic, Edo and
               Winkler, Alexander W and
               Buchli, Jonas},
  title     = {Robust Whole-Body Motion Control of Legged Robots},
  booktitle = {IEEE/RSJ International Conference on 
               Intelligent Robots and Systems (IROS)},
  year      = {2017},
  abstract  = {We introduce a robust control architecture for
               the whole-body motion control of torque controlled robots
               with arms and legs. The method is based on the robust
               control of contact forces in order to track a planned Center
               of Mass trajectory. Its appeal lies in the ability to guarantee
               robust stability and performance despite rigid body model
               mismatch, actuator dynamics, delays, contact surface stiffness,
               and unobserved ground profiles. Furthermore, we introduce a
               task space decomposition approach which removes the coupling
               effects between contact force controller and the other noncontact
               controllers. Finally, we verify our control performance
               on a quadruped robot and compare its performance to a
               standard inverse dynamics approach on hardware.}            
}

We introduce a robust control architecture for the whole-body motion control of torque controlled robots with arms and legs. The method is based on the robust control of contact forces in order to track a planned Center of Mass trajectory. Its appeal lies in the ability to guarantee robust stability and performance despite rigid body model mismatch, actuator dynamics, delays, contact surface stiffness, and unobserved ground profiles. Furthermore, we introduce a task space decomposition approach which removes the coupling effects between contact force controller and the other noncontact controllers. Finally, we verify our control performance on a quadruped robot and compare its performance to a standard inverse dynamics approach on hardware.
Hybrid direct collocation and control in the constraint- consistent subspace for dynamic legged robot locomotion. Pardo, D.; Neunert, M.; Winkler, A. W; Grandia, R.; and Buchli, J. In Robotics, Science and Systems (RSS). 2017
Hybrid direct collocation and control in the constraint- consistent subspace for dynamic legged robot locomotion [pdf] pdf   Hybrid direct collocation and control in the constraint- consistent subspace for dynamic legged robot locomotion [link] video   Hybrid direct collocation and control in the constraint- consistent subspace for dynamic legged robot locomotion [link] link   bibtex   abstract
@inproceedings{pardo17,
  author    = {Pardo, Diego and
               Neunert, Michael and 
               Winkler, Alexander W and
               Grandia, Ruben and
               Buchli, Jonas},
  title     = {Hybrid direct collocation and control in the constraint-
               consistent subspace for dynamic legged robot locomotion},
  booktitle = {Robotics, Science and Systems (RSS)},
  year      = {2017},
  abstract  = {In this paper, we present an algorithm for optimal planning and
               control of legged robot locomotion. Given the desired contact 
               sequence, this method generates gaits and dynamic motions for 
               legged robots without resorting to simplified stability criteria. 
               The method uses direct collocation for searching for solutions 
               within the constraint-consistent subspace defined by the robot’s 
               contact configuration. For the differential equation constraints 
               of the collocation algorithm, we use the so-called direct 
               dynamics of a constrained multibody system. The dynamics of a 
               legged robot is different for each contact configuration. Our 
               method deals with such a hybrid nature, and it allows for 
               velocity discontinuities when contacts are made. We introduce 
               the projected impact dynamics constraint to enforce consistency 
               during mode switching. We stabilize the plan using an inverse 
               dynamics controller consistent with the constraints and 
               compatible with the optimal feed-forward control of the motion 
               plan. As a whole, this approach reduces the complexity associated 
               with specifying dynamic motions of a floating-base robot under 
               the constant influence of contact forces. We apply this method 
               on a hydraulically actuated quadruped robot. We show two type of 
               gaits on the physical system (walking and trotting), and other 
               dynamic motions in simulation (jumping and leaping). The results 
               presented here are one of the few examples of an optimal control 
               problem satisfactorily solved and transferred to a real 
               torque-controlled legged robot.},       
}

