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.

ContactNet: Online Multi-Contact Planning for Acyclic Legged Robot Locomotion

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 to quickly choose the best feasible solution, even in complex environments. The low computation time, in the order of 1 ms, makes possible the execution of the contact planner concurrently with a trajectory optimizer in a Model Predictive Control (MPC) fashion. We demonstrate the effectiveness of the approach in simulation in different complex scenarios with the quadruped robot Solo12.

MPC with Sensor-Based Online Cost Adaptation

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.

Efficient Object Manipulation Planning with Monte Carlo Tree Search

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 used 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 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.

Nonlinear Stochastic Trajectory Optimization for Centroidal Momentum Motion Generation of Legged Robots

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 quality of the planned trajectories leading to unsafe motions. In this work, we propose to use stochastic trajectory optimization for generating robust centroidal momentum trajectories to account for additive uncertainties on the model dynamics and parametric uncertainties on contact locations. Through an alternation between the robust centroidal and whole-body trajectory optimizations, we generate robust momentum trajectories while being consistent with the whole-body dynamics. We perform an extensive set of simulations subject to different uncertainties on a quadruped robot showing that our stochastic trajectory optimization problem reduces the amount of foot slippage for different gaits while achieving better performance over deterministic planning.