Actuation-Aware Simplified Dynamic Models for Robotic Legged Locomotion

In recent years, we witnessed an ever increasing number of successful hardware implementations of motion planners for legged robots. If one common property is to be identified among these real-world applications, that is the ability of online planning. Online planning is forgiving, in the sense that it allows to relentlessly compensate for external disturbances of whatever form they might be, ranging from unmodeled dynamics to external pushes or unexpected obstacles and, at the same time, follow user commands. Initially replanning was restricted only to heuristic-based planners that exploit the low computational effort of simplified dynamic models. Such models deliberately only capture the main dynamics of the system, thus leaving to the controllers the issue of anchoring the desired trajectory to the whole body model of the robot. In recent years, however, we have seen a number of new approaches attempting to increase the accuracy of the dynamic formulation without trading-off the computational efficiency of simplified models. In this dissertation, as an example of successful hardware implementation of heuristics and simplified model-based locomotion, I describe the framework that I developed for the generation of an omni-directional bounding gait for the HyQ quadruped robot. By analyzing the stable limit cycles for the sagittal dynamics and the Center of Pressure (CoP) for the lateral stabilization, the described locomotion framework is able to achieve a stable bounding while adapting to terrains of mild roughness and to sudden changes of the user desired linear and angular velocities. The next topic reported and second contribution of this dissertation is my effort to formulate more descriptive simplified dynamic models, without trading off their computational efficiency, in order to extend the navigation capabilities of legged robots to complex geometry environments. With this in mind, I investigated the possibility of incorporating feasibility constraints in these template models and, in particular, I focused on the joint torques limits which are usually neglected at the planning stage. In this direction, the third contribution discussed in this thesis is the formulation of the so called actuation wrench polytope (AWP), defined as the set of feasible wrenches that an articulated robot can perform given its actuation limits. Interesected with the contact wrench cone (CWC), this yields a new 6D polytope that we name feasible wrench polytope (FWP), defined as the set of all wrenches that a legged robot can realize given its actuation capabilities and the friction constraints. Results are reported where, thanks to efficient computational geometry algorithms and to appropriate approximations, the FWP is employed for a one-step receding horizon optimization of center of mass trajectory and phase durations given a predefined step sequence on rough terrains. For the sake of reachable workspace augmentation, I then decided to trade off the generality of the FWP formulation for a suboptimal scenario in which a quasi-static motion is assumed. This led to the definition of the, so called, local/instantaneous actuation region and of the global actuation/feasible region. They both can be seen as different variants of 2D linear subspaces orthogonal to gravity where the robot is guaranteed to place its own center of mass while being able to carry its own body weight given its actuation capabilities. These areas can be intersected with the well known frictional support region, resulting in a 2D linear feasible region, thus providing an intuitive tool that enables the concurrent online optimization of actuation consistent CoM trajectories and target foothold locations on rough terrains

An Efficient Paradigm for Feasibility Guarantees in Legged Locomotion

Developing feasible body trajectories for legged systems on arbitrary terrains is a challenging task. Given some contact points, the trajectories for the Center of Mass (CoM) and body orientation, designed to move the robot, must satisfy crucial constraints to maintain balance, and to avoid violating physical actuation and kinematic limits. In this paper, we present a paradigm that allows to design feasible trajectories in an efficient manner. In continuation to our previous work, we extend the notion of the 2D feasible region, where static balance and the satisfaction of actuation limits were guaranteed, whenever the projection of the CoM lies inside the proposed admissible region. We here develop a general formulation of the improved feasible region to guarantee dynamic balance alongside the satisfaction of both actuation and kinematic limits for arbitrary terrains 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 HyQ robot and comparing them to a previously developed heuristic approach. Various scenarios and terrains that mimic confined and challenging environments are used for the validation.Comment: 17 pages, 13 figures, submitted to Transaction on Robotic

Multi-contact Walking Pattern Generation based on Model Preview Control of 3D COM Accelerations

We present a multi-contact walking pattern generator based on preview-control of the 3D acceleration of the center of mass (COM). A key point in the design of our algorithm is the calculation of contact-stability constraints. Thanks to a mathematical observation on the algebraic nature of the frictional wrench cone, we show that the 3D volume of feasible COM accelerations is a always a downward-pointing cone. We reduce its computation to a convex hull of (dual) 2D points, for which optimal O(n log n) algorithms are readily available. This reformulation brings a significant speedup compared to previous methods, which allows us to compute time-varying contact-stability criteria fast enough for the control loop. Next, we propose a conservative trajectory-wide contact-stability criterion, which can be derived from COM-acceleration volumes at marginal cost and directly applied in a model-predictive controller. We finally implement this pipeline and exemplify it with the HRP-4 humanoid model in multi-contact dynamically walking scenarios

