Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots

In this dissertation, we develop an efficient method of generating minimal jerk trajectories for redundant robots in trajectory following problems. We show that high jerk is a local phenomenon, and therefore focus on optimizing regions of high jerk that occur when using traditional trajectory generation methods. The optimal trajectory is shown to be located on the foliation of self-motion manifolds, and this property is exploited to express the problem as a minimal dimension Bolza optimal control problem. A numerical algorithm based on ideas from pseudo-spectral optimization methods is proposed and applied to two example planar robot structures with two redundant degrees of freedom. When compared with existing trajectory generation methods, the proposed algorithm reduces the integral jerk of the examples by 75% and 13%. Peak jerk is reduced by 98% and 33%. Finally a real time controller is proposed to accurately track the planned trajectory given real-time measurements of the tool-tip\u27s following error

Motion Planning and Safety for Autonomous Driving

This thesis discusses two different problems in motion planning for autonomous driving. The first is the problem of optimizing a lattice planner control set for any particular autonomous driving task, with the goal of reducing planning time for that task. The driving task is encoded in the form of a dataset of trajectories executed while performing said task. In addition to improving planning time, the optimized control set should capture the driving style of the dataset. In this sense, the control set is learned from the data and is tailored to a particular task. To determine the value of control actions to add to the control set, a modified version of the Fréchet distance is used to score how useful control actions are for generating paths similar to those in the dataset. This method is then compared to the state of the art lattice planner control set optimization technique in terms of planning runtime for the learned task. The second problem is the task of extending the Responsibility-Sensitive Safety (RSS) framework by introducing swerve manoeuvres in addition to the nominal braking manoeu- vres present in the framework. This includes comparing the clearance distances required by a swerve to the braking distances in the original framework. This comparison shows that swerve manoeuvres require less distance gap in order to reach safety from a braking agent in front of the autonomous vehicle at higher speeds. For more realistic swerve manoeuvres, the kinematic bicycle model is used rather than the 2-D double integrator model consid- ered in RSS. An upper bound is then computed on the required clearance distance for a swerve manoeuvre that satisfies bicycle kinematics. A longitudinal safe following distance is then derived that is provably safe, and is shown to be lower than the following distance required by RSS at higher speeds. The use of the kinematic bicycle model is then validated by computing swerve manoeuvres with a dynamic single-track car model and Pacejka tire model, and comparing the single-track swerves to the bicycle swerves

Sampling Based Motion Planning with Reachable Volumes

Motion planning for constrained systems is a version of the motion planning problem in which the motion of a robot is limited by constraints. For example, one can require that a humanoid robot such as a PR2 remain upright by constraining its torso to be above its base or require that an object such as a bucket of water remain upright by constraining the vertices of the object to be parallel to the robot’s base. Grasping can be modeled by requiring that the end effectors of the robot be located at specified handle positions. Constraints might require that the robot remain in contact with a surface, or that certain joints of the robot remain in contact with each other (e.g., closed chains). Such problems are particularly difficult because the constraints form a manifold in C-space, and planning must be restricted to this manifold. High degree of freedom motion planning and motion planning for constrained systems has applications in parallel robotics, grasping and manipulation, computational biology and molecular simulations, and animation. In this work, we introduce a new concept, reachable volumes, that are a geometric representation of the regions the joints and end effectors of a robot can reach, and use it to define a new planning space, called RV-space, where all points automatically satisfy a problem’s constraints. Visualizations of reachable volumes can enable operators to see the regions of workspace that different parts of the robot can reach. Samples and paths generated in RV-space naturally conform to constraints, making planning for constrained systems no more difficult than planning for unconstrained systems. Consequently, constrained motion planning problems that were previously difficult or unsolvable become manageable and in many cases trivial. We provide tools and techniques to extend the state of the art sampling based motion planning algorithms to RV-space. We define a reachable volume sampler, a reachable volume local planner and a reachable volume distance metric. We showcase the effectiveness of RV-space by applying these tools to motion planning problems for robots with constraints on the end effectors and/or internal joints of the robot. We show that RV-based planners are more efficient than existing methods, particularly for higher dimensional problems, solving problems with 1000+ degrees of freedom for multi-loop, and tree-like linkages

