Learning Complex Motor Skills for Legged Robot Fall Recovery

Falling is inevitable for legged robots in challenging real-world scenarios, where environments are unstructured and situations are unpredictable, such as uneven terrain in the wild. Hence, to recover from falls and achieve all-terrain traversability, it is essential for intelligent robots to possess the complex motor skills required to resume operation. To go beyond the limitation of handcrafted control, we investigated a deep reinforcement learning approach to learn generalized feedback-control policies for fall recovery that are robust to external disturbances. We proposed a design guideline for selecting key states for initialization, including a comparison to the random state initialization. The proposed learning-based pipeline is applicable to different robot models and their corner cases, including both small-/large-size bipeds and quadrupeds. Further, we show that the learned fall recovery policies are hardware-feasible and can be implemented on real robots

Stability Analysis of Discrete-Time Linear Complementarity Systems

A Discrete-Time Linear Complementarity System (DLCS) is a dynamical system in discrete time whose state evolution is governed by linear dynamics in states and algebraic variables that solve a Linear Complementarity Problem (LCP). The DLCS is the hybrid dynamical system that is the discrete-time counterpart of the well-known Linear Complementarity System (LCS). We derive sufficient conditions for Lyapunov stability of a DLCS when using a quadratic Lyapunov function that depends only on the state variables and a quadratic Lyapunov function that depends both on the state and the algebraic variables. The sufficient conditions require checking the feasibility of a copositive program over nonconvex cones. Our results only assume that the LCP is solvable and do not require the solutions to be unique. We devise a novel, exact cutting plane algorithm for the verification of stability and the computation of the Lyapunov functions. To the best of our knowledge, our algorithm is the first exact approach for stability verification of DLCS. A number of numerical examples are presented to illustrate the approach. Though our main object of study in this paper is the DLCS, the proposed algorithm can be readily applied to the stability verification of LCS. In this context, we show the equivalence between the stability of a LCS and the DLCS, resulting from a time-stepping procedure applied to the LCS for all sufficiently small time steps

Direct collocation methods for trajectory optimization in constrained robotic systems

© 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 works.Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained mechanical systems, i.e., those whose state coordinates are subject to holonomic or nonholonomic constraints, such as loop-closure or rolling-contact constraints. These constraints confine the robot trajectories to an implicitly-defined manifold, which complicates the computation of accurate solutions. Discretization errors inherent to the transcription of the problem easily make the trajectories drift away from this manifold, which results in physically inconsistent motions that are difficult to track with a controller. This article reviews existing methods to deal with this problem and proposes new ones to overcome their limitations. Current approaches either disregard the kinematic constraints (which leads to drift accumulation) or modify the system dynamics to keep the trajectory close to the manifold (which adds artificial forces or energy dissipation to the system). The methods we propose, in contrast, achieve full drift elimination on the discrete trajectory, or even along the continuous one, without artificial modifications of the system dynamics. We illustrate and compare the methods using various examples of different complexity.This work was supported in part by the Spanish Ministry of Science, Innovation, and Universities under Project DPI2017-88282-P and Project PID2020-117509GBI00/AEI/10.13039/50110001103 and in part by the German Federal Ministry for Economic Affairs and Energy (BMWi) via DyConPV (0324166B)Peer ReviewedPostprint (author's final draft

Optimization-Based Control for Dynamic Legged Robots

In a world designed for legs, quadrupeds, bipeds, and humanoids have the opportunity to impact emerging robotics applications from logistics, to agriculture, to home assistance. The goal of this survey is to cover the recent progress toward these applications that has been driven by model-based optimization for the real-time generation and control of movement. The majority of the research community has converged on the idea of generating locomotion control laws by solving an optimal control problem (OCP) in either a model-based or data-driven manner. However, solving the most general of these problems online remains intractable due to complexities from intermittent unidirectional contacts with the environment, and from the many degrees of freedom of legged robots. This survey covers methods that have been pursued to make these OCPs computationally tractable, with specific focus on how environmental contacts are treated, how the model can be simplified, and how these choices affect the numerical solution methods employed. The survey focuses on model-based optimization, covering its recent use in a stand alone fashion, and suggesting avenues for combination with learning-based formulations to further accelerate progress in this growing field.Comment: submitted for initial review; comments welcom

A contact-implicit direct trajectory optimization scheme for the study of legged maneuverability

For legged robots to move safely in unpredictable environments, they need to be manoeuvrable, but transient motions such as acceleration, deceleration and turning have been the subject of little research compared to constant-speed gait. They are difficult to study for two reasons: firstly, the way they are executed is highly sensitive to factors such as morphology and traction, and secondly, they can potentially be dangerous, especially when executed rapidly, or from high speeds. These challenges make it an ideal topic for study by simulation, as this allows all variables to be precisely controlled, and puts no human, animal or robotic subjects at risk. Trajectory optimization is a promising method for simulating these manoeuvres, because it allows complete motion trajectories to be generated when neither the input actuation nor the output motion is known. Furthermore, it produces solutions that optimize a given objective, such as minimizing the distance required to stop, or the effort exerted by the actuators throughout the motion. It has consequently become a popular technique for high-level motion planning in robotics, and for studying locomotion in biomechanics. In this dissertation, we present a novel approach to studying motion with trajectory optimization, by viewing it more as “trajectory generation” – a means of generating large quantities of synthetic data that can illuminate the differences between successful and unsuccessful motion strategies when studied in aggregate. One distinctive feature of this approach is the focus on whole-body models, which capture the specific morphology of the subject, rather than the highly-simplified “template” models that are typically used. Another is the use of “contact-implicit” methods, which allow an appropriate footfall sequence to be discovered, rather than requiring that it be defined upfront. Although contact-implicit methods are not novel, they are not widely-used, as they are computationally demanding, and unnecessary when studying comparatively-predictable constant speed locomotion. The second section of this dissertation describes innovations in the formulation of these trajectory optimization problems as nonlinear programming problems (NLPs). This “direct” approach allows these problems to be solved by general-purpose, open-source algorithms, making it accessible to scientists without the specialized applied mathematics knowledge required to solve NLPs. The design of the NLP has a significant impact on the accuracy of the result, the quality of the solution (with respect to the final value of the objective function), and the time required to solve the proble

