PYROBOCOP is a lightweight Python-based package for control and optimization of robotic systems described by nonlinear Differential Algebraic Equations (DAEs). In particular, the package can handle systems with contacts that are described by complementarity constraints and provides a general framework for specifying obstacle avoidance constraints. The package performs direct transcription of the DAEs into a set of nonlinear equations by performing orthogonal collocation on finite elements. The resulting optimization problem belongs to the class of Mathematical Programs with Complementarity Constraints (MPCCs). MPCCs fail to satisfy commonly assumed constraint qualifications and require special handling of the complementarity constraints in order for NonLinear Program (NLP) solvers to solve them effectively. PYROBOCOP provides automatic reformulation of the complementarity constraints that enables NLP solvers to perform optimization of robotic systems. The package is interfaced with ADOLC for obtaining sparse derivatives by automatic differentiation and IPOPT for performing optimization. We demonstrate the effectiveness of our approach in terms of speed and flexibility. We provide several numerical examples for several robotic systems with collision avoidance as well as contact constraints represented using complementarity constraints. We provide comparisons with other open source optimization packages like CasADi and Pyomo .

In this paper, we consider the use of black-box Gaussian process (GP) models for trajectory tracking control based on feedback linearization, in the context of mechanical systems. We considered two strategies. The first computes the control input directly by using the GP model, whereas the second computes the input after estimating the individual components of the dynamics. We tested the two strategies on a simulated manipulator with seven degrees of freedom, also varying the GP kernel choice. Results show that the second implementation is more robust w.r.t. the kernel choice and model inaccuracies. Moreover, as regards the choice of kernel, the obtained performance shows that the use of a structured kernel, such as a polynomial kernel, is advantageous, because of its effectiveness with both strategies.

Humans quickly solve tasks in novel systems with complex dynamics, without requiring much interaction. While deep reinforcement learning algorithms have achieved tremendous success in many complex tasks, these algorithms need a large number of samples to learn meaningful policies. In this paper, we present a task for navigating a marble to the center of a circular maze. While this system is very intuitive and easy for humans to solve, it can be very difficult and inefficient for standard reinforcement learning algorithms to learn meaningful policies. We present a model that learns to move a marble in the complex environment within minutes of interacting with the real system. Learning consists of initializing a physics engine with parameters estimated using data from the real system. The error in the physics engine is then corrected using Gaussian process regression, which is used to model the residual between real observations and physics engine simulations. The physics engine equipped with the residual model is then used to control the marble in the maze environment using a model-predictive feedback over a receding horizon. We contrast the learning behavior against the time taken by humans to solve the problem to show comparable behavior. To the best of our knowledge, this is the first time that a hybrid model consisting of a full physics engine along with a statistical function approximator has been used to control a complex physical system in real-time using nonlinear model-predictive control (NMPC). Codes for the simulation environment can be downloaded here https://www.merl.com/research/license/CME . A video describing our method could be found here https://youtu.be/xaxNCXBovpc .

We propose a trust region method for policy optimization that employs Quasi-Newton approximation for the Hessian, called Quasi-Newton Trust Region Policy Optimization QNTRPO. Gradient descent is the de facto algorithm for reinforcement learning tasks with continuous controls. The algorithm has achieved state-of-the-art performance when used in reinforcement learning across a wide range of tasks. However, the algorithm suffers from a number of drawbacks including: lack of stepsize selection criterion, and slow convergence. We investigate the use of a trust region method using dogleg step and a Quasi-Newton approximation for the Hessian for policy optimization. We demonstrate through numerical experiments over a wide range of challenging continuous control tasks that our particular choice is efficient in terms of number of samples and improves performance

This paper discusses online algorithms for inverse dynamics modelling in robotics. Several model classes including rigid body dynamics (RBD) models, data-driven models and semiparametric models (which are a combination of the previous two classes) are placed in a common framework. While model classes used in the literature typically exploit joint velocities and accelerations, which need to be approximated resorting to numerical differentiation schemes, in this paper a new `derivative-free' framework is proposed that does not require this preprocessing step. An extensive experimental study with real data from the right arm of the iCub robot is presented, comparing different model classes and estimation procedures, showing that the proposed `derivative-free' methods outperform existing methodologies.

This paper presents a problem of model learning to navigate a ball to a goal state in a circular maze environment with two degrees of freedom. Motion of the ball in the maze environment is influenced by several non-linear effects such as friction and contacts, which are difficult to model. We propose a hybrid model to estimate the dynamics of the ball in the maze based on Gaussian Process Regression equipped with basis functions obtained from physic first principles. The accuracy of the hybrid model is compared with standard algorithms for model learning to highlight its efficacy. The learned model is then used to design trajectories for the ball using a trajectory optimization algorithm. We also hope that the system presented in the paper can be used as a benchmark problem for reinforcement and robot learning for its interesting and challenging dynamics and its ease of reproducibility.

Learning robot tasks or controllers using deep reinforcement learning has been proven effective in simulations. Learning in simulation has several advantages. For example, one can fully control the simulated environment, including halting motions while performing computations. Another advantage when robots are involved, is that the amount of time a robot is occupied learning a task---rather than being productive---can be reduced by transferring the learned task to the real robot. Transfer learning requires some amount of fine-tuning on the real robot. For tasks which involve complex (non-linear) dynamics, the fine-tuning itself may take a substantial amount of time. In order to reduce the amount of fine-tuning we propose to learn robustified controllers in simulation. Robustified controllers are learned by exploiting the ability to change simulation parameters (both appearance and dynamics) for successive training episodes. An additional benefit for this approach is that it alleviates the precise determination of physics parameters for the simulator, which is a non-trivial task. We demonstrate our proposed approach on a real setup in which a robot aims to solve a maze puzzle, which involves complex dynamics due to static friction and potentially large accelerations. We show that the amount of fine-tuning in transfer learning for a robustified controller is substantially reduced compared to a non-robustified controller.

This paper presents a semi-parametric algorithm for online learning of a robot inverse dynamics model. It combines the strength of the parametric and non-parametric modeling. The former exploits the rigid body dynamics equa- tion, while the latter exploits a suitable kernel function. We provide an extensive comparison with other methods from the literature using real data from the iCub humanoid robot. In doing so we also compare two different techniques, namely cross validation and marginal likelihood optimization, for estimating the hyperparameters of the kernel function.

A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of regularization/Bayesian techniques. This approach guarantees the identification of stable predictors based on the prediction error minimization. Unluckily, the stability of the predictors does not guarantee the stability of the impulse response of the system. In this paper we propose and compare various techniques to address this issue. Simulations results comparing these techniques will be provided.