Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robots

This paper introduces a novel Model Predictive Control (MPC) implementation for legged robot locomotion that leverages GPU parallelization. Our approach enables both temporal and state-space parallelization by incorporating a parallel associative scan to solve the primal-dual Karush-Kuhn-Tucker (KKT) system. In this way, the optimal control problem is solved in $\mathcal{O}(n\log{N} + m)$ complexity, instead of $\mathcal{O}(N(n + m)^3)$, where $n$, $m$, and $N$ are the dimension of the system state, control vector, and the length of the prediction horizon. We demonstrate the advantages of this implementation over two state-of-the-art solvers (acados and crocoddyl), achieving up to a 60\% improvement in runtime for Whole Body Dynamics (WB)-MPC and a 700\% improvement for Single Rigid Body Dynamics (SRBD)-MPC when varying the prediction horizon length. The presented formulation scales efficiently with the problem state dimensions as well, enabling the definition of a centralized controller for up to 16 legged robots that can be computed in less than 25 ms. Furthermore, thanks to the JAX implementation, the solver supports large-scale parallelization across multiple environments, allowing the possibility of performing learning with the MPC in the loop directly in GPU.

Non-Gaited Legged Locomotion with Monte-Carlo Tree Search and Supervised Learning

Legged robots are able to navigate complex terrains by continuously interacting with the environment through careful selection of contact sequences and timings. However, the combinatorial nature behind contact planning hinders the applicability of such optimization problems on hardware. In this work, we present a novel approach that optimizes gait sequences and respective timings for legged robots in the context of optimization-based controllers through the use of sampling-based methods and supervised learning techniques. We propose to bootstrap the search by learning an optimal value function in order to speed-up the gait planning procedure making it applicable in real-time. To validate our proposed method, we showcase its performance both in simulation and on hardware using a 22 kg electric quadruped robot. The method is assessed on different terrains, under external perturbations, and in comparison to a standard control approach where the gait sequence is fixed a priori.

PACC: A Passive-Arm Approach for High-Payload Collaborative Carrying with Quadruped Robots Using Model Predictive Control

In this paper, we introduce the concept of using passive arm structures with intrinsic impedance for robot-robot and human-robot collaborative carrying with quadruped robots. The concept is meant for a leader-follower task and takes a minimalist approach that focuses on exploiting the robots' payload capabilities and reducing energy consumption, without compromising the robot locomotion capabilities. We introduce a preliminary arm mechanical design and describe how to use its joint displacements to guide the robot's motion. To control the robot's locomotion, we propose a decentralized Model Predictive Controller that incorporates an approximation of the arm dynamics and the estimation of the external forces from the collaborative carrying. We validate the overall system experimentally by performing both robot-robot and human-robot collaborative carrying on a stair-like obstacle and on rough terrain.

Accelerating Model Predictive Control for Legged Robots through Distributed Optimization

This paper presents a novel approach to enhance Model Predictive Control (MPC) for legged robots through Distributed Optimization. Our method focuses on decomposing the robot dynamics into smaller, parallelizable subsystems, and utilizing the Alternating Direction Method of Multipliers (ADMM) to ensure consensus among them. Each subsystem is managed by its own Optimal Control Problem, with ADMM facilitating consistency between their optimizations. This approach not only decreases the computational time but also allows for effective scaling with more complex robot configurations, facilitating the integration of additional subsystems such as articulated arms on a quadruped robot. We demonstrate, through numerical evaluations, the convergence of our approach on two systems with increasing complexity. In addition, we showcase that our approach converges towards the same solution when compared to a state-of-the-art centralized whole-body MPC implementation. Moreover, we quantitatively compare the computational efficiency of our method to the centralized approach, revealing up to a 75\% reduction in computational time. Overall, our approach offers a promising avenue for accelerating MPC solutions for legged robots, paving the way for more effective utilization of the computational performance of modern hardware.

Fast Convex Visual Foothold Adaptation for Quadrupedal Locomotion

This extended abstract provides a short introduction on our recently developed perception-based controller for quadrupedal locomotion. Compared to our previous approach based on Visual Foothold Adaptation (VFA) and Model Predictive Control (MPC), our new framework combines a fast approximation of the safe foothold regions based on Neural Network regression, followed by a convex decomposition routine in order to generate safe landing areas where the controller can freely optimize the footholds location. The aforementioned framework, which combines prediction, convex decomposition, and MPC solution, is tested in simulation on our 140kg hydraulic quadruped robot (HyQReal).