In this paper, we present an algorithm for optimal planning and control of legged robot locomotion. Given the desired contact sequence, this method generates gaits and dynamic motions for legged robots without resorting to simplified stability criteria. The method uses direct collocation for searching for solutions within the constraint-consistent subspace defined by the robot’s contact configuration. For the differential equation constraints of the collocation algorithm, we use the so-called direct dynamics of a constrained multibody system. The dynamics of a legged robot is different for each contact configuration. Our method deals with such a hybrid nature, and it allows for velocity discontinuities when contacts are made. We introduce the projected impact dynamics constraint to enforce consistency during mode switching. We stabilize the plan using an inverse dynamics controller consistent with the constraints and compatible with the optimal feed-forward control of the motion plan. As a whole, this approach reduces the complexity associated with specifying dynamic motions of a floating-base robot under the constant influence of contact forces. We apply this method on a hydraulically actuated quadruped robot. We show two type of gaits on the physical system (walking and trotting), and other dynamic motions in simulation (jumping and leaping). The results presented here are one of the few examples of an optimal control problem satisfactorily solved and transferred to a real torque-controlled legged robot.
Online Walking Motion and Foothold Optimization for Quadruped Locomotion. Winkler, A. W; Farshidian, F.; Neunert, M.; Pardo, D.; and Buchli, J. In IEEE International Conference on Robotics and Automation (ICRA). 2017
Online Walking Motion and Foothold Optimization for Quadruped Locomotion [pdf] pdf   Online Walking Motion and Foothold Optimization for Quadruped Locomotion [link] video   Online Walking Motion and Foothold Optimization for Quadruped Locomotion [link] slides   Online Walking Motion and Foothold Optimization for Quadruped Locomotion [link] link   doi   bibtex   abstract
@inproceedings{winkler17a,
  author    = {Winkler, Alexander W and 
               Farshidian, Farbod and 
               Neunert, Michael and 
               Pardo, Diego and 
               Buchli, Jonas},
  title     = {Online Walking Motion and Foothold Optimization 
               for Quadruped Locomotion},
  booktitle = {IEEE International Conference on Robotics and Automation (ICRA)},
  year      = {2017},
  pages     = {5308-5313},
  doi       = {10.1109/ICRA.2017.7989624},
  abstract  = {We present an algorithm that generates walking
               motions for quadruped robots without the use of an explicit
               footstep planner by simultaneously optimizing over both the
               Center of Mass (CoM) trajectory and the footholds. Feasibility
               is achieved by imposing stability constraints on the CoM
               related to the Zero Moment Point and explicitly enforcing
               kinematic constraints between the footholds and the CoM
               position. Given a desired goal state, the problem is solved 
               online by a Nonlinear Programming solver to generate the walking
               motion. Experimental trials show that the algorithm is able to
               generate walking gaits for multiple steps in milliseconds that
               can be executed on a real quadruped robot.} 
}

We present an algorithm that generates walking motions for quadruped robots without the use of an explicit footstep planner by simultaneously optimizing over both the Center of Mass (CoM) trajectory and the footholds. Feasibility is achieved by imposing stability constraints on the CoM related to the Zero Moment Point and explicitly enforcing kinematic constraints between the footholds and the CoM position. Given a desired goal state, the problem is solved online by a Nonlinear Programming solver to generate the walking motion. Experimental trials show that the algorithm is able to generate walking gaits for multiple steps in milliseconds that can be executed on a real quadruped robot.
An Efficient Optimal Planning and Control Framework For Quadrupedal Locomotion. Farshidian, F.; Neunert, M.; Winkler, A. W; Rey, G.; and Buchli, J. In IEEE International Conference on Robotics and Automation (ICRA). 2017
An Efficient Optimal Planning and Control Framework For Quadrupedal Locomotion [pdf] pdf   An Efficient Optimal Planning and Control Framework For Quadrupedal Locomotion [link] video   An Efficient Optimal Planning and Control Framework For Quadrupedal Locomotion [link] link   doi   bibtex   abstract
@inproceedings{farshidian17a,
  author    = {Farshidian, Farbod and 
              Neunert, Michael and 
              Winkler, Alexander W and 
              Rey, Gonzalo and 
              Buchli, Jonas},
  title     = {An Efficient Optimal Planning and Control Framework 
              For Quadrupedal Locomotion},
  booktitle = {IEEE International Conference on Robotics and Automation (ICRA)},
  year      = {2017},
  pages     = {93-100},
  doi       = {10.1109/ICRA.2017.7989016},
  abstract  = {In this paper, we present an efficient Dynamic
               Programing framework for optimal planning and control of
               legged robots. First we formulate this problem as an optimal
               control problem for switched systems. Then we propose a
               multi–level optimization approach to find the optimal switching
               times and the optimal continuous control inputs. Through
               this scheme, the decomposed optimization can potentially be
               done more efficiently than the combined approach. Finally,
               we present a continuous-time constrained LQR algorithm
               which simultaneously optimizes the feedforward and feedback
               controller with O(n) time-complexity. In order to validate our
               approach, we show the performance of our framework on a
               quadrupedal robot. We choose the Center of Mass dynamics
               and the full kinematic formulation as the switched system model
               where the switching times as well as the contact forces and the
               joint velocities are optimized for different locomotion tasks 
               such as gap crossing, walking and trotting.}
}