Dynamic Grasp Adaptation:From Humans To Robots

The human hand is an amazing tool, demonstrated by its incredible motor capability and remarkable sense of touch. To enable robots to work in a human-centric environment, it is desirable to endow robotic hands with human-like capabilities for grasping and object manipulation. However, due to its inherent complexity and inevitable model uncertainty, robotic grasping and manipulation remains a challenge. This thesis focuses on grasp adaptation in the face of model and sensing uncertainties: Given an object whose properties are not known with certainty (e.g., shape, weight and external perturbation), and a multifingered robotic hand, we aim at determining where to put the fingers and how the fingers should adaptively interact with the object using tactile sensing, in order to achieve either a stable grasp or a desired dynamic behaviour. A central idea in this thesis is the object-centric dynamics: namely, that we express all control constraints into an object-centric representation. This simplifies computa- tion and makes the control versatile to the type of hands. This is an essential feature that distinguishes our work from other robust grasping work in the literature, where generating a static stable grasp for a given hand is usually the primary goal. In this thesis, grasp adaptation is a dynamic process that flexibly adapts the grasp to fit some purpose from the objectâs perspective, in the presence of a variety of uncertainties and/or perturbations. When building a grasp adaptation for a given situation, there are two key problems that must be addressed: 1) the problem of choosing an initial grasp that is suitable for future adaptation, and more importantly 2) the problem of design- ing an adaptation strategy that can react adequately to achieve desired behaviour of the grasped object. To address challenge 1 (planning a grasp under shape uncertainty), we propose an approach to parameterizing the uncertainty in object shape using Gaussian Processes (GPs) and incorporate it as a constraint into contact-level grasp planning. To realize the planned contacts using different hands interchangeably, we further develop a prob- abilistic model to predict the feasible hand configurations, including hand pose and finger joints, given the desired contact points only. The model is built using the con- cept of Virtual Frame(VF), and it is independent from the choice of hand frame and object frame. The performance of the proposed approach is validated on two differ- ent robotic hands, an industrial gripper (4 DOF Barrett hand) and a humanoid hand (16 DOF Allegro hand) to manipulate objects of daily use with complex geometry and various texture (a spray bottle, a tea caddy, a jug and a bunny toy). In the second part of this thesis, we propose an approach to the design of adapta- tion strategy to ensure grasp stability in the presence of physical uncertainties of objects(object weight, friction at contacts and external perturbation). Based on an object-level impedance controller, we first design a grasp stability estimator in the object frame using the grasp experience and tactile sensing. Once a grasp is predicted to be unstable during online execution, the grasp adaptation strategy is triggered to improve the grasp stability, by either changing the stiffness at finger level or relocating the position of one fingertip to a better area

Motion planning for manipulation and/or navigation tasks with emphasis on humanoid robots

This thesis handles the motion planning problem for various robotic platforms. This is a fundamental problem, especially referring to humanoid robots for which it is particularly challenging for a number of reasons. The first is the high number of degrees of freedom. The second is that a humanoid robot is not a free-flying system in its configuration space: its motions must be generated appropriately. Finally, the implicit requirement that the robot maintains equilibrium, either static or dynamic, typically constrains the trajectory of the robot center of mass. In particular, we are interested in handling problems in which the robot must execute a task, possibly requiring stepping, in environments cluttered by obstacles. In order to solve this problem, we propose to use offline probabilistic motion planning techniques such as Rapidly Exploring Random Trees (RRTs) that consist in finding a solution by means of a graph built in an appropriately defined configuration space. The novelty of the approach is that it does not separate locomotion from task execution. This feature allows to generate whole-body movements while fulfilling the task. The task can be assigned as a trajectory or a single point in the task space or even combining tasks of different nature (e.g., manipulation and navigation tasks). The proposed method is also able to deform the task, if the assigned one is too difficult to be fulfilled. It automatically detects when the task should be deformed and which kind of deformation to apply. However, there are situations, especially when robots and humans have to share the same workspace, in which the robot has to be equipped with reactive capabilities (as avoiding moving obstacles), allowing to reach a basic level of safety. The final part of the thesis handles the rearrangement planning problem. This problem is interesting in view of manipulation tasks, where the robot has to interact with objects in the environment. Roughly speaking, the goal of this problem is to plan the motion for a robot whose assigned a task (e.g., move a target object in a goal region). Doing this, the robot is allowed to move some movable objects that are in the environment. The problem is difficult because we must plan in continuous, high-dimensional state and action spaces. Additionally, the physical constraints induced by the nonprehensile interaction between the robot and the objects in the scene must be respected. Our insight is to embed physics models in the planning stage, allowing robot manipulation and simultaneous objects interaction. Throughout the thesis, we evaluate the proposed planners through experiments on different robotic platforms