SafeSteps: Learning Safer Footstep Planning Policies for Legged Robots via Model-Based Priors

We present a footstep planning policy for quadrupedal locomotion that is able to directly take into consideration a-priori safety information in its decisions. At its core, a learning process analyzes terrain patches, classifying each landing location by its kinematic feasibility, shin collision, and terrain roughness. This information is then encoded into a small vector representation and passed as an additional state to the footstep planning policy, which furthermore proposes only safe footstep location by applying a masked variant of the Proximal Policy Optimization (PPO) algorithm. The performance of the proposed approach is shown by comparative simulations on an electric quadruped robot walking in different rough terrain scenarios. We show that violations of the above safety conditions are greatly reduced both during training and the successive deployment of the policy, resulting in an inherently safer footstep planner. Furthermore, we show how, as a byproduct, fewer reward terms are needed to shape the behavior of the policy, which in return is able to achieve both better final performances and sample efficiency

Quadrupedal Footstep Planning using Learned Motion Models of a Black-Box Controller

Legged robots are increasingly entering new domains and applications, including search and rescue, inspection, and logistics. However, for such systems to be valuable in real-world scenarios, they must be able to autonomously and robustly navigate irregular terrains. In many cases, robots that are sold on the market do not provide such abilities, being able to perform only blind locomotion. Furthermore, their controller cannot be easily modified by the end-user, requiring a new and time-consuming control synthesis. In this work, we present a fast local motion planning pipeline that extends the capabilities of a black-box walking controller that is only able to track high-level reference velocities. More precisely, we learn a set of motion models for such a controller that maps high-level velocity commands to Center of Mass (CoM) and footstep motions. We then integrate these models with a variant of the A star algorithm to plan the CoM trajectory, footstep sequences, and corresponding high-level velocity commands based on visual information, allowing the quadruped to safely traverse irregular terrains at demand.

Kinematically-Decoupled Impedance Control for Fast Object Visual Servoing and Grasping on Quadruped Manipulators

We propose a control pipeline for SAG (Searching, Approaching, and Grasping) of objects, based on a decoupled arm kinematic chain and impedance control, which integrates image-based visual servoing (IBVS). The kinematic decoupling allows for fast end-effector motions and recovery that leads to robust visual servoing. The whole approach and pipeline can be generalized for any mobile platform (wheeled or tracked vehicles), but is most suitable for dynamically moving quadruped manipulators thanks to their reactivity against disturbances. The compliance of the impedance controller makes the robot safer for interactions with humans and the environment. We demonstrate the performance and robustness of the proposed approach with various experiments on our 140 kg HyQReal quadruped robot equipped with a 7-DoF manipulator arm. The experiments consider dynamic locomotion, tracking under external disturbances, and fast motions of the target object.

ViTAL: Vision-Based Terrain-Aware Locomotion for Legged Robots

This work is on vision-based planning strategies for legged robots that separate locomotion planning into foothold selection and pose adaptation. Current pose adaptation strategies optimize the robot's body pose relative to given footholds. If these footholds are not reached, the robot may end up in a state with no reachable safe footholds. Therefore, we present a Vision-Based Terrain-Aware Locomotion (ViTAL) strategy that consists of novel pose adaptation and foothold selection algorithms. ViTAL introduces a different paradigm in pose adaptation that does not optimize the body pose relative to given footholds, but the body pose that maximizes the chances of the legs in reaching safe footholds. ViTAL plans footholds and poses based on skills that characterize the robot's capabilities and its terrain-awareness. We use the 90 kg HyQ and 140 kg HyQReal quadruped robots to validate ViTAL, and show that they are able to climb various obstacles including stairs, gaps, and rough terrains at different speeds and gaits. We compare ViTAL with a baseline strategy that selects the robot pose based on given selected footholds, and show that ViTAL outperforms the baseline.

A Whole-Body Controller Based on a Simplified Template for Rendering Impedances in Quadruped Manipulators

Quadrupedal manipulators require to be compliant when dealing with external forces during autonomous manipulation, tele-operation or physical human-robot interaction. This paper presents a whole-body controller that allows for the implementation of a Cartesian impedance control to coordinate tracking performance and desired compliance for the robot base and manipulator arm. The controller is formulated through an optimization problem using Quadratic Programming (QP) to impose a desired behavior for the system while satisfying friction cone constraints, unilateral force constraints, joint and torque limits. The presented strategy decouples the arm and the base of the platform, enforcing the behavior of a linear double-mass spring damper system, and allows to independently tune their inertia, stiffness and damping properties. The control architecture is validated through an extensive simulation study using the 90kg HyQ robot equipped with a 7-DoF manipulator arm. Simulation results show the impedance rendering performance when external forces are applied at the arm's end-effector. The paper presents results for full stance condition (all legs on the ground) and, for the first time, also shows how the impedance rendering is affected by the contact conditions during a dynamic gait.