In this paper, we present an efficient Dynamic Programing framework for optimal planning and control of legged robots. First we formulate this problem as an optimal control problem for switched systems. Then we propose a multi–level optimization approach to find the optimal switching times and the optimal continuous control inputs. Through this scheme, the decomposed optimization can potentially be done more efficiently than the combined approach. Finally, we present a continuous-time constrained LQR algorithm which simultaneously optimizes the feedforward and feedback controller with O(n) time-complexity. In order to validate our approach, we show the performance of our framework on a quadrupedal robot. We choose the Center of Mass dynamics and the full kinematic formulation as the switched system model where the switching times as well as the contact forces and the joint velocities are optimized for different locomotion tasks such as gap crossing, walking and trotting.
Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds. Neunert, M.; Farshidian, F.; Winkler, A. W.; and Buchli, J. IEEE Robotics and Automation Letters (RA-L). 2017
Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds [pdf] pdf   Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds [link] video   Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds [link] link   doi   bibtex   abstract
@article{neunert2017,
  author    = {Michael Neunert and 
               Farbod Farshidian and 
               Alexander W. Winkler and 
               Jonas Buchli},
  title     = {Trajectory Optimization Through Contacts and 
               Automatic Gait Discovery for Quadrupeds},
  journal   = {IEEE Robotics and Automation Letters (RA-L)},
  year      = {2017},
  pages     = {1502-1509},
  volume    = {2},
  doi       = {10.1109/LRA.2017.2665685},
  abstract  = {In this work we present a Trajectory Optimization
               framework for whole-body motion planning through contacts.
               We demonstrate how the proposed approach can be applied to
               automatically discover different gaits and dynamic motions on a
               quadruped robot. In contrast to most previous methods, we do
               not pre-specify contact-switches, -timings, -points or gait 
               patterns, but they are a direct outcome of the optimization. 
               Furthermore, we optimize over the entire dynamics of the robot, 
               which enables the optimizer to fully leverage the capabilities of
               the robot. To illustrate the spectrum of achievable motions, we 
               show eight different tasks, which would require very different 
               control structures when solved with state-of-the-art methods. 
               Using our Trajectory Optimization approach, we are solving each 
               task with a simple, high level cost function and without any 
               changes in the control structure. Furthermore, we fully integrate
               our approach with the robot’s control and estimation framework 
               such that we are able to run the optimization online. Through 
               several hardware experiments we show that the optimized 
               trajectories and control inputs can be directly applied to 
               physical systems.},
  keywords  = {Multilegged Robots, Motion and Path Planning,
               Optimization and Optimal Control}
}

