Search-based Motion Planning for Aggressive Flight in SE(3)

Quadrotors with large thrust-to-weight ratios are able to track aggressive trajectories with sharp turns and high accelerations. In this work, we develop a search-based trajectory planning approach that exploits the quadrotor maneuverability to generate sequences of motion primitives in cluttered environments. We model the quadrotor body as an ellipsoid and compute its flight attitude along trajectories in order to check for collisions against obstacles. The ellipsoid model allows the quadrotor to pass through gaps that are smaller than its diameter with non-zero pitch or roll angles. Without any prior information about the location of gaps and associated attitude constraints, our algorithm is able to find a safe and optimal trajectory that guides the robot to its goal as fast as possible. To accelerate planning, we first perform a lower dimensional search and use it as a heuristic to guide the generation of a final dynamically feasible trajectory. We analyze critical discretization parameters of motion primitive planning and demonstrate the feasibility of the generated trajectories in various simulations and real-world experiments.Comment: 8 pages, submitted to RAL and ICRA 201

A Partially Randomized Approach to Trajectory Planning and Optimization for Mobile Robots with Flat Dynamics

Motion planning problems are characterized by huge search spaces and complex obstacle structures with no concise mathematical expression. The fixed-wing airplane application considered in this thesis adds differential constraints and point-wise bounds, i. e. an infinite number of equality and inequality constraints. An optimal trajectory planning approach is presented, based on the randomized Rapidly-exploring Random Trees framework (RRT*). The local planner relies on differential flatness of the equations of motion to obtain tree branch candidates that automatically satisfy the differential constraints. Flat output trajectories, in this case equivalent to the airplane's flight path, are designed using Bézier curves. Segment feasibility in terms of point-wise inequality constraints is tested by an indicator integral, which is evaluated alongside the segment cost functional. Although the RRT* guarantees optimality in the limit of infinite planning time, it is argued by intuition and experimentation that convergence is not approached at a practically useful rate. Therefore, the randomized planner is augmented by a deterministic variational optimization technique. To this end, the optimal planning task is formulated as a semi-infinite optimization problem, using the intermediate result of the RRT(*) as an initial guess. The proposed optimization algorithm follows the feasible flavor of the primal-dual interior point paradigm. Discretization of functional (infinite) constraints is deferred to the linear subproblems, where it is realized implicitly by numeric quadrature. An inherent numerical ill-conditioning of the method is circumvented by a reduction-like approach, which tracks active constraint locations by introducing new problem variables. Obstacle avoidance is achieved by extending the line search procedure and dynamically adding obstacle-awareness constraints to the problem formulation. Experimental evaluation confirms that the hybrid approach is practically feasible and does indeed outperform RRT*'s built-in optimization mechanism, but the computational burden is still significant.Bewegungsplanungsaufgaben sind typischerweise gekennzeichnet durch umfangreiche Suchräume, deren vollständige Exploration nicht praktikabel ist, sowie durch unstrukturierte Hindernisse, für die nur selten eine geschlossene mathematische Beschreibung existiert. Bei der in dieser Arbeit betrachteten Anwendung auf Flächenflugzeuge kommen differentielle Randbedingungen und beschränkte Systemgrößen erschwerend hinzu. Der vorgestellte Ansatz zur optimalen Trajektorienplanung basiert auf dem Rapidly-exploring Random Trees-Algorithmus (RRT*), welcher die Suchraumkomplexität durch Randomisierung beherrschbar macht. Der spezifische Beitrag ist eine Realisierung des lokalen Planers zur Generierung der Äste des Suchbaums. Dieser erfordert ein flaches Bewegungsmodell, sodass differentielle Randbedingungen automatisch erfüllt sind. Die Trajektorien des flachen Ausgangs, welche im betrachteten Beispiel der Flugbahn entsprechen, werden mittels Bézier-Kurven entworfen. Die Einhaltung der Ungleichungsnebenbedingungen wird durch ein Indikator-Integral überprüft, welches sich mit wenig Zusatzaufwand parallel zum Kostenfunktional berechnen lässt. Zwar konvergiert der RRT*-Algorithmus (im probabilistischen Sinne) zu einer optimalen Lösung, jedoch ist die Konvergenzrate aus praktischer Sicht unbrauchbar langsam. Es ist daher naheliegend, den Planer durch ein gradientenbasiertes lokales Optimierungsverfahren mit besseren Konvergenzeigenschaften zu unterstützen. Hierzu wird die aktuelle Zwischenlösung des Planers als Initialschätzung für ein kompatibles semi-infinites Optimierungsproblem verwendet. Der vorgeschlagene Optimierungsalgorithmus erweitert das verbreitete innere-Punkte-Konzept (primal dual interior point method) auf semi-infinite Probleme. Eine explizite Diskretisierung der funktionalen Ungleichungsnebenbedingungen ist nicht erforderlich, denn diese erfolgt implizit durch eine numerische Integralauswertung im Rahmen der linearen Teilprobleme. Da die Methode an Stellen aktiver Nebenbedingungen nicht wohldefiniert ist, kommt zusätzlich eine Variante des Reduktions-Ansatzes zum Einsatz, bei welcher der Vektor der Optimierungsvariablen um die (endliche) Menge der aktiven Indizes erweitert wird. Weiterhin wurde eine Kollisionsvermeidung integriert, die in den Teilschritt der Liniensuche eingreift und die Problemformulierung dynamisch um Randbedingungen zur lokalen Berücksichtigung von Hindernissen erweitert. Experimentelle Untersuchungen bestätigen, dass die Ergebnisse des hybriden Ansatzes aus RRT(*) und numerischem Optimierungsverfahren der klassischen RRT*-basierten Trajektorienoptimierung überlegen sind. Der erforderliche Rechenaufwand ist zwar beträchtlich, aber unter realistischen Bedingungen praktisch beherrschbar

