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Author : Alexander W. Winkler
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (19 download)
Download or read book Optimization-based Motion Planning for Legged Robots written by Alexander W. Winkler and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jingwen Zhang
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Towards Application on Optimization-Based Methods for Motion Planning of Legged Robots written by Jingwen Zhang and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: As legged robots have demonstrated versatility, they are more and more favorable for many applications, such as logistics, surveillance, disaster relief, and even home service. Legged robots have the potential to explore and interact with the environment around humans but cannot be handled by robots of other types. A key difficulty in legged locomotion control is that the movement of the floating base cannot be commanded directly, but instead results from the contact forces between the robot and the environment. The contact forces introduce some physical constraints, such as friction cones and unilateral features. Additionally, the hybrid and highly nonlinear dynamics further complex the motion generation and also the motion execution. For tackling legged locomotion, the control framework is often designed hierarchically, in which the high level is in charge of planning reference motion trajectories, and the low level is responsible for tracking this reference trajectory under disturbances. The ideal case is that the reference motion from the high-level planner can be executed by the low-level controller perfectly. However, the discrepancy is always presented given model simplifications and task assumptions. The main objective of this dissertation is to make contributions to mitigate this discrepancy by focusing on high-level motion planning. In motion planning for legged robots, the motion can be categorized into two main types, quasi-static and dynamic motions. Quasi-static motions are defined with a series of discrete contact sequences while the acceleration is kept zero in every time instance. Although energy inefficient, it is often considered a high-risk task. In this dissertation, two motion planners are presented for a six-legged wall-climbing robot given a unique combination of constraints on contact points, contact forces, and body posture. For the first on-wall planner that decouples contact and force planning, on-wall contact points are generated using a mixed-integer convex programming (MICP) with a pre-specified contact sequence while contact forces are optimized subsequently with convex programming. For the second planner, the unscheduled contact sequence is optimized by solving nonlinear programming (NLP). We consider various motions on different environment setups via modeling contact constraints and limb switchability as complementarity conditions. With presented planners, the robot is able to overcome the transition phase between the ground and walls, and also climb vertically between two walls with irregular profiles using pure friction. As for dynamic motions which are seen more commonly in legged animals, trajectory optimization can be utilized to generate a more continuous motion while acceleration resulting from the model dynamics plays a key role. In this dissertation, a jumping planner is presented for a miniature bipedal robot with proprioceptive actuation. The algorithm adopts centroidal dynamics to consider whole-body mass and inertia distribution and generates various motions, directional jumps, twisting jumps, step jumps, and somersaults. The optimized motion can not only mimic human jumping behaviors but also compensate for undesired angular momentum. To prepare a more accurate model for the planner, optimization-based system identification is applied here. Additionally, a heuristic landing location planner based on real-time momentum feedback in the air phase is presented to improve landing stability when executing the jumping reference trajectory.
Author : Iordanis Chatzinikolaidis
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Optimization-based Multi-contact Motion Planning for Legged Robots written by Iordanis Chatzinikolaidis and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paolo Boscariol
Publisher :
ISBN 13 : 9783039430604
Total Pages : 266 pages
Book Rating : 4.4/5 (36 download)
Download or read book Optimization of Motion Planning and Control for Automatic Machines, Robots and Multibody Systems written by Paolo Boscariol and published by . This book was released on 2020-09-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The optimization of motion and trajectory planning is an effective and usually costless approach to improving the performance of robots, mechatronic systems, automatic machines and multibody systems. Indeed, wise planning increases precision and machine productivity, while reducing vibrations, motion time, actuation effort and energy consumption. On the other hand, the availability of optimized methods for motion planning allows for a cheaper and lighter system construction. The issue of motion planning is also tightly linked with the synthesis of high-performance feedback and feedforward control schemes, which can either enhance the effectiveness of motion planning or compensate for its gaps. To collect and disseminate a meaningful collection of these applications, this book proposes 15 novel research studies that cover different sub-areas, in the framework of motion planning and control.
