A geometrical approach to the motion planning problem for a submerged rigid body

The main focus of this paper is the motion planning problem for a deeply submerged rigid body. The equations of motion are formulated and presented by use of the framework of differential geometry and these equations incorporate external dissipative and restoring forces. We consider a kinematic reduction of the affine connection control system for the rigid body submerged in an ideal fluid, and present an extension of this reduction to the forced affine connection control system for the rigid body submerged in a viscous fluid. The motion planning strategy is based on kinematic motions; the integral curves of rank one kinematic reductions. This method is of particular interest to autonomous underwater vehicles which can not directly control all six degrees of freedom (such as torpedo shaped AUVs) or in case of actuator failure (i.e., under-actuated scenario). A practical example is included to illustrate our technique.

Multi-objective four-dimensional vehicle motion planning in large dynamic environments

This paper presents Multi-Step A* (MSA*), a search algorithm based on A* for multi-objective 4D vehicle motion planning (three spatial and one time dimension). The research is principally motivated by the need for offline and online motion planning for autonomous Unmanned Aerial Vehicles (UAVs). For UAVs operating in large, dynamic and uncertain 4D environments, the motion plan consists of a sequence of connected linear tracks (or trajectory segments). The track angle and velocity are important parameters that are often restricted by assumptions and grid geometry in conventional motion planners. Many existing planners also fail to incorporate multiple decision criteria and constraints such as wind, fuel, dynamic obstacles and the rules of the air. It is shown that MSA* finds a cost optimal solution using variable length, angle and velocity trajectory segments. These segments are approximated with a grid based cell sequence that provides an inherent tolerance to uncertainty. Computational efficiency is achieved by using variable successor operators to create a multi-resolution, memory efficient lattice sampling structure. Simulation studies on the UAV flight planning problem show that MSA* meets the time constraints of online replanning and finds paths of equivalent cost but in a quarter of the time (on average) of vector neighbourhood based A*.

Motion planning and stochastic control with experimental validation on a planetary rover

Motion planning for planetary rovers must consider control uncertainty in order to maintain the safety of the platform during navigation. Modelling such control uncertainty is difficult due to the complex interaction between the platform and its environment. In this paper, we propose a motion planning approach whereby the outcome of control actions is learned from experience and represented statistically using a Gaussian process regression model. This model is used to construct a control policy for navigation to a goal region in a terrain map built using an on-board RGB-D camera. The terrain includes flat ground, small rocks, and non-traversable rocks. We report the results of 200 simulated and 35 experimental trials that validate the approach and demonstrate the value of considering control uncertainty in maintaining platform safety.

Curiosity driven reinforcement learning for motion planning on humanoids

Most previous work on artificial curiosity (AC) and intrinsic motivation focuses on basic concepts and theory. Experimental results are generally limited to toy scenarios, such as navigation in a simulated maze, or control of a simple mechanical system with one or two degrees of freedom. To study AC in a more realistic setting, we embody a curious agent in the complex iCub humanoid robot. Our novel reinforcement learning (RL) framework consists of a state-of-the-art, low-level, reactive control layer, which controls the iCub while respecting constraints, and a high-level curious agent, which explores the iCub's state-action space through information gain maximization, learning a world model from experience, controlling the actual iCub hardware in real-time. To the best of our knowledge, this is the first ever embodied, curious agent for real-time motion planning on a humanoid. We demonstrate that it can learn compact Markov models to represent large regions of the iCub's configuration space, and that the iCub explores intelligently, showing interest in its physical constraints as well as in objects it finds in its environment.

Predictive motion planning for AUVs subject to strong time-varying currents and forecasting uncertainties

This paper presents a novel path planning method for minimizing the energy consumption of an autonomous underwater vehicle subjected to time varying ocean disturbances and forecast model uncertainty. The algorithm determines 4-Dimensional path candidates using Nonlinear Robust Model Predictive Control (NRMPC) and solutions optimised using A*-like algorithms. Vehicle performance limits are incorporated into the algorithm with disturbances represented as spatial and temporally varying ocean currents with a bounded uncertainty in their predictions. The proposed algorithm is demonstrated through simulations using a 4-Dimensional, spatially distributed time-series predictive ocean current model. Results show the combined NRMPC and A* approach is capable of generating energy-efficient paths which are resistant to both dynamic disturbances and ocean model uncertainty.

Error Detection and Recovery for Robot Motion Planning with Uncertainty

Robots must plan and execute tasks in the presence of uncertainty. Uncertainty arises from sensing errors, control errors, and uncertainty in the geometry of the environment. The last, which is called model error, has received little previous attention. We present a framework for computing motion strategies that are guaranteed to succeed in the presence of all three kinds of uncertainty. The motion strategies comprise sensor-based gross motions, compliant motions, and simple pushing motions.