In this work we present a Trajectory Optimization framework for whole-body motion planning through contacts. We demonstrate how the proposed approach can be applied to automatically discover different gaits and dynamic motions on a quadruped robot. In contrast to most previous methods, we do not pre-specify contact-switches, -timings, -points or gait patterns, but they are a direct outcome of the optimization. Furthermore, we optimize over the entire dynamics of the robot, which enables the optimizer to fully leverage the capabilities of the robot. To illustrate the spectrum of achievable motions, we show eight different tasks, which would require very different control structures when solved with state-of-the-art methods. Using our Trajectory Optimization approach, we are solving each task with a simple, high level cost function and without any changes in the control structure. Furthermore, we fully integrate our approach with the robot’s control and estimation framework such that we are able to run the optimization online. Through several hardware experiments we show that the optimized trajectories and control inputs can be directly applied to physical systems.
Optimal and Learning Control for Autonomous Robots. Buchli, J.; Farshidian, F.; Winkler, A. W.; Sandy, T.; and Gifthaler, M. In arXiv. 2017
Optimal and Learning Control for Autonomous Robots [pdf] pdf   bibtex   abstract
@inproceedings{buchli2017,
  author    = {Jonas Buchli and 
               Farbod Farshidian and 
               Alexander W. Winkler and 
               Timothy Sandy and
               Markus Gifthaler},
  title     = {Optimal and Learning Control for Autonomous Robots},
  booktitle = {arXiv},
  year      = {2017},
  abstract  = {Optimal and Learning Control for Autonomous Robots has been taught 
               in the Robotics, Systems and Controls Masters at ETH Zurich with the 
               aim to teach optimal control and reinforcement learning for closed loop 
               control problems from a unified point of view. The starting point is the 
               formulation of of an optimal control problem and deriving the different 
               types of solutions and algorithms from there. These lecture notes aim at 
               supporting this unified view with a unified notation wherever possible, 
               and a bit of a translation help to compare the terminology and notation 
               in the different fields. The course assumes basic knowledge of Control 
               Theory, Linear Algebra and Stochastic Calculus.}
}

Optimal and Learning Control for Autonomous Robots has been taught in the Robotics, Systems and Controls Masters at ETH Zurich with the aim to teach optimal control and reinforcement learning for closed loop control problems from a unified point of view. The starting point is the formulation of of an optimal control problem and deriving the different types of solutions and algorithms from there. These lecture notes aim at supporting this unified view with a unified notation wherever possible, and a bit of a translation help to compare the terminology and notation in the different fields. The course assumes basic knowledge of Control Theory, Linear Algebra and Stochastic Calculus.
Evaluating direct transcription and nonlinear optimization methods for robot motion planning. Pardo, D.; Moeller, L.; Neunert, M.; Winkler, A. W.; and Buchli, J. IEEE Robotics and Automation Letters (RA-L). 2016
Evaluating direct transcription and nonlinear optimization methods for robot motion planning [pdf] pdf   Evaluating direct transcription and nonlinear optimization methods for robot motion planning [link] video   Evaluating direct transcription and nonlinear optimization methods for robot motion planning [link] link   doi   bibtex   abstract
@article{pardo16,
  author    = {Pardo, Diego and 
              Moeller, Lukas and 
              Neunert, Michael and 
              Winkler, Alexander W. and
              Buchli, Jonas},
  title     = {Evaluating direct transcription and nonlinear optimization 
              methods for robot motion planning},
  journal   = {IEEE Robotics and Automation Letters (RA-L)},
  pages     = {946-953},
  doi       = {10.1109/LRA.2016.2527062},
  year      = {2016},
  abstract  = {This paper studies existing direct transcription
               methods for trajectory optimization applied to robot motion
               planning. There are diverse alternatives for the implementation
               of direct transcription. In this study we analyze the effects of
               such alternatives when solving a robotics problem. Different
               parameters such as integration scheme, number of discretization
               nodes, initialization strategies and complexity of the problem
               are evaluated. We measure the performance of the methods in
               terms of computational time, accuracy and quality of the solu-
               tion. Additionally, we compare two optimization methodologies
               frequently used to solve the transcribed problem, namely Sequen-
               tial Quadratic Programming (SQP) and Interior Point Method
               (IPM). As a benchmark, we solve different motion tasks on an
               underactuated and non-minimal-phase ball-balancing robot with
               a 10 dimensional state space and 3 dimensional input space.
               Additionally, we validate the results on a simulated 3D quadrotor.
               Finally, as a verification of using direct transcription methods
               for trajectory optimization on real robots, we present hardware
               experiments on a motion task including path constraints and
               actuation limits.},
  keywords  = {Optimization and Optimal Control, Underactuated Robots},
}