ProbRobScene: A Probabilistic Specification Language for 3D Robotic Manipulation Environments

Robotic control tasks are often first run in simulation for the purposes of verification, debugging and data augmentation. Many methods exist to specify what task a robot must complete, but few exist to specify what range of environments a user expects such tasks to be achieved in. ProbRobScene is a probabilistic specification language for describing robotic manipulation environments. Using the language, a user need only specify the relational constraints that must hold between objects in a scene. ProbRobScene will then automatically generate scenes which conform to this specification. By combining aspects of probabilistic programming languages and convex geometry, we provide a method for sampling this space of possible environments efficiently. We demonstrate the usefulness of our language by using it to debug a robotic controller in a tabletop robot manipulation environment

Teleprogramming: Overcoming Communication Delays in Remote Manipulation (Dissertation Proposal)

Modern industrial processes (nuclear, chemical industry), public service needs (firefighting, rescuing), and research interests (undersea, outer space exploration) have established a clear need to perform work remotely. Whereas a purely autonomous manipulative capability would solve the problem, its realization is beyond the state of the art in robotics [Stark et al.,1988]. Some of the problems plaguing the development of autonomous systems are: a) anticipation, detection, and correction of the multitude of possible error conditions arising during task execution, b) development of general strategy planning techniques transcending any particular limited task domain, c) providing the robot system with real-time adaptive behavior to accommodate changes in the remote environment, d) allowing for on-line learning and performance improvement through experience , etc. The classical approach to tackle some of these problems has been to introduce problem solvers and expert systems as part of the remote robot workcell control system. However, such systems tend to be limited in scope (to remain intellectually and implementationally manageable), too slow to be useful in real-time robot task execution, and generally fail to adequately represent and model the complexities of the real world environment. These problems become particularly severe when only partial information about the remote environment is available

Hybrid Stiff/Compliant Workspace Control for Robotized Minimally Invasive Surgery

Abstract-This paper presents a novel control architecture for hybrid stiff and compliant control for minimally invasive surgery which satisfies the constraints of zero lateral velocity at the entry point for serial manipulators. For minimally invasive surgery it is required that there is no sideways motion at the point where the robots enter the abdomen. This is necessary to avoid any damage to the patient's body when the robot moves. We solve this at a kinematic level, i.e., we find a Jacobian matrix that maps the velocities in joint space to the end-effector velocities and at the same time guarantees that certain velocities at the entry point are zero. Because the new velocity variables are defined in the end-effector workspace we can use these for hybrid motion/force control. The approach is verified experimentally by implementing hybrid stiff and compliant control of the end effector and we show that the insertion point constraints are always satisfied

An ontology-based approach towards coupling task and path planning for the simulation of manipulation tasks

