Humanoid robots dynamically navigate an environment by interacting with it via contact wrenches exerted at intermittent contact poses. Therefore, it is important to consider dynamics when planning a contact sequence. Traditional contact planning approaches assume a quasi-static balance criterion to reduce the computational challenges of selecting a contact sequence over a rough terrain. This however limits the applicability of the approach when dynamic motions are required, such as when walking down a steep slope or crossing a wide gap. Recent methods overcome this limitation with the help of efficient mixed integer convex programming solvers capable of synthesizing dynamic contact sequences. Nevertheless, its exponential-time complexity limits its applicability to short time horizon contact sequences within small environments. In this paper, we go beyond current approaches by learning a prediction of the dynamic evolution of the robot centroidal momenta, which can then be used for quickly generating dynamically robust contact sequences for robots with arms and legs using a search-based contact planner. We demonstrate the efficiency and quality of the results of the proposed approach in a set of dynamically challenging scenarios.
Approaches to synthesize dynamically feasible multi-contact motions have also been extensively studied @cite_8 @cite_14 @cite_31 @cite_40 @cite_36 . However, it is not trivial to include planning of contact poses in these approaches because contacts planning in general involves discrete or non-convex constraints for the contact poses. @cite_21 addresses the non-convexity by decomposing the environment into a set of convex regions and approximating the rotation using piecewise affine functions. The problem is then formulated as a mixed integer convex program and solved to global optimality. Although @cite_21 only uses foot contact, and does not consider dynamics, it points a direction to include contact planning in an optimization problem.
@cite_14 @cite_8 @cite_36 @cite_21 @cite_40 @cite_31
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Most animal and human locomotion behaviors for solving complex tasks involve dynamic motions and rich contact interaction. In fact, complex maneuvers need to consider dynamic movement and contact events at the same time. We present a hierarchical trajectory optimization approach for planning dynamic movements with unscheduled contact sequences. We compute whole-body motions that achieve goals that cannot be reached in a kinematic fashion. First, we find a feasible CoM motion according to the centroidal dynamics of the robot. Then, we refine the solution by applying the robot's full-dynamics model, where the feasible CoM trajectory is used as a warm-start point. To accomplish the unscheduled contact behavior, we use complementarity constraints to describe the contact model, i.e. environment geometry and non-sliding active contacts. Both optimization phases are posed as Mathematical Program with Complementarity Constraints (MPCC). Experimental trials demonstrate the performance of our planning approach in a set of challenging tasks. This paper presents the contact-consistent elastic strips (CES) framework, a motion planning approach capable of producing complex multi-contact whole-body humanoid behaviors in dynamic environments. Planning multi-contact motions for humanoid robots is known to be non-trivial since it involves aspects of autonomous balancing, obstacle avoidance, ensuring global connectivity of the workspace and concurrent consideration of the kinematic and dynamic constraints. Previous works at motion planning for humanoid systems tend to focus on joint space planning and deal with obstacle avoidance and contact-point searching as the separated problems. CES framework, however, simultaneously considers all these requirements and constraints in task space while planning a valid sequence of contact-points and corresponding motions. This resulted in considerable improvements to efficiency and significantly reduced planning time. With the use of CES framework, complex multi-contact locomotion behaviors and real-time adjustments to the robot motions in 3D unstructured environments is possible. Several simulations are demonstrated to evaluate and verify the performance of CES framework. Traditional motion planning approaches for multilegged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or nonconvex optimization with intractable computation time. In this letter, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions, and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a prespecified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where nonconvexity and flat terrain assumptions might lead to suboptimal or unstable plans. Our method increases the motion robustness while keeping a low computation time. We tackle the transition feasibility problem, that is the issue of determining whether there exists a feasible motion connecting two configurations of a legged robot. To achieve this we introduce CROC, a novel method for computing centroidal dynamics trajectories in multi-contact planning contexts. Our approach is based on a conservative and convex reformulation of the problem, where we represent the center of mass trajectory as a Bezier curve comprising a single free control point as a variable. Under this formulation, the transition problem is solved efficiently with a Linear Program (LP)of low dimension. We use this LP as a feasibility criterion, incorporated in a sampling-based contact planner, to discard efficiently unfeasible contact plans. We are thus able to produce robust contact sequences, likely to define feasible motion synthesis problems. We illustrate this application on various multi-contact scenarios featuring HRP2 and HyQ. We also show that we can use CROC to compute valuable initial guesses, used to warm-start non-linear solvers for motion generation methods. This method could also be used for the 0 and 1-Step capturability problem. The source code of CROC is available under an open source BSD-2 License. This paper introduces an optimization-based framework for robust multilegged walking motion planning. Previous approaches use fixed gait sequences, and rely on Zero Moment Point (ZMP) to guarantee dynamic stability. While this combination works well on flat ground, it does not generalize to uneven terrain requiring aggressive gait or gait transition. To overcome such difficulties, in this paper, we present an optimization framework, that can plan both the contact location and gait sequence simultaneously in a mixed-integer convex optimization program. Moreover, we rely on the Contact Wrench Cone (CWC) stability criterion, which generalizes the ZMP criterion to uneven terrain with friction