This paper studies existing direct transcription methods for trajectory optimization applied to robot motion planning. There are diverse alternatives for the implementation of direct transcription. In this study we analyze the effects of such alternatives when solving a robotics problem. Different parameters such as integration scheme, number of discretization nodes, initialization strategies and complexity of the problem are evaluated. We measure the performance of the methods in terms of computational time, accuracy and quality of the solu- tion. Additionally, we compare two optimization methodologies frequently used to solve the transcribed problem, namely Sequen- tial Quadratic Programming (SQP) and Interior Point Method (IPM). As a benchmark, we solve different motion tasks on an underactuated and non-minimal-phase ball-balancing robot with a 10 dimensional state space and 3 dimensional input space. Additionally, we validate the results on a simulated 3D quadrotor. Finally, as a verification of using direct transcription methods for trajectory optimization on real robots, we present hardware experiments on a motion task including path constraints and actuation limits.
Planning and Execution of Dynamic Whole-Body Locomotion for a Hydraulic Quadruped on Challenging Terrain. Winkler, A. W.; Mastalli, C.; Havoutis, I.; Focchi, M.; Caldwell, D.; and Semini, C. In IEEE International Conference on Robotics and Automation (ICRA). 2015
Planning and Execution of Dynamic Whole-Body Locomotion for a Hydraulic Quadruped on Challenging Terrain [pdf] pdf   Planning and Execution of Dynamic Whole-Body Locomotion for a Hydraulic Quadruped on Challenging Terrain [link] video   Planning and Execution of Dynamic Whole-Body Locomotion for a Hydraulic Quadruped on Challenging Terrain [link] link   doi   bibtex   abstract
@inproceedings{winkler15,
  author    = {Winkler, Alexander W. and 
               Mastalli, Carlos and
               Havoutis, Ioannis and 
               Focchi, Michele and 
               Caldwell, Darwin and
               Semini, Claudio},
  booktitle = {IEEE International Conference on Robotics and Automation (ICRA)},   
  title     = {Planning and Execution of Dynamic Whole-Body Locomotion 
               for a Hydraulic Quadruped on Challenging Terrain},
  year      = {2015},
  pages     = {5148-5154},
  doi       = {10.1109/ICRA.2015.7139916},
  abstract  = {We present a framework for dynamic
               quadrupedal locomotion over challenging terrain, where
               the choice of appropriate footholds is crucial for the success
               of the behaviour. We build a model of the environment on-line
               and on-board using an efficient occupancy grid representation.
               We use Any-time-Repairing A* (ARA*) to search over a tree
               of possible actions, choose a rough body path and select the
               locally-best footholds accordingly. We run a n-step lookahead
               optimization of the body trajectory using a dynamic stability
               metric, the Zero Moment Point (ZMP), that generates natural
               dynamic whole-body motions. A combination of floating-base
               inverse dynamics and virtual model control accurately
               executes the desired motions on an actively compliant system.
               Experimental trials show that this framework allows us to
               traverse terrains at nearly 6 times the speed of our previous
               work, evaluated over the same set of trials.}
}

