Infinite-Horizon Value Function Approximation for Model Predictive Control

Model Predictive Control has emerged as a popular tool for robots to generate complex motions. However, the real-time requirement has limited the use of hard constraints and large preview horizons, which are necessary to ensure safety and stability. In practice, practitioners have to carefully design cost functions that can imitate an infinite horizon formulation, which is tedious and often results in local minima. In this work, we study how to approximate the infinite horizon value function of constrained optimal control problems with neural networks using value iteration and trajectory optimization. Furthermore, we demonstrate how using this value function approximation as a terminal cost provides global stability to the model predictive controller. The approach is validated on two toy problems and a real-world scenario with online obstacle avoidance on an industrial manipulator where the value function is conditioned to the goal and obstacle.

Should We Learn Contact-Rich Manipulation Policies from Sampling-Based Planners?

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 of current teleoperation interfaces. We investigate how to leverage model-based planning and optimization to generate training data for contact-rich dexterous manipulation tasks. Our analysis reveals that popular sampling-based planners like rapidly exploring random tree (RRT), while efficient for motion planning, produce demonstrations with unfavorably high entropy. This motivates modifications to our data generation pipeline that prioritizes demonstration consistency while maintaining solution diversity. Combined with a diffusion-based goal-conditioned BC approach, our method enables effective policy learning and zero-shot transfer to hardware for two challenging contact-rich manipulation tasks.

Safe Reinforcement Learning of Robot Trajectories in the Presence of Moving Obstacles

In this paper, we present an approach for learning collision-free robot trajectories in the presence of moving obstacles. As a first step, we train a backup policy to generate evasive movements from arbitrary initial robot states using model-free reinforcement learning. When learning policies for other tasks, the backup policy can be used to estimate the potential risk of a collision and to offer an alternative action if the estimated risk is considered too high. No matter which action is selected, our action space ensures that the kinematic limits of the robot joints are not violated. We analyze and evaluate two different methods for estimating the risk of a collision. A physics simulation performed in the background is computationally expensive but provides the best results in deterministic environments. If a data-based risk estimator is used instead, the computational effort is significantly reduced, but an additional source of error is introduced. For evaluation, we successfully learn a reaching task and a basketball task while keeping the risk of collisions low. The results demonstrate the effectiveness of our approach for deterministic and stochastic environments, including a human-robot scenario and a ball environment, where no state can be considered permanently safe. By conducting experiments with a real robot, we show that our approach can generate safe trajectories in real time.

Accelerated gradient descent for high frequency Model Predictive Control

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 first-order methods and show on a torque controlled manipulator that they can equal the performances of second-order methods.

iDb-RRT: Sampling-based Kinodynamic Motion Planning with Motion Primitives and Trajectory Optimization

Rapidly-exploring Random Trees (RRT) and its variations have emerged as a robust and efficient tool for finding collision-free paths in robotic systems. However, adding dynamic constraints makes the motion planning problem significantly harder, as it requires solving two-value boundary problems (computationally expensive) or propagating random control inputs (uninformative). Alternatively, Iterative Discontinuity Bounded A* (iDb-A*), introduced in our previous study, combines search and optimization iteratively. The search step connects short trajectories (motion primitives) while allowing a bounded discontinuity between the motion primitives, which is later repaired in the trajectory optimization step. Building upon these foundations, in this paper, we present iDb-RRT, a sampling-based kinodynamic motion planning algorithm that combines motion primitives and trajectory optimization within the RRT framework. iDb-RRT is probabilistically complete and can be implemented in forward or bidirectional mode. We have tested our algorithm across a benchmark suite comprising 30 problems, spanning 8 different systems, and shown that iDb-RRT can find solutions up to 10x faster than previous methods, especially in complex scenarios that require long trajectories or involve navigating through narrow passages.

Efficient Search and Learning for Agile Locomotion on Stepping Stones

Legged robots have become capable of performing highly dynamic maneuvers in the past few years. However, agile locomotion in highly constrained environments such as stepping stones is still a challenge. In this paper, we propose a combination of model-based control, search, and learning to design efficient control policies for agile locomotion on stepping stones. In our framework, we use nonlinear model predictive control (NMPC) to generate whole-body motions for a given contact plan. To efficiently search for an optimal contact plan, we propose to use Monte Carlo tree search (MCTS). While the combination of MCTS and NMPC can quickly find a feasible plan for a given environment (a few seconds), it is not yet suitable to be used as a reactive policy. Hence, we generate a dataset for optimal goal-conditioned policy for a given scene and learn it through supervised learning. In particular, we leverage the power of diffusion models in handling multi-modality in the dataset. We test our proposed framework on a scenario where our quadruped robot Solo12 successfully jumps to different goals in a highly constrained environment.

Multi-contact Stochastic Predictive Control for Legged Robots with Contact Locations Uncertainty

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 location constraints by making contact at unintended locations, and as a consequence leading to unsafe motion plans. This work addresses the problem of robust kino-dynamic whole-body trajectory optimization using stochastic nonlinear model predictive control (SNMPC) by considering additive uncertainties on the model dynamics subject to contact location chance-constraints as a function of robot's full kinematics. We demonstrate the benefit of using SNMPC over classic nonlinear MPC (NMPC) for whole-body trajectory optimization in terms of contact location constraint satisfaction (safety). We run extensive Monte-Carlo simulations for a quadruped robot performing agile trotting and bounding motions over small stepping stones, where contact location satisfaction becomes critical. Our results show that SNMPC is able to perform all motions safely with 100% success rate, while NMPC failed 48.3% of all motions.

Risk-Sensitive Extended Kalman Filter

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 present a risk-sensitive Extended Kalman Filter that allows doing output-feedback Model Predictive Control (MPC) safely. This filter adapts its estimation to the control objective. By taking a pessimistic estimate concerning 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). Moreover, the filter has the same complexity as an EKF, so that it can be used for real-time model-predictive control. The paper evaluates the risk-sensitive behavior of the proposed filter when used in a nonlinear model-predictive control 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 abilities of the approach to improve performance in the face of uncertainties significantly.

Path Planning Under Uncertainty to Localize mmWave Sources

In this paper, we study a navigation problem where a mobile robot needs to locate a mmWave wireless signal. Using the directionality properties of the signal, we propose an estimation and path planning algorithm that can efficiently navigate in cluttered indoor environments. We formulate Extended Kalman filters for emitter location estimation in cases where the signal is received in line-of-sight or after reflections. We then propose to plan motion trajectories based on belief-space dynamics in order to minimize the uncertainty of the position estimates. The associated non-linear optimization problem is solved by a state-of-the-art constrained iLQR solver. In particular, we propose a method that can handle a large number of obstacles (~300) with reasonable computation times. We validate the approach in an extensive set of simulations. We show that our estimators can help increase navigation success rate and that planning to reduce estimation uncertainty can improve the overall task completion speed.

Visual-Inertial and Leg Odometry Fusion for Dynamic Locomotion

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.