Michele Focchi

Riccardo Bussola, Michele Focchi, Andrea Del Prete et al.

In this work, we consider the complex control problem of making a monopod reach a target with a jump. The monopod can jump in any direction and the terrain underneath its foot can be uneven. This is a template of a much larger class of problems, which are extremely challenging and computationally expensive to solve using standard optimisation-based techniques. Reinforcement Learning (RL) could be an interesting alternative, but the application of an end-to-end approach in which the controller must learn everything from scratch, is impractical. The solution advocated in this paper is to guide the learning process within an RL framework by injecting physical knowledge. This expedient brings to widespread benefits, such as a drastic reduction of the learning time, and the ability to learn and compensate for possible errors in the low-level controller executing the motion. We demonstrate the advantage of our approach with respect to both optimization-based and end-to-end RL approaches.

Riccardo Bussola, Michele Focchi, Giulio Turrisi et al.

Jumping poses a significant challenge for quadruped robots, despite being crucial for many operational scenarios. While optimisation methods exist for controlling such motions, they are often time-consuming and demand extensive knowledge of robot and terrain parameters, making them less robust in real-world scenarios. Reinforcement learning (RL) is emerging as a viable alternative, yet conventional end-to-end approaches lack efficiency in terms of sample complexity, requiring extensive training in simulations, and predictability of the final motion, which makes it difficult to certify the safety of the final motion. To overcome these limitations, this paper introduces a novel guided reinforcement learning approach that leverages physical intuition for efficient and explainable jumping, by combining Bézier curves with a Uniformly Accelerated Rectilinear Motion (UARM) model. Extensive simulation and experimental results clearly demonstrate the advantages of our approach over existing alternatives.

Ruben Malacarne, Ioannis Tsikelis, Enrico Mingo Hoffman et al.

This paper presents a planning pipeline framework for locomotion in rope-assisted robots climbing vertical surfaces. The proposed framework is formulated as a bi-level optimization scheme that addresses a mixed-integer problem: selecting feasible terrain regions for landing while simultaneously optimizing the control inputs, namely rope tensions and leg forces, and landing location. The outer level of the optimization is solved using the Cross-Entropy Method, while the inner level relies on gradient-based nonlinear optimization to compute dynamically feasible motions. The approach is validated on a novel climbing robot platform, ALPINE, across a variety of challenging terrain configurations.

Niraj Rathod, Angelo Bratta, Michele Focchi et al.

Re-planning in legged locomotion is crucial to track the desired user velocity while adapting to the terrain and rejecting external disturbances. In this work, we propose and test in experiments a real-time Nonlinear Model Predictive Control (NMPC) tailored to a legged robot for achieving dynamic locomotion on a variety of terrains. We introduce a mobility-based criterion to define an NMPC cost that enhances the locomotion of quadruped robots while maximizing leg mobility and improves adaptation to the terrain features. Our NMPC is based on the real-time iteration scheme that allows us to re-plan online at $25\,\mathrm{Hz}$ with a prediction horizon of $2$ seconds. We use the single rigid body dynamic model defined in the center of mass frame in order to increase the computational efficiency. In simulations, the NMPC is tested to traverse a set of pallets of different sizes, to walk into a V-shaped chimney,and to locomote over rough terrain. In real experiments, we demonstrate the effectiveness of our NMPC with the mobility feature that allowed IIT's $87\, \mathrm{kg}$ quadruped robot HyQ to achieve an omni-directional walk on flat terrain, to traverse a static pallet, and to adapt to a repositioned pallet during a walk.

Abdelrahman Abdallah, Michele Focchi, Romeo Orsolino et al.

Developing feasible body trajectories for legged systems on arbitrary terrains is a challenging task. In this paper, we present a paradigm that allows to design feasible Center of Mass (CoM) and body trajectories in an efficient manner. In our previous work [1], we introduced the notion of the 2D feasible region, where static balance and the satisfaction of joint torque limits were guaranteed, whenever the projection of the CoM lied inside the proposed admissible region. In this work we propose a general formulation of the improved feasible region that guarantees dynamic balance alongside the satisfaction of both joint-torque and kinematic limits in an efficient manner. To incorporate the feasibility of the kinematic limits, we introduce an algorithm that computes the reachable region of the CoM. Furthermore, we propose an efficient planning strategy that utilizes the improved feasible region to design feasible CoM and body orientation trajectories. Finally, we validate the capabilities of the improved feasible region and the effectiveness of the proposed planning strategy, using simulations and experiments on the 90 kg Hydraulically actuated Quadruped (HyQ) and the 21 kg Aliengo robots.