Feasible Wrench Set Computation for Legged Robots

During locomotion, legged robots interact with the ground by sequentially establishing and breaking contact. The interaction wrenches that arise from contact are used to steer the robot Center of Mass (CoM) and reject perturbations that make the system deviate from the desired trajectory and often make them fall. The feasibility of a given control target (desired CoM wrench or acceleration) is conditioned by the contact point distribution, ground friction, and actuation limits. In this work, we develop a method to compute the set of feasible wrenches that a legged robot can exert on its CoM through contact. The presented method can be used with any amount of non-co-planar contacts and takes into account actuation limits and limitations based on an inelastic contact model with Coulomb friction. This is exemplified with a planar biped model standing with the feet at different heights. Exploiting assumptions from the contact model, we explain how to compute the set of wrenches that are feasible on the CoM when the contacts remain in position as well as the ones that are feasible when some of the contacts are broken. Therefore, this method can be used to assess whether a switch in contact configuration is feasible while achieving a given control task. Furthermore, the method can be used to identify the directions in which the system is not actuated (i.e. a wrench cannot be exerted in those directions). We show how having a joint be actuated or passive can change the non-actuated wrench directions of a robot at a given pose using a spatial model of a lower-extremity exoskeleton. Therefore, this method is also a useful tool for the design phase of the system. This work presents a useful tool for the control and design of legged systems that extends on the current state of the art.Comment: \c{opyright} 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work

Bridging Vision and Dynamic Legged Locomotion

Legged robots have demonstrated remarkable advances regarding robustness and versatility in the past decades. The questions that need to be addressed in this field are increasingly focusing on reasoning about the environment and autonomy rather than locomotion only. To answer some of these questions visual information is essential. If a robot has information about the terrain it can plan and take preventive actions against potential risks. However, building a model of the terrain is often computationally costly, mainly because of the dense nature of visual data. On top of the mapping problem, robots need feasible body trajectories and contact sequences to traverse the terrain safely, which may also require heavy computations. This computational cost has limited the use of visual feedback to contexts that guarantee (quasi-) static stability, or resort to planning schemes where contact sequences and body trajectories are computed before starting to execute motions. In this thesis we propose a set of algorithms that reduces the gap between visual processing and dynamic locomotion. We use machine learning to speed up visual data processing and model predictive control to achieve locomotion robustness. In particular, we devise a novel foothold adaptation strategy that uses a map of the terrain built from on-board vision sensors. This map is sent to a foothold classifier based on a convolutional neural network that allows the robot to adjust the landing position of the feet in a fast and continuous fashion. We then use the convolutional neural network-based classifier to provide safe future contact sequences to a model predictive controller that optimizes target ground reaction forces in order to track a desired center of mass trajectory. We perform simulations and experiments on the hydraulic quadruped robots HyQ and HyQReal. For all experiments the contact sequences, the foothold adaptations, the control inputs and the map are computed and processed entirely on-board. The various tests show that the robot is able to leverage the visual terrain information to handle complex scenarios in a safe, robust and reliable manner

Bounded haptic teleoperation of a quadruped robot’s foot posture for sensing and manipulation

This paper presents a control framework to teleoperate a quadruped robot's foot for operator-guided haptic exploration of the environment. Since one leg of a quadruped robot typically only has 3 actuated degrees of freedom (DoFs), the torso is employed to assist foot posture control via a hierarchical whole-body controller. The foot and torso postures are controlled by two analytical Cartesian impedance controllers cascaded by a null space projector. The contact forces acting on supporting feet are optimized by quadratic programming (QP). The foot's Cartesian impedance controller may also estimate contact forces from trajectory tracking errors, and relay the force-feedback to the operator. A 7D haptic joystick, Sigma.7, transmits motion commands to the quadruped robot ANYmal, and renders the force feedback. Furthermore, the joystick's motion is bounded by mapping the foot's feasible force polytope constrained by the friction cones and torque limits in order to prevent the operator from driving the robot to slipping or falling over. Experimental results demonstrate the efficiency of the proposed framework.Comment: Under review. Video Available at https://www.youtube.com/watch?v=htI8202vfe