cone constraints, and we plan the walking motion together with the angular momentum through a convex optimization program. Our approach is successfully tested on a LittleDog quadruped over simulated scenarios. We show that on the flat ground, our planner generates a periodic gait, same as Central Pattern Generator + ZMP planner; while on uneven terrain, our planner can successfully generate a motion containing different gaits, with a center-of-mass motion that respects the friction cone constraints, which are violated by ZMP planners. This improvement clearly demonstrates the advantage of our approach over traditional planning strategies. This paper introduces an optimization-based approach to synthesizing hand manipulations from a starting grasping pose. We describe an automatic method that takes as input an initial grasping pose and partial object trajectory, and produces as output physically plausible hand animation that effects the desired manipulation. In response to different dynamic situations during manipulation, our algorithm can generate a range of possible hand manipulations including changes in joint configurations, changes in contact points, and changes in the grasping force. Formulating hand manipulation as an optimization problem is key to our algorithm's ability to generate a large repertoire of hand motions from limited user input. We introduce an objective function that accentuates the detailed hand motion and contacts adjustment. Furthermore, we describe an optimization method that solves for hand motion and contacts efficiently while taking into account long-term planning of contact forces. Our algorithm does not require any tuning of parameters, nor does it require any prescribed hand motion sequences. Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform. We propose a humanoid robot navigation planning framework that reuses previous experience to decrease planning time. The framework is intended for navigating complex unstructured environments using both palm and foot contacts. In a complex environment, discrete-search-based contact space planners trade-off between high branching factor and action flexibility. Although approaches such as weighted A∗, ARA∗ and ANA∗ could speed up the search by compromising on optimality, they can be very slow when the heuristic is inaccurate. In the proposed framework, an experience-retrieval module is added in parallel to ANA∗. This module collects previously-generated motion plans and clusters them based on contact pose similarity to form a motion plan library. To retrieve an appropriate plan from the library for a given environment, the framework uses a distance between the contact poses in the plan and environment surfaces. Candidate plans are then modified with local trajectory optimization until a plan fitting the query environment is found. Our experiments show that the proposed framework outperforms planning-from-scratch in success rate in unstructured environments by at least 28 and can navigate difficult environments such as rubble and narrow corridors. We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . In this paper, we present a convex optimization problem to generate Center of Mass (CoM) and momentum trajectories of a walking robot, such that the motion robustly satisfies the friction cone constraints on uneven terrain. We adopt the Contact Wrench Cone (CWC) criterion to measure a robot's dynamical stability, which generalizes the venerable Zero Moment Point (ZMP) criterion. Unlike the ZMP criterion, which is ideal for walking on flat ground with unbounded tangential friction forces, the CWC criterion incorporates non-coplanar contacts with friction cone constraints. We measure the robustness of the motion using the margin in the Contact Wrench Cone at each time instance, which quantifies the capability of the robot to instantaneously resist external force torque disturbance, without causing the foot to tip over or slide. For pre-specified footstep location and time, we formulate a convex optimization problem to search for robot linear and angular momenta that satisfy the CWC criterion. We aim to maximize the CWC margin to improve the robustness of the motion, and minimize the centroidal angular momentum (angular momentum about CoM) to make the motion natural. Instead of directly minimizing the non-convex centroidal angular momentum, we resort to minimizing a convex upper bound. We show that our CWC planner can generate motion similar to the result of the ZMP planner on flat ground with sufficient friction. Moreover, on an uneven terrain course with friction cone constraints, our CWC planner can still find feasible motion, while the outcome of the ZMP planner violates the friction limit. This paper investigates real-time control strategies for dynamical systems that involve frictional contact interactions. Hybridness and underactuation are key characteristics of these systems that complicate the design of feedback controllers. In this research, we examine and test a novel feedback controller design on a planar pushing system, where the purpose is to control the motion of a sliding object on a flat surface using a point robotic pusher. The pusher-slider is a simple dynamical system that retains many of the challenges that are typical of robotic manipulation tasks. Our results show that a model predictive control approach used in tandem with integer programming offers a powerful solution to capture the dynamic constraints associated with the friction cone as well as the hybrid nature of the contact. In order to achieve real-time control, simplifications are proposed to speed up the integer program. The concept of Family of Modes (FOM) is introduced to solve an online convex optimization problem by selecting a set of contact mode schedules that spans a large set of dynamic behaviors that can occur during the prediction horizon. The controller design is applied to stabilize the motion of a sliding object about a nominal trajectory, and to re-plan its trajectory in real-time to follow a moving target. We validate the controller design through numerical simulations and experimental results on an industrial ABB IRB 120 robotic arm. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Manipulation planning involves planning the combined motion of objects in the environment as well as the robot motions to achieve them. In this paper, we explore a hierarchical approach to planning sequences of non-prehensile and prehensile actions. We subdivide the planning problem into three stages (object contacts, object poses and robot contacts) and thereby reduce the size of search space that is explored. We show that this approach is more efficient than earlier strategies that search in the combined robot-object configuration space directly. Feedback control of robotic systems interacting with the environment through contacts is a central topic in legged robotics. One of the main challenges posed by this problem is the choice of a model sufficiently complex to capture the discontinuous nature of the dynamics but simple enough to allow online computations. Linear models have proved to be the most effective and reliable choice for smooth systems; we believe that piecewise affine (PWA) models represent their natural extension when contact phenomena occur. Discrete-time PWA systems have been deeply analyzed in the field of hybrid Model Predictive Control (MPC), but the straightforward application of MPC techniques to complex systems, such as a humanoid robot, leads to mixed-integer optimization problems which are not solvable at real-time rates. Explicit MPC methods can construct the entire control policy offline, but the resulting policy becomes too complex to compute for systems at the scale of a humanoid robot. In this paper we propose a novel algorithm which splits the computational burden between an offline sampling phase and a limited number of online convex optimizations, enabling the application of hybrid predictive controllers to higher-dimensional systems. In doing so we are willing to partially sacrifice feedback optimality, but we set stability of the system as an inviolable requirement. Simulation results of a simple planar humanoid that balances by making contact with its environment are presented to validate the proposed controller. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . We present a new method for planning footstep placements for a robot walking on uneven terrain with obstacles, using a mixed-integer quadratically-constrained quadratic program (MIQCQP). Our approach is unique in that it handles obstacle avoidance, kinematic reachability, and rotation of footstep placements, which typically have required non-convex constraints, in a single mixed-integer optimization that can be efficiently solved to its global optimum. Reachability is enforced through a convex inner approximation of the reachable space for the robot's feet. Rotation of the footsteps is handled by a piecewise linear approximation of sine and cosine, designed to ensure that the approximation never overestimates the robot's reachability. Obstacle avoidance is ensured by decomposing the environment into convex regions of obstacle-free configuration space and assigning each footstep to one such safe region. We demonstrate this technique in simple 2D and 3D environments and with real environments sensed by a humanoid robot. We also discuss computational performance of the algorithm, which is currently capable of planning short sequences of a few steps in under one second or longer sequences of 10–30 footsteps in tens of seconds to minutes on common laptop computer hardware. Our implementation is available within the Drake MATLAB toolbox [1]. The challenge of aerial robotic contact-based inspection is the driving motivation of this paper. The problem is approached on both levels of control and path-planning by introducing algorithms and control laws that ensure optimal inspection through contact and controlled aerial robotic physical interaction. Regarding the flight and physical interaction stabilization, a hybrid model predictive control framework is proposed, based on which a typical quadrotor becomes capable of stable and active interaction, accurate trajectory tracking on environmental surfaces as well as force control. Convex optimization techniques enabled the explicit computation of such a controller which accounts for the dynamics in free-flight as well as during physical interaction, ensures the global stability of the hybrid system and provides optimal responses while respecting the physical limitations of the vehicle. Further augmentation of this scheme, allowed the incorporation of a last-resort obstacle avoidance mechanism at the control level. Relying on such a control law, a contact-based inspection planner was developed which computes the optimal route within a given set of inspection points while avoiding any obstacles or other no-fly zones on the environmental surface. Extensive experimental studies that included complex "aerial-writing" tasks, interaction with non-planar and textured surfaces, execution of multiple inspection operations and obstacle avoidance maneuvers, indicate the efficiency of the proposed methods and the potential capabilities of aerial robotic inspection through contact. Abstract : To plan dynamic, whole-body motions for robots one conventionally faces the choice between a complex, fullbody dynamic model containing every link and actuator of the robot, or a highly simplified model of the robot as a point mass. In this paper we explore a powerful middle ground between these extremes. We present an approach to generate whole-body motions using a simple dynamics model, which enforces that the linear and angular momentum of the robot be consistent with the external wrenches on the robot, and a full-body kinematics model that enforces rich geometric constraints, such as end-effector positioning or collision avoidance. We obtain a trajectory for the robot and profiles of contact wrenches by solving a nonlinear optimization problem (NLP). We further demonstrate that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance. We demonstrate that this algorithm is capable of generating highly-dynamic motion plans with examples of a humanoid robot negotiating obstacle course elements and gait optimization for a quadrupedal robot. Contact constraints, such as those between a foot and the ground or a hand and an object, are inherent in many robotic tasks. These constraints define a manifold of feasible states; while well understood mathematically, they pose numerical challenges to many algorithms for planning and controlling whole-body dynamic motions. In this paper, we present an approach to the synthesis and stabilization of complex trajectories for both fully-actuated and underactuated robots subject to contact constraints. We introduce a trajectory optimization algorithm (DIRCON) that extends the direct collocation method, naturally incorporating manifold constraints to produce a nominal trajectory with third-order integration accuracy—a critical feature for achieving reliable tracking control. We adapt the classical time-varying linear quadratic regulator to produce a local cost-to-go in the manifold tangent plane. Finally, we descend the cost-to-go using a quadratic program that incorporates unilateral friction and torque constraints. This approach is demonstrated on three complex walking and climbing locomotion examples in simulation. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60]