Author : Daniel Chávez-Clemente
Publisher : Stanford University
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4.F/5 ( download)
Download or read book Gait Optimization for Multi-legged Walking Robots, with Application to a Lunar Hexapod written by Daniel Chávez-Clemente and published by Stanford University. This book was released on 2011 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest in using legged robots for a variety of terrestrial and space applications has grown steadily since the 1960s. At the present time, a large fraction of these robots relies on electric motors at the joints to achieve mobility. The load distributions inherent to walking, coupled with design constraints, can cause the motors to operate near their maximum torque capabilities or even reach saturation. This is especially true in applications like space exploration, where critical mass and power constraints limit the size of the actuators. Consequently, these robots can benefit greatly from motion optimization algorithms that guarantee successful walking with maximum margin to saturation. Previous gait optimization techniques have emphasized minimization of power requirements, but have not addressed the problem of saturation directly. This dissertation describes gait optimization techniques specifically designed to enable operation as far as possible from saturation during walking. The benefits include increasing the payload mass, preserving actuation capabilities to react to unforeseen events, preventing damage to hardware due to excessive loading, and reducing the size of the motors. The techniques developed in this work follow the approach of optimizing a reference gait one move at a time. As a result, they are applicable to a large variety of purpose-specific gaits, as well as to the more general problem of single pose optimization for multi-limbed walking and climbing robots. The first part of this work explores a zero-interaction technique that was formulated to increase the margin to saturation through optimal displacements of the robot's body in 3D space. Zero-interaction occurs when the robot applies forces only to sustain its weight, without squeezing the ground. The optimization presented here produces a swaying motion of the body while preserving the original footfall locations. Optimal displacements are found by solving a nonlinear optimization problem using sequential quadratic programming (SQP). Improvements of over 20% in the margin to saturation throughout the gait were achieved with this approach in simulation and experiments. The zero-interaction technique is the safest in the absence of precise knowledge of the contact mechanical properties and friction coefficients. The second part of the dissertation presents a technique that uses the null space of contact forces to achieve greater saturation margins. Interaction forces can significantly contribute to saturation prevention by redirecting the net contact force relative to critical joints. A method to obtain the optimal distribution of forces for a given pose via linear programming (LP) is presented. This can be applied directly to the reference gait, or combined with swaying motion. Improvements of up to 60% were observed in simulation by combining the null space with sway. The zero-interaction technique was implemented and validated on the All Terrain Hex-Limbed Extra-Terrestrial Explorer (ATHLETE), a hexapod robot developed by NASA for the transport of heavy cargo on the surface of the moon. Experiments with ATHLETE were conducted at the Jet Propulsion Laboratory in Pasadena, California, confirming the benefits predicted in simulation. The results of these experiments are also presented and discussed in this dissertation.
Author : Matthew Thomas Chignoli
Publisher :
ISBN 13 :
Total Pages : 73 pages
Book Rating : 4.:/5 (125 download)
Download or read book Trajectory Optimization for Dynamic Aerial Motions of Legged Robots written by Matthew Thomas Chignoli and published by . This book was released on 2021 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel framework for planning and executing dynamic aerial motions for legged robots is developed. These dynamic capabilities allow legged robots to conquer challenging obstacles like gaps and hurdles that cannot be traversed via standard walking and running gaits. The framework consists of two main steps. First, a motion planning step uses trajectory optimization to generate a dynamically feasible motion of the robot that achieves a desired behavior. The desired behavior, which comes from a higher-level planner or a human operator, can specify an arbitrary 3D motion task such as jumping onto a platform or performing a front flip. The trajectory optimization simultaneously optimizes the centroidal dynamics and joint-level kinematics of the robot to plan general 3D motions. Novel actuator constraints are imposed on the optimization that ensure all planned motions are feasible for implementation on hardware, and a two-stage formulation of the optimization automatically generates dynamically-informed warm starts to the optimization that dramatically reduce solve times. The second step of the framework is a unified whole-body controller that tracks these planned motions. The whole-body controller uses a prioritized task hierarchy that is optimized for robust tracking and safe landing of dynamic aerial motions. The ability of the proposed framework to reliably produce 3D aerial motions such as running jumps, barrel rolls, and flips is demonstrated on the MIT Humanoid robot in simulation and on the MIT Mini Cheetah robot both in simulation as well on hardware.
