We present an iterative inverse reinforcement learning algorithm to infer optimal cost functions in continuous spaces. Based on a popular maximum entropy criteria, our approach iteratively finds a weight improvement step and proposes a method to find an appropriate step size that ensures learned cost function features remain similar to the demonstrated trajectory features. In contrast to similar approaches, our algorithm can individually tune the effectiveness of each observation for the partition function based on the current estimate of the cost function parameters, guiding the algorithm towards better estimates in the following iterations. In addition, it does not need a large sample set, enabling faster learning. We generate sample trajectories by solving an optimal control problem instead of random sampling, leading to more informative trajectories. The performance of our method is compared to two state of the art algorithms to demonstrate its benefits in several simulated environments.

The promise of model-predictive control in robotics has led to extensive development of efficient numerical optimal control solvers in line with differential dynamic programming because it exploits the sparsity induced by time. In this work, we argue that this effervescence has hidden the fact that sparsity can be equally exploited by standard nonlinear optimization. In particular, we show how a tailored implementation of sequential quadratic programming achieves state-of-the-art model-predictive control. Then, we clarify the connections between popular algorithms from the robotics community and well-established optimization techniques. Further, the sequential quadratic program formulation naturally encompasses the constrained case, a notoriously difficult problem in the robotics community. Specifically, we show that it only requires a sparsity-exploiting implementation of a state-of-the-art quadratic programming solver. We illustrate the validity of this approach in a comparative study and experiments on a torque-controlled manipulator. To the best of our knowledge, this is the first demonstration of closed loop nonlinear model-predictive control with constraints on a real robot.

Designing robust algorithms in the face of estimation uncertainty is a challenging task. Indeed, controllers seldom consider estimation uncertainty and only rely on the most likely estimated state. Consequently, sudden changes in the environment or the robot’s dynamics can lead to catastrophic behaviors. Leveraging recent results in risk-sensitive optimal control, this paper presents a risk-sensitive Extended Kalman Filter that can adapt its estimation to the control objective, hence allowing safe output-feedback Model Predictive Control (MPC). By taking a pessimistic estimate of the value function resulting from the MPC controller, the filter provides increased robustness to the controller in phases of uncertainty as compared to a standard Extended Kalman Filter (EKF). The filter has the same computational complexity as an EKF and can be used for real-time control. The paper evaluates the risk-sensitive behavior of the proposed filter when used in a nonlinear MPC loop on a planar drone and industrial manipulator in simulation, as well as on an external force estimation task on a real quadruped robot. These experiments demonstrate the ability of the approach to significantly improve performance in face of uncertainties.

Implementing dynamic locomotion behaviors on legged robots requires a high-quality state estimation module. Especially when the motion includes flight phases, state-of-the-art approaches fail to produce reliable estimation of the robot posture, in particular base height. In this paper, we propose a novel approach for combining visual-inertial odometry (VIO) with leg odometry in an extended Kalman filter (EKF) based state estimator. The VIO module uses a stereo camera and IMU to yield low-drift 3D position and yaw orientation and drift-free pitch and roll orientation of the robot base link in the inertial frame. However, these values have a considerable amount of latency due to image processing and optimization, while the rate of update is quite low which is not suitable for low-level control. To reduce the latency, we predict the VIO state estimate at the rate of the IMU measurements of the VIO sensor. The EKF module uses the base pose and linear velocity predicted by VIO, fuses them further with a second high-rate IMU and leg odometry measurements, and produces robot state estimates with a high frequency and small latency suitable for control. We integrate this lightweight estimation framework with a nonlinear model predictive controller and show successful implementation of a set of agile locomotion behaviors, including trotting and jumping at varying horizontal speeds, on a torque-controlled quadruped robot.

Model predictive control is a powerful tool to generate complex motions for robots. However, it often requires solving non-convex problems online to produce rich behaviors, which is computationally expensive and not always practical in real time. Additionally, direct integration of high dimensional sensor data (e.g. RGB-D images) in the feedback loop is challenging with current state-space methods. This paper aims to address both issues. It introduces a model predictive control scheme, where a neural network constantly updates the cost function of a quadratic program based on sensory inputs, aiming to minimize a general non-convex task loss without solving a non-convex problem online. By updating the cost, the robot is able to adapt to changes in the environment directly from sensor measurement without requiring a new cost design. Furthermore, since the quadratic program can be solved efficiently with hard constraints, a safe deployment on the robot is ensured. Experiments with a wide variety of reaching tasks on an industrial robot manipulator demonstrate that our method can efficiently solve complex non-convex problems with high-dimensional visual sensory inputs, while still being robust to external disturbances.

