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 \gls{ocp}, 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.
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).
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
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.
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.
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.
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.
To traverse complex scenarios reliably a legged robot needs to move its base aided by the ground reaction forces, which can only be generated by the legs that are momentarily in contact with the ground. A proper selection of footholds is crucial for maintaining balance. In this paper, we propose a foothold evaluation criterion that considers the transition feasibility for both linear and angular dynamics to overcome complex scenarios. We devise convex and nonlinear formulations as a direct extension of the Continuous Convex Resolution of Centroidal Dynamic Trajectories (C-CROC) in a receding-horizon fashion to grant dynamic feasibility for future behaviours. The criterion is integrated with a Vision-based Foothold Adaptation (VFA) strategy that takes into account the robot kinematics, leg collisions and terrain morphology. We verify the validity of the selected footholds and the generated trajectories in simulation and experiments with the 90kg quadruped robot HyQ.
The ability of legged systems to traverse highly-constrained environments depends by and large on the performance of their motion and balance controllers. This paper presents a controller that excels in a scenario that most state-of-the-art balance controllers have not yet addressed: line walking, or walking on nearly null support regions. Our approach uses a low-dimensional virtual model (2-DoF) to generate balancing actions through a previously derived four-term balance controller and transforms them to the robot through a derived kinematic mapping. The capabilities of this controller are tested in simulation, where we show the 90kg quadruped robot HyQ crossing a bridge of only 6 cm width (compared to its 4 cm diameter foot sphere), by balancing on two feet at any time while moving along a line. Additional simulations are carried to test the performance of the controller and the effect of external disturbances. The same controller is then used on the real robot to present for the first time a legged robot balancing on a contact line of nearly null support area.
Advances in legged robotics are strongly rooted in animal observations. A clear illustration of this claim is the generalization of Central Pattern Generators (CPG), first identified in the cat spinal cord, to generate cyclic motion in robotic locomotion. Despite a global endorsement of this model, physiological and functional experiments in mammals have also indicated the presence of descending signals from the cerebellum, and reflex feedback from the lower limb sensory cells, that closely interact with CPGs. To this day, these interactions are not fully understood. In some studies, it was demonstrated that pure reflex-based locomotion in the absence of oscillatory signals could be achieved in realistic musculoskeletal simulation models or small compliant quadruped robots. At the same time, biological evidence has attested the functional role of the cerebellum for predictive control of balance and stance within mammals. In this paper, we promote both approaches and successfully apply reflex-based dynamic locomotion, coupled with a balance and gravity compensation mechanism, on the state-of-art HyQ robot. We discuss the importance of this stability module to ensure a correct foot lift-off and maintain a reliable gait. The robotic platform is further used to test two different architectural hypotheses inspired by the cerebellum. An analysis of experimental results demonstrates that the most biologically plausible alternative also leads to better results for robust locomotion.