Trajectory planning of a robot using learning algorithms

The authors consider the problem of a robot manipulator operating in a noisy workspace. The manipulator is required to move from an initial position P(i) to a final position P(f). P(i) is assumed to be completely defined. However, P(f) is obtained by a sensing operation and is assumed to be fixed but unknown. The authors approach to this problem involves the use of three learning algorithms, the discretized linear reward-penalty (DLR-P) automaton, the linear reward-penalty (LR-P) automaton and a nonlinear reinforcement scheme. An automaton is placed at each joint of the robot and by acting as a decision maker, plans the trajectory based on noisy measurements of P(f).

Semiautomatic Cochleostomy Target and Insertion Trajectory Planning for Minimally Invasive Cochlear Implantation

A major component of minimally invasive cochlear implantation is atraumatic scala tympani (ST) placement of the electrode array. This work reports on a semiautomatic planning paradigm that uses anatomical landmarks and cochlear surface models for cochleostomy target and insertion trajectory computation. The method was validated in a human whole head cadaver model (n = 10 ears). Cochleostomy targets were generated from an automated script and used for consecutive planning of a direct cochlear access (DCA) drill trajectory from the mastoid surface to the inner ear. An image-guided robotic system was used to perform both, DCA and cochleostomy drilling. Nine of 10 implanted specimens showed complete ST placement. One case of scala vestibuli insertion occurred due to a registration/drilling error of 0.79 mm. The presented approach indicates that a safe cochleostomy target and insertion trajectory can be planned using conventional clinical imaging modalities, which lack sufficient resolution to identify the basilar membrane.

Dynamically balanced and plausible trajectory planning for human-like characters

International audience

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.

Evolutionary trajectory optimization for redundant robots

The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms have been investigated in the last years. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms. In this case the trajectory planning is formulated as an optimization problem with constraints.

An evolutionary approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms are needed. The pseudoinverse control is not repeatable, causing drift in joint space which is undesirable for physical control. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms, leading to an optimization criterion for repeatable control of redundant manipulators, and avoiding the joint angle drift problem. Computer simulations performed based on redundant and hyper-redundant planar manipulators show that, when the end-effector traces a closed path in the workspace, the robot returns to its initial configuration. The solution is repeatable for a workspace with and without obstacles in the sense that, after executing several cycles, the initial and final states of the manipulator are very close.

AUTOFLY-Aid: Flight Deck Automation Support with Dynamic 4D Trajectory Management for Responsive and Adaptive Airborne Collision Avoidance

AUTOFLY-Aid Project aims to develop and demonstrate novel automation support algorithms and tools to the flight crew for flight critical collision avoidance using “dynamic 4D trajectory management”. The automation support system is envisioned to improve the primary shortcomings of TCAS, and to aid the pilot through add-on avionics/head-up displays and reality augmentation devices in dynamically evolving collision avoidance scenarios. The main theoretical innovative and novel concepts to be developed by AUTOFLY-Aid project are a) design and development of the mathematical models of the full composite airspace picture from the flight deck’s perspective, as seen/measured/informed by the aircraft flying in SESAR 2020, b) design and development of a dynamic trajectory planning algorithm that can generate at real-time (on the order of seconds) flyable (i.e. dynamically and performance-wise feasible) alternative trajectories across the evolving stochastic composite airspace picture (which includes new conflicts, blunder risks, terrain and weather limitations) and c) development and testing of the Collision Avoidance Automation Support System on a Boeing 737 NG FNPT II Flight Simulator with synthetic vision and reality augmentation while providing the flight crew with quantified and visual understanding of collision risks in terms of time and directions and countermeasures.

Analysis of the geometric altimetry to support aircraft optimal trajectories within the future 4d trajectory management

Over the past few years, the common practice within air traffic management has been that commercial aircraft fly by following a set of predefined routes to reach their destination. Currently, aircraft operators are requesting more flexibility to fly according to their prefer- ences, in order to achieve their business objectives. Due to this reason, much research effort is being invested in developing different techniques which evaluate aircraft optimal trajectory and traffic synchronisation. Also, the inefficient use of the airspace using barometric altitude overall in the landing and takeoff phases or in Continuous Descent Approach (CDA) trajectories where currently it is necessary introduce the necessary reference setting (QNH or QFE). To solve this problem and to permit a better airspace management born the interest of this research. Where the main goals will be to evaluate the impact, weakness and strength of the use of geometrical altitude instead of the use of barometric altitude. Moreover, this dissertation propose the design a simplified trajectory simulator which is able to predict aircraft trajectories. The model is based on a three degrees of freedom aircraft point mass model that can adapt aircraft performance data from Base of Aircraft Data, and meteorological information. A feature of this trajectory simulator is to support the improvement of the strategic and pre-tactical trajectory planning in the future Air Traffic Management. To this end, the error of the tool (aircraft Trajectory Simulator) is measured by comparing its performance variables with actual flown trajectories obtained from Flight Data Recorder information. The trajectory simulator is validated by analysing the performance of different type of aircraft and considering different routes. A fuel consumption estimation error was identified and a correction is proposed for each type of aircraft model. In the future Air Traffic Management (ATM) system, the trajectory becomes the fundamental element of a new set of operating procedures collectively referred to as Trajectory-Based Operations (TBO). Thus, governmental institutions, academia, and industry have shown a renewed interest for the application of trajectory optimisation techniques in com- mercial aviation. The trajectory optimisation problem can be solved using optimal control methods. In this research we present and discuss the existing methods for solving optimal control problems focusing on direct collocation, which has received recent attention by the scientific community. In particular, two families of collocation methods are analysed, i.e., Hermite-Legendre-Gauss-Lobatto collocation and the pseudospectral collocation. They are first compared based on a benchmark case study: the minimum fuel trajectory problem with fixed arrival time. For the sake of scalability to more realistic problems, the different meth- ods are also tested based on a real Airbus 319 El Cairo-Madrid flight. Results show that pseudospectral collocation, which has shown to be numerically more accurate and computa- tionally much faster, is suitable for the type of problems arising in trajectory optimisation with application to ATM. Fast and accurate optimal trajectory can contribute properly to achieve the new challenges of the future ATM. As atmosphere uncertainties are one of the most important issues in the trajectory plan- ning, the final objective of this dissertation is to have a magnitude order of how different is the fuel consumption under different atmosphere condition. Is important to note that in the strategic phase planning the optimal trajectories are determined by meteorological predictions which differ from the moment of the flight. The optimal trajectories have shown savings of at least 500 [kg] in the majority of the atmosphere condition (different pressure, and temperature at Mean Sea Level, and different lapse rate temperature) with respect to the conventional procedure simulated at the same atmosphere condition.This results show that the implementation of optimal profiles are beneficial under the current Air traffic Management (ATM).

