Ludovic Righetti

New York University | NYU · Department of Electrical and Computer Engineering

The tremendous success of behavior cloning (BC) in robotic manipulation has been largely confined to tasks where demonstrations can be effectively collected through human teleoperation. However, demonstrations for contact-rich manipulation tasks that require complex coordination of multiple contacts are difficult to collect due to the limitations o...

The recent promises of Model Predictive Control in robotics have motivated the development of tailored second-order methods to solve optimal control problems efficiently. While those methods benefit from strong convergence properties, tailored efficient implementations are challenging to derive. In this work, we study the potential effectiveness of...

Parkour poses a significant challenge for legged robots, requiring navigation through complex environments with agility and precision based on limited sensory inputs. In this work, we introduce a novel method for training end-to-end visual policies, from depth pixels to robot control commands, to achieve agile and safe quadruped locomotion. We form...

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 nonl...

Trajectory optimization under uncertainties is a challenging problem for robots in contact with the environment. Such uncertainties are inevitable due to estimation errors, control imperfections, and model mismatches between planning models used for control and the real robot dynamics. This induces control policies that could violate the contact lo...

Hierarchical least-squares programs with linear constraints (HLSP) are a type of optimization problem very common in robotics. Each priority level contains an objective in least-squares form which is subject to the linear constraints of the higher priority levels. Active-set methods are a popular choice for solving them. However, they can perform p...

In robotics, designing robust algorithms in the face of estimation uncertainty is a challenging task. Indeed, controllers often do not consider the 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. In this work, we pres...

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...

Generation of robust trajectories for legged robots remains a challenging task due to the underlying nonlinear, hybrid and intrinsically unstable dynamics which needs to be stabilized through limited contact forces. Furthermore, disturbances arising from unmodelled contact interactions with the environment and model mismatches can hinder the qualit...

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 odome...

Online trajectory optimization techniques generally depend on heuristic-based contact planners in order to have low computation times and achieve high replanning frequencies. In this work, we propose ContactNet, a fast acyclic contact planner based on a multi-output regression neural network. ContactNet ranks discretized stepping regions, allowing...

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 lo...

We present a general, two-stage reinforcement learning approach to create robust policies that can be deployed on real robots without any additional training using a single demonstration generated by trajectory optimization. The demonstration is used in the first stage as a starting point to facilitate initial exploration. In the second stage, the...

In this letter, we study dynamic game optimal control with imperfect state observations and introduce an iterative method to find a local Nash equilibrium. The algorithm consists of an iterative procedure combining a backward recursion similar to minimax differential dynamic programming and a forward recursion resembling a risk-sensitive Kalman smo...

In this letter, we study dynamic game optimal control with imperfect state observations and introduce an iterative method to find a local Nash equilibrium. The algorithm consists of an iterative procedure combining a backward recursion similar to minimax differential dynamic programming and a forward recursion resembling a risk-sensitive Kalman smo...

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-val...

Being able to seamlessly generalize across different tasks is fundamental for robots to act in our world. However, learning representations that generalize quickly to new scenarios is still an open research problem in reinforcement learning. In this paper we present a framework to meta-learn the critic for gradient-based policy learning. Concretely...

The simulation of multibody systems with frictional contacts is a fundamental tool for many fields, such as robotics, computer graphics, and mechanics. Hard frictional contacts are particularly troublesome to simulate because they make differential equations stiff, calling for computationally demanding implicit integration schemes. We suggest to ta...

State of the art legged robots are either capable of measuring torque at the output of their drive systems, or have transparent drive systems which enable the computation of joint torques from motor currents. In either case, this sensor modality is seldom used in state estimation. In this paper, we propose to use joint torque measurements to estima...

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 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 gai...

Optimal control is a successful approach to generate motions for complex robots, in particular for legged locomotion. However, these techniques are often too slow to run in real time for model predictive control or one needs to drastically simplify the dynamics model. In this work, we present a method to learn to predict the gradient and hessian of...

Model predictive control (MPC) has shown great success for controlling complex systems, such as legged robots. However, when closing the loop, the performance and feasibility of the finite horizon optimal control problem (OCP) solved at each control cycle are not guaranteed anymore. This is due to model discrepancies, the effect of low-level contro...

Model predictive control (MPC) has shown great success for controlling complex systems such as legged robots. However, when closing the loop, the performance and feasibility of the finite horizon optimal control problem solved at each control cycle is not guaranteed anymore. This is due to model discrepancies, the effect of low-level controllers, u...

In this paper, we propose a novel framework capable of generating various walking and running gaits for bipedal robots. The main goal is to relax the fixed center of mass (CoM) height assumption of the linear inverted pendulum model (LIPM) and generate a wider range of walking and running motions, without a considerable increase in complexity. To d...

In this paper, we propose a novel framework capable of generating various walking and running gaits for bipedal robots. The main goal is to relax the fixed center of mass (CoM) height assumption of the linear inverted pendulum model (LIPM) and generate a wider range of walking and running motions, without a considerable increase in complexity. To d...

This work addresses the problem of risk-sensitive control for nonlinear systems with imperfect state observations, extending results for the linear case. In particular, we derive an algorithm that can compute local solutions with computational complexity similar to the iterative linear quadratic regulator algorithm. The proposed algorithm introduce...

Oscillators have two main limitations: their synchronization properties are limited (i.e they have a finite synchronization region) and they have no memory of past interactions (i.e. they return to their intrinsic frequency whenever the entraining signal disappears). We previously proposed a general mechanism to transform an oscillator into an adap...

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 mor...

In this work we present a general, two-stage reinforcement learning approach for going from a single demonstration trajectory to a robust policy that can be deployed on hardware without any additional training. The demonstration is used in the first stage as a starting point to facilitate initial exploration. In the second stage, the relevant task...

Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function approximators such as neural networks to capture the system dynamics directly from sensor measurements. As for now, c...

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 clos...

Cost functions have the potential to provide compact and understandable generalizations of motion. The goal of Inverse Optimal Control (IOC) is to analyze an observed behavior which is assumed to be optimal with respect to an unknown cost function, and infer this cost function. Here we develop a method for characterizing cost functions of legged lo...

This paper addresses the problem of computing optimal impedance schedules for legged locomotion tasks involving complex contact interactions. We formulate the problem of impedance regulation as a trade-off between disturbance rejection and measurement uncertainty. We extend a stochastic optimal control algorithm known as Risk Sensitive Control to t...

In this paper, we present a novel two-level variable Horizon Model Predictive Control (VH-MPC) framework for bipedal locomotion. In this framework, the higher level computes the landing location and timing (horizon length) of the swing foot to stabilize the unstable part of the center of mass (CoM) dynamics, using feedback from the CoM states. The...

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...

In the past decade, numerous machine learning algorithms have been shown to successfully learn optimal policies to control real robotic systems. However, it is common to encounter failing behaviors as the learning loop progresses. Specifically, in robot applications where failing is undesired but not catastrophic, many algorithms struggle with leve...

The simulation of multi-body systems with frictional contacts is a fundamental tool for many fields, such as robotics, computer graphics, and mechanics. Hard frictional contacts are particularly troublesome to simulate because they make the differential equations stiff, calling for computationally demanding implicit integration schemes. We suggest...

Contacts between robots and environment are often assumed to be rigid for control purposes. This assumption can lead to poor performance when contacts are soft and/or underdamped. However, the problem of balancing on soft contacts has not received much attention in the literature. This paper presents two novel approaches to control a legged robot b...

This paper addresses the problem of computing optimal impedance schedules for legged locomotion tasks involving complex contact interactions. We formulate the problem of impedance regulation as a trade-off between disturbance rejection and measurement uncertainty. We extend a stochastic optimal control algorithm known as Risk Sensitive Control to t...

Learning for model based control can be sample-efficient and generalize well, however successfully learning models and controllers that represent the problem at hand can be challenging for complex tasks. Using inaccurate models for learning can lead to sub-optimal solutions, that are unlikely to perform well in practice. In this work, we present a...

Whole-body optimizers have been successful at automatically computing complex dynamic locomotion behaviors. However they are often limited to offline planning as they are computationally too expensive to replan with a high frequency. Simpler models are then typically used for online replanning. In this paper we present a method to generate whole bo...

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 using reinforcement learning to approximately learn the 3D capture region for such systems. We propose a novel 3D reactive stepper...

In this paper, we present a novel two-level variable Horizon Model Predictive Control (VH-MPC) framework for bipedal locomotion. In this framework, the higher level computes the landing location and timing (horizon length) of the swing foot to stabilize the unstable part of the center of mass (CoM) dynamics, using feedback from the CoM state. The l...

In the past decade, numerous machine learning algorithms have been shown to successfully learn optimal policies to control real robotic systems. However, it is not rare to encounter failing behaviors as the learning loop progresses. Specifically, in robot applications where failing is undesired but not catastrophic, many algorithms struggle with le...

This paper investigates the problem of efficient computation of physically consistent multi-contact 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...

Dexterous object manipulation remains an open problem in robotics, despite the rapid progress in machine learning during the past decade. We argue that a hindrance is the high cost of experimentation on real systems, in terms of both time and money. We address this problem by proposing an open-source robotic platform which can safely operate withou...

Reinforcement learning algorithms have shown great success in solving different problems ranging from playing video games to robotics. However, they struggle to solve delicate robotic problems, especially those involving contact interactions. Though in principle a policy directly outputting joint torques should be able to learn to perform these tas...

Linear Model Predictive Control (MPC) has been successfully used for generating feasible walking motions for humanoid robots. However, the effect of uncertainties on constraints satisfaction has only been studied using Robust MPC (RMPC) approaches, which account for the worst-case realization of bounded disturbances at each time instant. In this le...

Stochastic Optimal Control (SOC) typically considers noise only in the process model, i.e. unknown disturbances. However, in many robotic applications involving interaction with the environment, such as locomotion and manipulation, uncertainty also comes from lack of precise knowledge of the world, which is not an actual disturbance. We analyze the...

Step adjustment can improve the gait robustness of biped robots; however, the adaptation of step timing is often neglected as it gives rise to nonconvex problems when optimized over several footsteps. In this article, we argue that it is not necessary to optimize walking over several steps to ensure gait viability and show that it is sufficient to...

We introduce Crocoddyl (Contact RObot COntrol by Differential DYnamic Library), an open-source framework tailored for efficient multi-contact optimal control. Crocoddyl efficiently computes the state trajectory and the control policy for a given predefined sequence of contacts. Its efficiency is due to the use of sparse analytical derivatives, expl...

We present a new open-source torque-controlled legged robot system, with a low-cost and low-complexity actuator module at its core. It consists of a high-torque brushless DC motor and a low-gear-ratio transmission suitable for impedance and force control. We also present a novel foot contact sensor suitable for legged locomotion with hard impacts....

Humanoid robots maintain balance and navigate by controlling the contact wrenches applied to the environment. While it is possible to plan dynamically-feasible motion that applies appropriate wrenches using existing methods, a humanoid may also be affected by external disturbances. Existing systems typically rely on controllers to reactively recove...

We present a new open-source torque-controlled legged robot system, with a low cost and low complexity actuator module at its core. It consists of a low-weight high torque brushless DC motor and a low gear ratio transmission suitable for impedance and force control. We also present a novel foot contact sensor suitable for legged locomotion with har...