Author : Kristoffer Bergman
Publisher : Linköping University Electronic Press
ISBN 13 : 9176850579
Total Pages : 91 pages
Book Rating : 4.1/5 (768 download)
Download or read book On Motion Planning Using Numerical Optimal Control written by Kristoffer Bergman and published by Linköping University Electronic Press. This book was released on 2019-05-28 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last decades, motion planning for autonomous systems has become an important area of research. The high interest is not the least due to the development of systems such as self-driving cars, unmanned aerial vehicles and robotic manipulators. In this thesis, the objective is not only to find feasible solutions to a motion planning problem, but solutions that also optimize some kind of performance measure. From a control perspective, the resulting problem is an instance of an optimal control problem. In this thesis, the focus is to further develop optimal control algorithms such that they be can used to obtain improved solutions to motion planning problems. This is achieved by combining ideas from automatic control, numerical optimization and robotics. First, a systematic approach for computing local solutions to motion planning problems in challenging environments is presented. The solutions are computed by combining homotopy methods and numerical optimal control techniques. The general principle is to define a homotopy that transforms, or preferably relaxes, the original problem to an easily solved problem. The approach is demonstrated in motion planning problems in 2D and 3D environments, where the presented method outperforms both a state-of-the-art numerical optimal control method based on standard initialization strategies and a state-of-the-art optimizing sampling-based planner based on random sampling. Second, a framework for automatically generating motion primitives for lattice-based motion planners is proposed. Given a family of systems, the user only needs to specify which principle types of motions that are relevant for the considered system family. Based on the selected principle motions and a selected system instance, the algorithm not only automatically optimizes the motions connecting pre-defined boundary conditions, but also simultaneously optimizes the terminal state constraints as well. In addition to handling static a priori known system parameters such as platform dimensions, the framework also allows for fast automatic re-optimization of motion primitives if the system parameters change while the system is in use. Furthermore, the proposed framework is extended to also allow for an optimization of discretization parameters, that are are used by the lattice-based motion planner to define a state-space discretization. This enables an optimized selection of these parameters for a specific system instance. Finally, a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems is presented. The main idea is to combine the strengths of sampling-based path planners and numerical optimal control. The lattice-based path planner is applied to the problem in a first step using a discretized search space, where system dynamics and objective function are chosen to coincide with those used in a second numerical optimal control step. This novel tight combination of a sampling-based path planner and numerical optimal control makes, in a structured way, benefit of the former method’s ability to solve combinatorial parts of the problem and the latter method’s ability to obtain locally optimal solutions not constrained to a discretized search space. The proposed approach is shown in several practically relevant path planning problems to provide improvements in terms of computation time, numerical reliability, and objective function value.
Author : Kensuke Harada
Publisher : Springer Science & Business Media
ISBN 13 : 1849962200
Total Pages : 320 pages
Book Rating : 4.8/5 (499 download)
Download or read book Motion Planning for Humanoid Robots written by Kensuke Harada and published by Springer Science & Business Media. This book was released on 2010-08-12 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on humanoid robots has been mostly with the aim of developing robots that can replace humans in the performance of certain tasks. Motion planning for these robots can be quite difficult, due to their complex kinematics, dynamics and environment. It is consequently one of the key research topics in humanoid robotics research and the last few years have witnessed considerable progress in the field. Motion Planning for Humanoid Robots surveys the remarkable recent advancement in both the theoretical and the practical aspects of humanoid motion planning. Various motion planning frameworks are presented in Motion Planning for Humanoid Robots, including one for skill coordination and learning, and one for manipulating and grasping tasks. The problem of planning sequences of contacts that support acyclic motion in a highly constrained environment is addressed and a motion planner that enables a humanoid robot to push an object to a desired location on a cluttered table is described. The main areas of interest include: • whole body motion planning, • task planning, • biped gait planning, and • sensor feedback for motion planning. Torque-level control of multi-contact behavior, autonomous manipulation of moving obstacles, and movement control and planning architecture are also covered. Motion Planning for Humanoid Robots will help readers to understand the current research on humanoid motion planning. It is written for industrial engineers, advanced undergraduate and postgraduate students.
Author : Xuan Lin
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)
Download or read book Developing Combinatorial Optimization and Data-driven Methods for Multi-modal Motion Planning written by Xuan Lin and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Legged robots require fast and reliable motion planners and controllers to satisfy real-time implementation requirements. In this dissertation, we investigate the model-based motion planning and control techniques for robotics problems involving contact, including multi-legged robot walking and vertical climbing, item manipulation inside a cluttered environment, and self-reconfigurable robot systems. Each of them can be formulated into a mixed-integer nonlinear (non-convex) program problem for optimization solvers to resolve. In general, mixed-integer nonconvex programs are challenging to solve. In this dissertation, we adopted several approaches including the decoupling approach, coupled approaches such as ADMM, and data-driven approaches. In the end, we benchmark the performance of the proposed approaches on the bookshelf manipulation problem. Through comparison of various approaches, we show that the data-driven approach can potentially achieve a high success rate, fast solving speed, and good objective function value, given that the new problem is within the trained distribution. Planned trajectories are validated on the hardware showing the planner's capability of generating real-world feasible trajectories.
