arXiv subjects

Michael Neunert

Publications and source records attributed to Michael Neunert.

29 records · Page 2Linked to original sources

arXiv2018

The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control

We introduce the Control Toolbox (CT), an open-source C++ library for efficient modeling, control, estimation, trajectory optimization and Model Predictive Control. The CT is applicable to a broad class of dynamic systems but features interfaces to modeling tools specifically designed for robotic applications. This paper outlines the general concept of the toolbox, its main building blocks, and highlights selected application examples. The library contains several tools to design and evaluate controllers, model dynamical systems and solve optimal control problems. The CT was designed for intuitive modeling of systems governed by ordinary differential or difference equations. It supports rapid prototyping of cost functions and constraints and provides standard interfaces for different optimal control solvers. To date, we support Single Shooting, the iterative Linear-Quadratic Regulator, Gauss-Newton Multiple Shooting and classical Direct Multiple Shooting. We provide interfaces to general purpose NLP solvers and Riccati-based linear-quadratic optimal control solvers. The CT was designed to solve large-scale optimal control and estimation problems efficiently and allows for online control of dynamic systems. Some of the key features to enable fast run-time performance are full compatibility with Automatic Differentiation, derivative code generation, and multi-threading. Still, the CT is designed as a modular framework whose building blocks can also be used for other control and estimation applications such as inverse dynamics control, extended Kalman filters or kinematic planning.

cs.RO↗

arXiv2018

Learning by Playing - Solving Sparse Reward Tasks from Scratch

We propose Scheduled Auxiliary Control (SAC-X), a new learning paradigm in the context of Reinforcement Learning (RL). SAC-X enables learning of complex behaviors - from scratch - in the presence of multiple sparse reward signals. To this end, the agent is equipped with a set of general auxiliary tasks, that it attempts to learn simultaneously via off-policy RL. The key idea behind our method is that active (learned) scheduling and execution of auxiliary policies allows the agent to efficiently explore its environment - enabling it to excel at sparse reward RL. Our experiments in several challenging robotic manipulation settings demonstrate the power of our approach.

cs.LG↗

arXiv2018

Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning.

cs.RO↗

arXiv2017

A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward initialization and a closed-loop forward integration. All algorithms have similar computational complexity, i.e. linear complexity in the time horizon, and can be derived in the same computational framework. We compare the full-step variants of our algorithms and present several simulation examples, including a high-dimensional underactuated robot subject to contact switches. Simulation results show that our multiple-shooting algorithms can achieve faster convergence, better local contraction rates and much shorter runtimes than classical iLQR, which makes them a superior choice for nonlinear model predictive control applications.

eess.SY↗

arXiv2017

Whole-Body Nonlinear Model Predictive Control Through Contacts for Quadrupeds

In this work 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, thorough 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 form of periodic and non-periodic tasks are applied to two quadrupeds with different actuation systems. The obtained results underline the performance, transferability and robustness of the approach.

cs.RO↗

arXiv2017

Fast Trajectory Optimization for Legged Robots using Vertex-based ZMP Constraints

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.

cs.RO↗

arXiv2017

An Efficient Optimal Planning and Control Framework For Quadrupedal Locomotion

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.

eess.SY↗

arXiv2016

Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds

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, here 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 integrated our approach with the robot's control and estimation framework such that optimization can be run online. By demonstrating a rough manipulation task with multiple dynamic contact switches, we exemplarily show how optimized trajectories and control inputs can be directly applied to hardware.

cs.RO↗

arXiv2016

An Open Source, Fiducial Based, Visual-Inertial Motion Capture System

Many robotic tasks rely on the accurate localization of moving objects within a given workspace. This information about the objects' poses and velocities are used for control,motion planning, navigation, interaction with the environment or verification. Often motion capture systems are used to obtain such a state estimate. However, these systems are often costly, limited in workspace size and not suitable for outdoor usage. Therefore, we propose a lightweight and easy to use, visual-inertial Simultaneous Localization and Mapping approach that leverages cost-efficient, paper printable artificial landmarks, socalled fiducials. Results show that by fusing visual and inertial data, the system provides accurate estimates and is robust against fast motions and changing lighting conditions. Tight integration of the estimation of sensor and fiducial pose as well as extrinsics ensures accuracy, map consistency and avoids the requirement for precalibration. By providing an open source implementation and various datasets, partially with ground truth information, we enable community members to run, test, modify and extend the system either using these datasets or directly running the system on their own robotic setups.

cs.RO↗

arXiv2016

Evaluating direct transcription and nonlinear optimization methods for robot motion planning

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 solution. Additionally, we compare two optimization methodologies frequently used to solve the transcribed problem, namely Sequential 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.

math.OC↗

arXiv2015

Projection based whole body motion planning for legged robots

In this paper we present a new approach for dynamic motion planning for legged robots. We formulate a trajectory optimization problem based on a compact form of the robot dynamics. Such a form is obtained by projecting the rigid body dynamics onto the null space of the Constraint Jacobian. As consequence of the projection, contact forces are removed from the model but their effects are still taken into account. This approach permits to solve the optimal control problem of a floating base constrained multibody system while avoiding the use of an explicit contact model. We use direct transcription to numerically solve the optimization. As the contact forces are not part of the decision variables the size of the resultant discrete mathematical program is reduced and therefore solutions can be obtained in a tractable time. Using a predefined sequence of contact configurations (phases), our approach solves motions where contact switches occur. Transitions between phases are automatically resolved without using a model for switching dynamics. We present results on a hydraulic quadruped robot (HyQ), including single phase (standing, crouching) as well as multiple phase (rearing, diagonal leg balancing and stepping) dynamic motions.

cs.RO↗