This work deals with the simulation and the validation of complex manipulation tasks under strong geometric constraints in virtual environments. The targeted applications relate to the industry 4.0 framework; as up-to-date products are more and more integrated and the economic competition increases, industrial companies express the need to validate, from design stage on, not only the static CAD models of their products but also the tasks (e.g., assembly or maintenance) related to their Product Lifecycle Management (PLM). The scientific community looked at this issue from two points of view: - Task planning decomposes a manipulation task to be realized into a sequence of primitive actions (i.e., a task plan) - Path planning computes collision-free trajectories, notably for the manipulated objects. It traditionally uses purely geometric data, which leads to classical limitations (possible high computational processing times, low relevance of the proposed trajectory concerning the task to be performed, or failure); recent works have shown the interest of using higher abstraction level data. Joint task and path planning approaches found in the literature usually perform a classical task planning step, and then check out the feasibility of path planning requests associated with the primitive actions of this task plan. The link between task and path planning has to be improved, notably because of the lack of loopback between the path planning level and the task planning level: - The path planning information used to question the task plan is usually limited to the motion feasibility where richer information such as the relevance or the complexity of the proposed path would be needed; - path planning queries traditionally use purely geometric data and/or “blind” path planning methods (e.g., RRT), and no task-related information is used at the path planning level Our work focuses on using task level information at the path planning level. The path planning algorithm considered is RRT; we chose such a probabilistic algorithm because we consider path planning for the simulation and the validation of complex tasks under strong geometric constraints. We propose an ontology-based approach to use task level information to specify path planning queries for the primitive actions of a task plan. First, we propose an ontology to conceptualize the knowledge about the 3D environment in which the simulated task takes place. The environment where the simulated task takes place is considered as a closed part of 3D Cartesian space cluttered with mobile/fixed obstacles (considered as rigid bodies). It is represented by a digital model relying on a multilayer architecture involving semantic, topologic and geometric data. The originality of the proposed ontology lies in the fact that it conceptualizes heterogeneous knowledge about both the obstacles and the free space models. Second, we exploit this ontology to automatically generate a path planning query associated to each given primitive action of a task plan. Through a reasoning process involving the primitive actions instantiated in the ontology, we are able to infer the start and the goal configurations, as well as task-related geometric constraints. Finally, a multi-level path planner is called to generate the corresponding trajectory. The contributions of this work have been validated by full simulation of several manipulation tasks under strong geometric constraints. The results obtained demonstrate that using task-related information allows better control on the RRT path planning algorithm involved to check the motion feasibility for the primitive actions of a task plan, leading to lower computational time and more relevant trajectories for primitive actions

Model Based Teleoperation to Eliminate Feedback Delay NSF Grant BCS89-01352 First Report

We are conducting research in the area of teleoperation with feedback delay. Delay occurs with earth-based teleoperation in space and with surface-based teleoperation with untethered submersibles when acoustic communication links are involved. the delay in obtaining position and force feedback from remote slave arms makes teleoperation extremely difficult. We are proposing a novel combination of graphics and manipulator programming to solve the problem by interfacing a teleoperator master arm to a graphics based simulator of the remote environment coupled with a robot manipulator at the remote, delayed site. the operator\u27s actions will be monitored to provide both kinesthetic and visual feedback and to generate symbolic motion commands to the remote slave. the slave robot will then execute these symbolic commands delayed in time. While much of a task will proceed error free, when an error does occur the slave system will transmit data back to the master and the master environment will be reset to the error state

Volumetric error compensation for industrial robots and machine tools

“A more efficient and increasingly popular volumetric error compensation method for machine tools is to compute compensation tables in axis space with tool tip volumetric measurements. However, machine tools have high-order geometric errors and some workspace is not reachable by measurement devices, the compensation method suffers a curve-fitting challenge, overfitting measurements in measured space and losing accuracy around and out of the measured space. Paper I presents a novel method that aims to uniformly interpolate and extrapolate the compensation tables throughout the entire workspace. By using a uniform constraint to bound the tool tip error slopes, an optimal model with consistent compensation capability is constructed. In addition to machine tools, industrial robots, are also becoming popularly used in manufacturing field. However, typical robot volumetric error compensation methods only consider constant errors such as link length and assembly errors while neglecting complicated kinematic errors such as strain wave gearing and out of rotating plane errors. Paper II presents a high-order joint-dependent model which describes both simple and complicated robot kinematic errors. A laser tracker with advantages of rapid data collection and a self-oriented position retroreflector are used for data collection. The experimental results show that nearly 20% of the robot kinematic errors are joint-dependent which are successfully captured by the proposed method. Paper III continues using the high-order joint-dependent robot error model while utilizing a new retroreflector with the ability of measuring robot position and orientation information simultaneously. More than 60% of measurement time is saved. Both position and orientation accuracy are also further improved”--Abstract, page iv

Proceedings of the Fifth NASA/NSF/DOD Workshop on Aerospace Computational Control

The Fifth Annual Workshop on Aerospace Computational Control was one in a series of workshops sponsored by NASA, NSF, and the DOD. The purpose of these workshops is to address computational issues in the analysis, design, and testing of flexible multibody control systems for aerospace applications. The intention in holding these workshops is to bring together users, researchers, and developers of computational tools in aerospace systems (spacecraft, space robotics, aerospace transportation vehicles, etc.) for the purpose of exchanging ideas on the state of the art in computational tools and techniques