We present a framework for dynamic quadrupedal locomotion over challenging terrain, where the choice of appropriate footholds is crucial for the success of the behaviour. We build a model of the environment on-line and on-board using an efficient occupancy grid representation. We use Any-time-Repairing A* (ARA*) to search over a tree of possible actions, choose a rough body path and select the locally-best footholds accordingly. We run a n-step lookahead optimization of the body trajectory using a dynamic stability metric, the Zero Moment Point (ZMP), that generates natural dynamic whole-body motions. A combination of floating-base inverse dynamics and virtual model control accurately executes the desired motions on an actively compliant system. Experimental trials show that this framework allows us to traverse terrains at nearly 6 times the speed of our previous work, evaluated over the same set of trials.
On-line and on-board planning for quadrupedal locomotion, using practical, on-board perception. Mastalli, C.; Havoutis, I.; Winkler, A. W.; Caldwell, D.; and Semini, C. In IEEE International Conference on Practial Robot Applications. 2015
On-line and on-board planning for quadrupedal locomotion, using practical, on-board perception [pdf] pdf   bibtex   abstract
@inproceedings{mastalli2015,
  author    = {Mastalli, Carlos and 
               Havoutis, Ioannis and 
               Winkler, Alexander W. and  
               Caldwell, Darwin and 
               Semini, Claudio},
  booktitle = {IEEE International Conference on Practial Robot Applications},
  title     = {On-line and on-board planning for quadrupedal locomotion, 
               using practical, on-board perception},
  year      = {2015},
  abstract  = {We present a legged motion planning approach
               for quadrupedal locomotion over challenging terrain. We de-
               compose the problem into body action planning and footstep
               planning. We use a lattice representation together with a set of
               defined body movement primitives for computing a body action
               plan. The lattice representation allows us to plan versatile 
               move ments that ensure feasibility for every possible plan. To
               this end, we propose a set of rules that define the footstep 
               search regions and footstep sequence given a body action. We use
               Anytime Repairing A* (ARA*) search that guarantees bounded sub-
               optimal plans. Our main contribution is a planning approach
               that generates on-line versatile movements. Experimental trials
               demonstrate the performance of our planning approach in a
               set of challenging terrain conditions. The terrain information
               and plans are computed on-line and on-board.},
}

We present a legged motion planning approach for quadrupedal locomotion over challenging terrain. We de- compose the problem into body action planning and footstep planning. We use a lattice representation together with a set of defined body movement primitives for computing a body action plan. The lattice representation allows us to plan versatile move ments that ensure feasibility for every possible plan. To this end, we propose a set of rules that define the footstep search regions and footstep sequence given a body action. We use Anytime Repairing A* (ARA*) search that guarantees bounded sub- optimal plans. Our main contribution is a planning approach that generates on-line versatile movements. Experimental trials demonstrate the performance of our planning approach in a set of challenging terrain conditions. The terrain information and plans are computed on-line and on-board.
Path planning with force-based foothold adaptation and virtual model control for torque controlled quadruped robots. Winkler, A. W.; Havoutis, I.; Bazeille, S.; Ortiz, J.; Focchi, M.; Dillmann, R.; Caldwell, D.; and Semini, C. In IEEE International Conference on Robotics and Automation (ICRA). 2014
Path planning with force-based foothold adaptation and virtual model control for torque controlled quadruped robots [pdf] pdf   Path planning with force-based foothold adaptation and virtual model control for torque controlled quadruped robots [link] video   Path planning with force-based foothold adaptation and virtual model control for torque controlled quadruped robots [link] link   doi   bibtex   abstract
@inproceedings{winkler14,
  author    = {Winkler, Alexander W. and 
              Havoutis, Ioannis and 
              Bazeille, Stephane and 
              Ortiz, Jesus and 
              Focchi, Michele and 
              Dillmann, Ruediger and 
              Caldwell, Darwin and 
              Semini, Claudio},
  title     = {Path planning with force-based foothold adaptation and virtual 
               model control for torque controlled quadruped robots},
  booktitle = {IEEE International Conference on Robotics and Automation (ICRA)},
  pages     = {6476--6482},
  year      = {2014},
  doi       = {10.1109/ICRA.2014.6907815},
  isbn      = {9781479936847},
  abstract  = {We present a framework for quadrupedal locomotion over highly 
               challenging terrain where the choice of appropriate footholds 
               is crucial for the success of the behaviour. We use a path 
               planning approach which shares many similarities with the results
               of the DARPA Learning Locomotion challenge and extend it to 
               allow more flexibility and increased robustness. During 
               execution we incorporate an on-line force-based foothold 
               adaptation mechanism that updates the planned motion according 
               to the perceived state of the environment. This way we exploit 
               the active compliance of our system to smoothly interact with 
               the environment, even when this is inaccurately perceived or 
               dynamically changing, and update the planned path on-the-fly. 
               In tandem we use a virtual model controller that provides the
               feed-forward torques that allow increased accuracy together 
               with highly compliant behaviour on an otherwise naturally very
               stiff robotic system. We leverage the full set of benefits 
               that a high performance torque controlled quadruped robot can 
               provide and demonstrate the flexibility and robustness of our 
               approach on a set of experimental trials of increasing 
               difficulty.}
}