Motion Planning for Underactuated Systems through Path Parameterisation

Underactuated systems are becoming an essential field of study within robotics given the rapid advancement and prevalence of legged and flying systems within the modern world. Planning motions that are dynamically feasible for these systems is integral to achieving natural and dynamic movement, however, a great difficulty posed by underactuation is that the space of feasible motions for these systems is strongly constrained by their dynamics. This thesis investigates the viability of extending path-parameterised motion planning to underactuated systems, where algorithms are proposed in two key areas, sample-based and optimisation-based planning. A focus is placed on systems with a single degree of underactuation, where the scalar dynamics revealed under a path parameterisation can be used for efficient kinodynamic querying and dynamic feasibility verification of generated paths. Within a sample-based context, these features are exploited through the development of a path-parameterised RRT algorithm with a state-based steering strategy that accommodates this degree of underactuation. Within the numerical optimisation front, these features are used to develop a path-parameterised trajectory optimisation method with dynamic feasibility detection, enabling the rapid generation of feasible motions with fine dynamical accuracy. This work demonstrates the advantages of these algorithms in relation to existing approaches, highlighting the successes attributed to the exploitation of this class of underactuated system under a path parameterisation

Dyadic collaborative manipulation formalism for optimizing human-robot teaming

Dyadic collaborative Manipulation (DcM) is a term we use to refer to a team of two individuals, the agent and the partner, jointly manipulating an object. The two individuals partner together to form a distributed system, augmenting their manipulation abilities. Effective collaboration between the two individuals during joint action depends on: (i) the breadth of the agent’s action repertoire, (ii) the level of model acquaintance between the two individuals, (iii) the ability to adapt online of one’s own actions to the actions of their partner, and (iv) the ability to estimate the partner’s intentions and goals. Key to the successful completion of co-manipulation tasks with changing goals is the agent’s ability to change grasp-holds, especially in large object co-manipulation scenarios. Hence, in this work we developed a Trajectory Optimization (TO) method to enhance the repertoire of actions of robotic agents, by enabling them to plan and execute hybrid motions, i.e. motions that include discrete contact transitions, continuous trajectories and force profiles. The effectiveness of the TO method is investigated numerically and in simulation, in a number of manipulation scenarios with both a single and a bimanual robot. In addition, it is worth noting that transitions from free motion to contact is a challenging problem in robotics, in part due to its hybrid nature. Additionally, disregarding the effects of impacts at the motion planning level often results in intractable impulsive contact forces. To address this challenge, we introduce an impact-aware multi-mode TO method that combines hybrid dynamics and hybrid control in a coherent fashion. A key concept in our approach is the incorporation of an explicit contact force transmission model into the TO method. This allows the simultaneous optimization of the contact forces, contact timings, continuous motion trajectories and compliance, while satisfying task constraints. To demonstrate the benefits of our method, we compared our method against standard compliance control and an impact-agnostic TO method in physical simulations. Also, we experimentally validated the proposed method with a robot manipulator on the task of halting a large-momentum object. Further, we propose a principled formalism to address the joint planning problem in DcM scenarios and we solve the joint problem holistically via model-based optimization by representing the human's behavior as task space forces. The task of finding the partner-aware contact points, forces and the respective timing of grasp-hold changes are carried out by a TO method using non-linear programming. Using simulations, the capability of the optimization method is investigated in terms of robot policy changes (trajectories, timings, grasp-holds) to potential changes of the collaborative partner policies. We also realized, in hardware, effective co-manipulation of a large object by the human and the robot, including eminent grasp changes as well as optimal dyadic interactions to realize the joint task. To address the online adaptation challenge of joint motion plans in dyads, we propose an efficient bilevel formulation which combines graph search methods with trajectory optimization, enabling robotic agents to adapt their policy on-the-fly in accordance to changes of the dyadic task. This method is the first to empower agents with the ability to plan online in hybrid spaces; optimizing over discrete contact locations, contact sequence patterns, continuous trajectories, and force profiles for co-manipulation tasks. This is particularly important in large object co-manipulation tasks that require on-the-fly plan adaptation. We demonstrate in simulation and with robot experiments the efficacy of the bilevel optimization by investigating the effect of robot policy changes in response to real-time alterations of the goal. This thesis provides insight into joint manipulation setups performed by human-robot teams. In particular, it studies computational models of joint action and exploits the uncharted hybrid action space, that is especially relevant in general manipulation and co-manipulation tasks. It contributes towards developing a framework for DcM, capable of planning motions in the contact-force space, realizing these motions while considering impacts and joint action relations, as well as adapting on-the-fly these motion plans with respect to changes of the co-manipulation goals