Carlos Mastalli, Ioannis Havoutis, Michele Focchi et al.

Planning whole-body motions while taking into account the terrain conditions is a challenging problem for legged robots since the terrain model might produce many local minima. Our coupled planning method uses stochastic and derivatives-free search to plan both foothold locations and horizontal motions due to the local minima produced by the terrain model. It jointly optimizes body motion, step duration and foothold selection, and it models the terrain as a cost-map. Due to the novel attitude planning method, the horizontal motion plans can be applied to various terrain conditions. The attitude planner ensures the robot stability by imposing limits to the angular acceleration. Our whole-body controller tracks compliantly trunk motions while avoiding slippage, as well as kinematic and torque limits. Despite the use of a simplified model, which is restricted to flat terrain, our approach shows remarkable capability to deal with a wide range of non-coplanar terrains. The results are validated by experimental trials and comparative evaluations in a series of terrains of progressively increasing complexity.

Angelo Bratta, Romeo Orsolino, Michele Focchi et al.

Simplified models are useful to increase the computational efficiency of a motion planning algorithm, but their lack of accuracy have to be managed. We propose two feasibility constraints to be included in a Single Rigid Body Dynamicsbased trajectory optimizer in order to obtain robust motions in challenging terrain. The first one finds an approximate relationship between joint-torque limits and admissible contact forces, without requiring the joint positions. The second one proposes a leg model to prevent leg collision with the environment. Such constraints have been included in a simplified nonlinear nonconvex trajectory optimization problem. We demonstrate the feasibility of the resulting motion plans both in simulation and on the Hydraulically actuated Quadruped (HyQ) robot, considering experiments on an irregular terrain.

Shamel Fahmi, Michele Focchi, Andreea Radulescu et al.

Whole-body Control (WBC) has emerged as an important framework in locomotion control for legged robots. However, most of WBC frameworks fail to generalize beyond rigid terrains. Legged locomotion over soft terrain is difficult due to the presence of unmodeled contact dynamics that WBCs do not account for. This introduces uncertainty in locomotion and affects the stability and performance of the system. In this paper, we propose a novel soft terrain adaptation algorithm called STANCE: Soft Terrain Adaptation and Compliance Estimation. STANCE consists of a WBC that exploits the knowledge of the terrain to generate an optimal solution that is contact consistent and an online terrain compliance estimator that provides the WBC with terrain knowledge. We validated STANCE both in simulation and experiment on the Hydraulically actuated Quadruped (HyQ) robot, and we compared it against the state of the art WBC. We demonstrated the capabilities of STANCE with multiple terrains of different compliances, aggressive maneuvers, different forward velocities, and external disturbances. STANCE allowed HyQ to adapt online to terrains with different compliances (rigid and soft) without pre-tuning. HyQ was able to successfully deal with the transition between different terrains and showed the ability to differentiate between compliances under each foot.

Romeo Orsolino, Michele Focchi, Stéphane Caron et al.

In legged locomotion the projection of the robot Center of Mass (CoM) being inside the convex hull of the contact points is a commonly accepted sufficient condition to achieve static balancing. However, some of these configurations cannot be realized because the joint torques required to sustain them would be above their limits (actuation limits). In this manuscript we rule out such configurations and define the Feasible Region, a revisited support region that guarantees both global static stability in the sense of tipover and slippage avoidance and of existence of a set of joint-torques that are able to sustain the robot body weight. We show that the feasible region can be employed for the selection of feasible footholds and CoM trajectories to achieve static locomotion on rough terrains, also in presence of load intensive tasks. Key results of our approach include the efficiency in the computation of the feasible region thanks to an Iterative Projection algorithm. This allowed us to carry out successful experiments on the HyQ robot, that was able to negotiate obstacles of moderate dimensions while carrying an extra 10 kg payload.