We present a framework for quadrupedal locomotion over highly challenging terrain where the choice of appropriate footholds is crucial for the success of the behaviour. We use a path planning approach which shares many similarities with the results of the DARPA Learning Locomotion challenge and extend it to allow more flexibility and increased robustness. During execution we incorporate an on-line force-based foothold adaptation mechanism that updates the planned motion according to the perceived state of the environment. This way we exploit the active compliance of our system to smoothly interact with the environment, even when this is inaccurately perceived or dynamically changing, and update the planned path on-the-fly. In tandem we use a virtual model controller that provides the feed-forward torques that allow increased accuracy together with highly compliant behaviour on an otherwise naturally very stiff robotic system. We leverage the full set of benefits that a high performance torque controlled quadruped robot can provide and demonstrate the flexibility and robustness of our approach on a set of experimental trials of increasing difficulty.
Path Planning and Adaptive Execution based on Force-Feedback for Quadruped Locomotion. Winkler, A. W. Technical Report Karlsruhe Institute of Technology and Italian Institute of Technology. Masters Thesis, 2013
Path Planning and Adaptive Execution based on Force-Feedback for Quadruped Locomotion [pdf] pdf   bibtex
@techreport{winkler13,
  author      = {Winkler, Alexander W.},
  title       = {Path Planning and Adaptive Execution based on Force-Feedback 
                 for Quadruped Locomotion},
  institution = {Karlsruhe Institute of Technology and
                 Italian Institute of Technology},
  year        = {2013},
  note        = {Masters Thesis},
  url_pdf     = {mypdfs/13-msc-thesis-winkler.pdf},
}

Implementation of a Software-Agent to Control a Microgripper in a Dezentralized Manner. Winkler, A. W. Technical Report Karlsruhe Institute of Technology. Bachelors Thesis, 2012.
Implementation of a Software-Agent to Control a Microgripper in a Dezentralized Manner [pdf] pdf   bibtex
@techreport{winkler12,
  author      = {Winkler, Alexander W.},
  title       = {Implementation of a Software-Agent to Control
                 a Microgripper in a Dezentralized Manner},
  institution = {Karlsruhe Institute of Technology},
  year        = {2012},
  note        = {Bachelors Thesis},
}
Adapted from BibBase.org

Blog

Welcome to my blog :-) So far a bit philosophy, a bit diary, let's see where it goes...

Collect memories or things?

Why they're not so different

2018-12-24  ·  4 min read

It's Christmas Eve and I'm waiting for my plane at LAX scrolling through my Instagram feed. An image of a turquoise ocean with a wooden pier stretching out towards the horizon displ... read more

Living like a Buddhist monk

10 days of silent meditation

2018-10-27  ·  10 min read

My ass hurt, my concentration was gone and time seemed to stand still. I squinted open my eyes just enough to see motionless silhouettes sitting like statues of Buddha in a dim-lit ... read more

Why I'm travelling

Exploration vs exploitation

2018-10-09  ·  4 min read

Nowadays, the reasons for travel are assumed to be so obvious, the benefits so universally agreed-upon, that it seems almost inappropriate to ask: Wait, why exactly are you doing ... read more

How to postpone your dreams

Why money can help

2018-09-12  ·  3 min read

Of a 168-hour week, 56 hours are typically spent sleeping and 40 hours earning money. That leaves 72 hours every week to watch cat videos on YouTube  -  this we call spare ... read more