Motion Planning with Six Degrees of Freedom

The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given high-level specifications of tasks and geometric models of the robot and obstacles. The Mover's problem is to find a continuous, collision-free path for a moving object through an environment containing obstacles. We present an implemented algorithm for the classical formulation of the three-dimensional Mover's problem: given an arbitrary rigid polyhedral moving object P with three translational and three rotational degrees of freedom, find a continuous, collision-free path taking P from some initial configuration to a desired goal configuration. This thesis describes the first known implementation of a complete algorithm (at a given resolution) for the full six degree of freedom Movers' problem. The algorithm transforms the six degree of freedom planning problem into a point navigation problem in a six-dimensional configuration space (called C-Space). The C-Space obstacles, which characterize the physically unachievable configurations, are directly represented by six-dimensional manifolds whose boundaries are five dimensional C-surfaces. By characterizing these surfaces and their intersections, collision-free paths may be found by the closure of three operators which (i) slide along 5-dimensional intersections of level C-Space obstacles; (ii) slide along 1- to 4-dimensional intersections of level C-surfaces; and (iii) jump between 6 dimensional obstacles. Implementing the point navigation operators requires solving fundamental representational and algorithmic questions: we will derive new structural properties of the C-Space constraints and shoe how to construct and represent C-Surfaces and their intersection manifolds. A definition and new theoretical results are presented for a six-dimensional C-Space extension of the generalized Voronoi diagram, called the C-Voronoi diagram, whose structure we relate to the C-surface intersection manifolds. The representations and algorithms we develop impact many geometric planning problems, and extend to Cartesian manipulators with six degrees of freedom.

On Motion Planning with Uncertainty

Robots must successfully plan and execute tasks in the presence of uncertainty. Uncertainty arises from errors in modeling, sensing, and control. Planning in the presence of uncertainty constitutes one facet of the general motion planning problem in robotics. This problem is concerned with the automatic synthesis of motion strategies from high level task specification and geometric models of environments. In order to develop successful motion strategies, it is necessary to understand the effect of uncertainty on the geometry of object interactions. Object interactions, both static and dynamic, may be represented in geometrical terms. This thesis investigates geometrical tools for modeling and overcoming uncertainty. The thesis describes an algorithm for computing backprojections o desired task configurations. Task goals and motion states are specified in terms of a moving object's configuration space. Backprojections specify regions in configuration space from which particular motions are guaranteed to accomplish a desired task. The backprojection algorithm considers surfaces in configuration space that facilitate sliding towards the goal, while avoiding surfaces on which motions may prematurely halt. In executing a motion for a backprojection region, a plan executor must be able to recognize that a desired task has been accomplished. Since sensors are subject to uncertainty, recognition of task success is not always possible. The thesis considers the structure of backprojection regions and of task goals that ensures goal recognizability. The thesis also develops a representation of friction in configuration space, in terms of a friction cone analogous to the real space friction cone. The friction cone provides the backprojection algorithm with a geometrical tool for determining points at which motions may halt.

Improved APF strategies for dual-arm local motion planning

Manipulator motion planning is a classic problem in robotics, with a number of complete solutions available for their motion in controlled (industrial) environments. Owing to recent technological advances in the field of robotics, there has been a significant development of more complex robots with high-fidelity sensors and more computational power. One such example has been a rise in the production of humanoid robots equipped with dual-arm manipulators which require complex motion planning algorithms. Also, the technological advances have resulted in a shift from using manipulators in strictly controlled environments, to investigating the deployment of manipulators in dynamic or unknown environments. As a result, a greater emphasis has been put on the development of local motion planners, which can provide real-time solutions to these problems. Artificial Potential Fields (APFs) is one such popular local motion planning technique, which can be applied to manipulator motion planning, however, the basic algorithm is severely prone to local minima problems. Here, two modified APF-based strategies for solving the dual-arm motion planning task in unknown environments are proposed. Both techniques make use of configuration sampling and subgoal selection to assist the APFs in avoiding these local minima scenarios. Extensive simulation results are presented to validate the efficacy of the proposed methodology.

A multi-objective approach for the motion planning of redundant manipulators

Kinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.

A fractional approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots through the pseudoinverse control leads to undesirable drift in the joint space. This paper presents a new technique to solve the inverse kinematics problem of redundant manipulators, which uses a fractional differential of order α to control the joint positions. Two performance measures are defined to examine the strength and weakness of the proposed method. The positional error index measures the precision of the manipulator's end-effector at the target position. The repeatability performance index is adopted to evaluate if the joint positions are repetitive when the manipulator execute repetitive trajectories in the operational workspace. Redundant and hyper-redundant planar manipulators reveal that it is possible to choose in a large range of possible values of α in order to get repetitive trajectories in the joint space.