Shamel Fahmi, Carlos Mastalli, Michele Focchi et al.

We present experimental results using a passive whole-body control approach for quadruped robots that achieves dynamic locomotion while compliantly balancing the robot's trunk. We formulate the motion tracking as a Quadratic Program (QP) that takes into account the full robot rigid body dynamics, the actuation limits, the joint limits and the contact interaction. We analyze the controller's robustness against inaccurate friction coefficient estimates and unstable footholds, as well as its capability to redistribute the load as a consequence of enforcing actuation limits. Additionally, we present practical implementation details gained from the experience with the real platform. Extensive experimental trials on the 90 kg Hydraulically actuated Quadruped (HyQ) robot validate the capabilities of this controller under various terrain conditions and gaits. The proposed approach is superior for accurate execution of highly dynamic motions with respect to the current state of the art.

Octavio Villarreal, Victor Barasuol, Marco Camurri et al.

Legged robots can outperform wheeled machines for most navigation tasks across unknown and rough terrains. For such tasks, visual feedback is a fundamental asset to provide robots with terrain-awareness. However, robust dynamic locomotion on difficult terrains with real-time performance guarantees remains a challenge. We present here a real-time, dynamic foothold adaptation strategy based on visual feedback. Our method adjusts the landing position of the feet in a fully reactive manner, using only on-board computers and sensors. The correction is computed and executed continuously along the swing phase trajectory of each leg. To efficiently adapt the landing position, we implement a self-supervised foothold classifier based on a Convolutional Neural Network (CNN). Our method results in an up to 200 times faster computation with respect to the full-blown heuristics. Our goal is to react to visual stimuli from the environment, bridging the gap between blind reactive locomotion and purely vision-based planning strategies. We assess the performance of our method on the dynamic quadruped robot HyQ, executing static and dynamic gaits (at speeds up to 0.5 m/s) in both simulated and real scenarios; the benefit of safe foothold adaptation is clearly demonstrated by the overall robot behavior.

Romeo Orsolino, Michele Focchi, Carlos Mastalli et al.

Motion planning in multi-contact scenarios has recently gathered interest within the legged robotics community, however actuator force/torque limits are rarely considered. We believe that these limits gain paramount importance when the complexity of the terrains to be traversed increases. We build on previous research from the field of robotic grasping to propose two new six-dimensional bounded polytopes named the Actuation Wrench Polytope (AWP) and the Feasible Wrench Polytope (FWP). We define the AWP as the set of all the wrenches that a robot can generate while considering its actuation limits. This considers the admissible contact forces that the robot can generate given its current configuration and actuation capabilities. The Contact Wrench Cone (CWC), instead, includes features of the environment such as the contact normal or the friction coefficient. The intersection of the AWP and of the CWC results in a convex polytope, the FWP, which turns out to be more descriptive of the real robot capabilities than existing simplified models, while maintaining the same compact representation. We explain how to efficiently compute the vertex-description of the FWP that is then used to evaluate a feasibility factor that we adapted from the field of robotic grasping. This allows us to optimize for robustness to external disturbance wrenches. Based on this, we present an implementation of a motion planner for our quadruped robot HyQ that provides online Center of Mass (CoM) trajectories that are guaranteed to be statically stable and actuation consistent.

Romeo Orsolino, Michele Focchi, Carlos Mastalli et al.

The motivation of our current research is to devise motion planners for legged locomotion that are able to exploit the robot's actuation capabilities. This means, when possible, to minimize joint torques or to propel as much as admissible when required. For this reason we define two new 6 dimensional bounded polytopes that we name Actuation-consistent Wrench Polytope (AWP) and Feasible Wrench Polytope (FWP). These objects turn out to be very useful in motion planning for the definition of constraints on the accelerations of the Center of Mass of the robot that respect the friction cones and the actuation limits. The AWP and the FWP could be used also in the robot design phase to size the actuators of the system based on some predefined reference motion.

Marco Frigerio, Victor Barasuol, Michele Focchi et al.

This short technical report illustrates the results of a test procedure we performed to validate the computer simulation of the HyQ robot.