This paper presents an efficient approach to object manipulation planning using Monte Carlo Tree Search (MCTS) to find contact sequences and an efficient ADMM-based trajectory optimization algorithm to evaluate the dynamic feasibility of candidate contact sequences. To accelerate MCTS, we propose a methodology to learn a goal-conditioned policy-value network and a feasibility classifier to direct the search towards promising nodes. Further, manipulation-specific heuristics enable to drastically reduce the search space. Systematic object manipulation experiments in a physics simulator and on real hardware demonstrate the efficiency of our approach. In particular, our approach scales favorably for long manipulation sequences thanks to the learned policy-value network, significantly improving planning success rate. All source code including the baseline can be found at https://hzhu.io/contact-mcts.

Online planning of whole-body motions for legged robots is challenging due to the inherent nonlinearity in the robot dynamics. In this work, we propose a nonlinear model predictive control (MPC) framework, the BiConMP which can generate whole body trajectories online by efficiently exploiting the structure of the robot dynamics. BiConMP is used to generate various cyclic gaits on a real quadruped robot and its performance is evaluated on different terrain, countering unforeseen pushes, and transitioning online between different gaits. Furthermore, the ability of BiConMP to generate nontrivial acyclic whole-body dynamic motions on the robot is presented. The same approach is also used to generate various dynamic motions in MPC on a humanoid robot (Talos) and another quadruped robot (AnYmal) in simulation. Finally, an extensive empirical analysis on the effects of planning horizon and frequency on the nonlinear MPC framework is reported and discussed.

Model Predictive Control (MPC) promises to endow robots with enough reactivity to perform complex tasks in dynamic environments by frequently updating their motion plan based on measurements. Despite its appeal, it has seldom been deployed on real machines because of scaling constraints. This paper presents the first hardware implementation of closed-loop nonlinear MPC on a 7-DoF torque-controlled robot. Our controller leverages a state-of-the art optimal control solver, namely Differential Dynamic Programming (DDP), in order to replan state and control trajectories at real-time rates (1kHz). In addition to this experimental proof of concept, an exhaustive performance analysis shows that our controller outperforms open-loop MPC on a rapid cyclic end-effector task. We also exhibit the importance of a sufficient preview horizon and full robot dynamics through comparisons with inverse dynamics and kinematic optimization.

Reactive stepping and push recovery for biped robots is often restricted to flat terrains because of the difficulty in computing capture regions for nonlinear dynamic models. In this paper, we address this limitation by proposing a novel 3D reactive stepper, the DeepQ stepper, that can approximately learn the 3D capture regions of both simplified and full robot dynamic models using reinforcement learning, which can then be used to find optimal steps. The stepper can take into account the entire dynamics of the robot, ignored in most reactive steppers, leading to a significant improvement in performance. The DeepQ stepper can handle nonconvex terrain with obstacles, walk on restricted surfaces like stepping stones while tracking different velocities, and recover from external disturbances for a constant low computational cost.

In this paper we explore the use of block coordinate descent (BCD) to optimize the centroidal momentum dynamics for dynamically consistent multi-contact behaviors. The centroidal dynamics have recently received a large amount of attention in order to create physically realizable motions for robots with hands and feet while being computationally more tractable than full rigid body dynamics models. Our contribution lies in exploiting the structure of the dynamics in order to simplify the original non-convex problem into two convex subproblems. We iterate between these two subproblems for a set number of iterations or until a consensus is reached. We explore the properties of the proposed optimization method for the centroidal dynamics and verify in simulation that motions generated by our approach can be tracked by the quadruped Solo12. In addition, we compare our method to a recently proposed convexification using a sequence of convex relaxations as well as a more standard interior point method used in the off-the-shelf solver IPOPT to show that our approach finds similar, if not better, trajectories (in terms of cost), and is more than four times faster than both approaches. Finally, compared to previous approaches, we note its practicality due to the convex nature of each subproblem which allows our method to be used with any off-the-shelf quadratic programming solver.

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.

Ancient Sanskrit manuscripts are a rich source of knowledge about Science, Mathematics, Hindu mythology, Indian civilization, and culture. It therefore becomes critical that access to these manuscripts is made easy, to share this knowledge with the world and to facilitate further research on this Ancient literature. In this paper, we propose a Convolutional Neural Network (CNN) based Optical Character Recognition system (OCR) which accurately digitizes Ancient Sanskrit manuscripts (Devanagari Script) that are not necessarily in good condition. We use an image segmentation algorithm for calculating pixel intensities to identify letters in the image. The OCR considers typical compound characters (half letter combinations) as separate classes in order to improve the segmentation accuracy. The novelty of the OCR is its robustness to image quality, image contrast, font style and font size, which makes it an ideal choice for digitizing soiled and poorly maintained Sanskrit manuscripts.