Author : Nasser Sadati
Publisher : John Wiley & Sons
ISBN 13 : 1118393724
Total Pages : 201 pages
Book Rating : 4.1/5 (183 download)
Download or read book Hybrid Control and Motion Planning of Dynamical Legged Locomotion written by Nasser Sadati and published by John Wiley & Sons. This book was released on 2012-09-11 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the need in the field for a comprehensive review of motion planning algorithms and hybrid control methodologies for complex legged robots. Introducing a multidisciplinary systems engineering approach for tackling many challenges posed by legged locomotion, the book provides engineering detail including hybrid models for planar and 3D legged robots, as well as hybrid control schemes for asymptotically stabilizing periodic orbits in these closed-loop systems. Complete with downloadable MATLAB code of the control algorithms and schemes used in the book, this book is an invaluable guide to the latest developments and future trends in dynamical legged locomotion.
Author : Kris Hauser
Publisher :
ISBN 13 :
Total Pages : 164 pages
Book Rating : 4.F/5 ( download)
Download or read book Motion Planning for Legged and Humanoid Robots written by Kris Hauser and published by . This book was released on 2008 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Matt Zucker
Publisher :
ISBN 13 :
Total Pages : 95 pages
Book Rating : 4.:/5 (733 download)
Download or read book Learning and Optimization Methods for High Level Planning written by Matt Zucker and published by . This book was released on 2010 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Motion planning for complex systems such as legged robots and mobile manipulators has proven to be a difficult task due to the high dimensional configuration spaces that underly such systems, and also due to the variety of constraints which must be met at all times. One way to escape the so-called 'curse of dimensionality', or exponential explosion of search space, is to create a hierarchy of planners and controllers which at its highest level reasons about sequences of coarse behaviors operating on a simplified model of the system. This high level approach to robot behavior planning has been used successfully for several diverse robotic platforms, including footstep planning for the rough terrain quadruped described in this thesis. Despite its advantages, high level planning introduces several challenges of its own. Because the planner considers a coarse approximation of reality, it is typically difficult -- if not impossible -- to directly optimize its performance with respect to a concrete objective in the real world. Furthermore, since different modules of the planning and control hierarchy reason about the system in varying granularity, care needs to be taken to ensure that the planner does not commit to actions at a coarse level of planning which are in fact infeasible in reality. This thesis describes broad strategies for addressing the challenges of high level planning for robotic systems, harnessing both numerical optimization and machine learning techniques in order to produce effective behaviors in real time. These frameworks and algorithms are demonstrated on the Boston Dynamics Inc. LittleDog quadruped robot in the context of rough terrain locomotion."
Author : Andrés Klee Valenzuela
Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.:/5 (952 download)
Download or read book Mixed-integer Convex Optimization for Planning Aggressive Motions of Legged Robots Over Rough Terrain written by Andrés Klee Valenzuela and published by . This book was released on 2016 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Planning dynamic motions for a legged robot entails addressing both the continuous question of how its joints should move and the combinatorial question of which hand or foot should touch which surface and in what order. Fortunately, these two questions are linked by the centroidal dynamics of the robot, which we can express either in terms of its joint angle trajectories or in terms of its foot placements and applied forces. Based on this insight, I formulate a pair of mathematical programs for planning highly dynamic motions for legged robots. The first is a mixed-integer convex program, specifically, a mixed-integer quadratic program (MIQP), that yields a sequence of footholds/handholds as well as center of mass (COM) and angular momentum trajectories. The second is a trajectory optimization, formulated as a nonlinear program (NLP), that returns trajectories for the COM, angular momentum, and joint angles subject to the footholds/handholds chosen by the MIQP step. While any number of trajectory optimization schemes could be used here, we present one which is particularly useful in this case, as it enforces the system's dynamics directly in terms of its COM motion and angular momentum. As a result, the solution to the MIQP provides constraints (where each end-effector is required to make contact with the environment) for the NLP and also gives seeds for the decision variables corresponding to the robot's centroidal motion. Thus, the three primary contributions of this thesis are: an MIQP-based approach to gait selection over irregular terrain, a trajectory optimization formulation for floating-base systems subject to external forces and kinematic constraints, and a planning methodology that integrates both of those to generate highly dynamic motions in challenging environments. I apply these techniques to models of a quadruped and a humanoid (Boston Dynamics' LittleDog and Atlas respectively) to generate motion plans for running, jumping, and other dynamic behaviors.
Author : Yunong Zhang
Publisher : Springer Science & Business Media
ISBN 13 : 3642375189
Total Pages : 201 pages
Book Rating : 4.6/5 (423 download)
Download or read book Repetitive Motion Planning and Control of Redundant Robot Manipulators written by Yunong Zhang and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Repetitive Motion Planning and Control of Redundant Robot Manipulators presents four typical motion planning schemes based on optimization techniques, including the fundamental RMP scheme and its extensions. These schemes are unified as quadratic programs (QPs), which are solved by neural networks or numerical algorithms. The RMP schemes are demonstrated effectively by the simulation results based on various robotic models; the experiments applying the fundamental RMP scheme to a physical robot manipulator are also presented. As the schemes and the corresponding solvers presented in the book have solved the non-repetitive motion problems existing in redundant robot manipulators, it is of particular use in applying theoretical research based on the quadratic program for redundant robot manipulators in industrial situations. This book will be a valuable reference work for engineers, researchers, advanced undergraduate and graduate students in robotics fields. Yunong Zhang is a professor at The School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China; Zhijun Zhang is a research fellow working at the same institute.
Author : Dian Jiao
Publisher :
ISBN 13 : 9780355465037
Total Pages : 58 pages
Book Rating : 4.4/5 (65 download)
Download or read book Horizontal Motion Planning for Multi-legged Robots written by Dian Jiao and published by . This book was released on 2017 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving legged robot navigation problems is challenging because of the robots' locomotion limitations and its complex kinematics and dynamics. Generic locomotion models for the legged robots such as the Spring Loaded Inverted Pendulum (SLIP) and the Lateral Leg Spring (LLS) involve masses, accelerations and second-order differential equations. Common path planning methods such as the Probabilistic Roadmap (PRM) and the Rapidly-exploring Random Tree (RRT) have their own limitations. Both of them typically assume that the robots do not have any kinematic limitations. In addition, RRT and PRM are open-loop, and as such, they do not produce the feedback strategies that correct when the robot is away from the desired path. Consequently, re-planning is practically required for implementations of the RRT and PRM. ☐ Templates are simplified models that capture salient features of robot motion behavior. The SLIP and LLS are considered templates. Karydis et al. provides a new locomotion template: the Switching Four Bar Mechanism (SFM) for legged robots. The SFM gives a static map between model parameters and robot displacement, and models the robot's motion without differential equation. On the other hand, the SFM offers the robot's configuration in closed form. The number of variables of the SFM can be reduced to one. ☐ In this thesis, we derive the inverse kinematics of the SFM, which maps the robot displacement to model parameters. We also provide a method for solving the problem of legged robot navigation in a way that provides feedback strategies in cluttered planar environments. This is achieved by combing the SFM as the locomotion template for the legged robots with navigation functions for motion planning. In this way, an existing, multi-variable, probably correct motion planning method, is transformed into a tractable single-variable. Locomotion-specific optimization algorithms are applied to our navigation method and are adjusted to hit a trade-off between efficacy and processing speed. Because our method provides feedback strategies, re-planning is not required. We provide some convergence conditions for our navigation method so that we can ensure that motion plans are always safe with regards to collisions with environmental boundaries. In conclusion, this thesis provides an approach that can be used for solving the planar navigation problem for robotic vehicle systems with kinematics given in closed-form.
Author : Kevin M. Lynch
Publisher : Cambridge University Press
ISBN 13 : 1107156300
Total Pages : 545 pages
Book Rating : 4.1/5 (71 download)
Download or read book Modern Robotics written by Kevin M. Lynch and published by Cambridge University Press. This book was released on 2017-05-25 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern and unified treatment of the mechanics, planning, and control of robots, suitable for a first course in robotics.
Author : Romeo Orsolino
Publisher : Istitituto Italiano di Tecnologia (IIT)
ISBN 13 :
Total Pages : 146 pages
Book Rating : 4./5 ( download)
Download or read book Actuation-Aware Simplified Dynamic Models for Robotic Legged Locomotion written by Romeo Orsolino and published by Istitituto Italiano di Tecnologia (IIT). This book was released on 2019-02-14 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 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 performing online (re)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, a number of novel Model Predictive Control (MPC) approaches have been presented that attempt to increase the accuracy of the obtained solutions by employing more complex dynamic formulations, this 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 first describe the control 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 gait while adapting the footsteps 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 compromising 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-torque limits, which are usually neglected at the planning stage. Along the same 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. In order to augment the robot’s reachable workspace, 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 a new concept that I refer to under the name of feasible region. This can be seen as a different variant of 2D linear subspaces orthogonal to gravity where the robot is guaranteed to place its own center of mass (CoM) while being able to carry its own body weight given its actuation capabilities. The feasible region provides an intuitive tool for the visualization in 2D of the actuation capabilities of legged robots. The low dimensionality of the feasible region also enables the concurrent online optimization of actuation consistent CoM trajectories and target foothold locations on rough terrains, which can hardly be achieved with other state-of-the-art approaches.