A ROS-based Workspace Control and Trajectory Planner for a seven degrees of freedom Robotic arm

In this Bachelor Thesis I want to provide readers with tools and scripts for the control of a 7DOF manipulator, backed up by some theory of Robotics and Computer Science, in order to better contextualize the work done. In practice, we will see most common software, and developing environments, used to cope with our task: these include ROS, along with visual simulation by VREP and RVIZ, and an almost "stand-alone" ROS extension called MoveIt!, a very complete programming interface for trajectory planning and obstacle avoidance. As we will better appreciate and understand in the introduction chapter, the capability of detecting collision objects through a camera sensor, and re-plan to the desired end-effector pose, are not enough. In fact, this work is implemented in a more complex system, where recognition of particular objects is needed. Through a package of ROS and customized scripts, a detailed procedure will be provided on how to distinguish a particular object, retrieve its reference frame with respect to a known one, and then allow navigation to that target. Together with technical details, the aim is also to report working scripts and a specific appendix (A) you can refer to, if desiring to put things together.

Motion Planning and Controls with Safety and Temporal Constraints

Motion planning, or trajectory planning, commonly refers to a process of converting high-level task specifications into low-level control commands that can be executed on the system of interest. For different applications, the system will be different. It can be an autonomous vehicle, an Unmanned Aerial Vehicle(UAV), a humanoid robot, or an industrial robotic arm. As human machine interaction is essential in many of these systems, safety is fundamental and crucial. Many of the applications also involve performing a task in an optimal manner within a given time constraint. Therefore, in this thesis, we focus on two aspects of the motion planning problem. One is the verification and synthesis of the safe controls for autonomous ground and air vehicles in collision avoidance scenarios. The other part focuses on the high-level planning for the autonomous vehicles with the timed temporal constraints. In the first aspect of our work, we first propose a verification method to prove the safety and robustness of a path planner and the path following controls based on reachable sets. We demonstrate the method on quadrotor and automobile applications. Secondly, we propose a reachable set based collision avoidance algorithm for UAVs. Instead of the traditional approaches of collision avoidance between trajectories, we propose a collision avoidance scheme based on reachable sets and tubes. We then formulate the problem as a convex optimization problem seeking control set design for the aircraft to avoid collision. We apply our approach to collision avoidance scenarios of quadrotors and fixed-wing aircraft. In the second aspect of our work, we address the high level planning problems with timed temporal logic constraints. Firstly, we present an optimization based method for path planning of a mobile robot subject to timed temporal constraints, in a dynamic environment. Temporal logic (TL) can address very complex task specifications such as safety, coverage, motion sequencing etc. We use metric temporal logic (MTL) to encode the task specifications with timing constraints. We then translate the MTL formulae into mixed integer linear constraints and solve the associated optimization problem using a mixed integer linear program solver. We have applied our approach on several case studies in complex dynamical environments subjected to timed temporal specifications. Secondly, we also present a timed automaton based method for planning under the given timed temporal logic specifications. We use metric interval temporal logic (MITL), a member of the MTL family, to represent the task specification, and provide a constructive way to generate a timed automaton and methods to look for accepting runs on the automaton to find an optimal motion (or path) sequence for the robot to complete the task.

TOPS (Task optimization in the presence of signal-dependent noise) model

This paper proposes a movement trajectory planning model, which is a maximum task achievement model in which signal-dependent noise is added to the movement command. In the proposed model, two optimization criteria are combined, maximum task achievement and minimum energy consumption. The proposed model has the feature that the end-point boundary conditions for position, velocity, and acceleration need not be prespecified. Consequently, the method can be applied not only to the simple point-to-point movement, but to any task. In the method in this paper, the hand trajectory is derived by a psychophysical experiment and a numerical experiment for the case in which the target is not stationary, but is a moving region. It is shown that the trajectory predicted from the minimum jerk model or the minimum torque change model differs considerably from the results of the psychophysical experiment. But the trajectory predicted from the maximum task achievement model shows good qualitative agreement with the hand trajectory obtained from the psychophysical experiment. © 2004 Wiley Periodicals, Inc.

一种空间飞行器编队重组的轨道优化方法

现有的空间飞行器编队重组的轨道规划方法在求解能量最优策略时,都预先给定了变轨花费的时间,但没有说明给定的时间是怎么选择的。将空间飞行器主从编队重组的轨道规划视为一个多目标优化问题,提出了一种小生境进化算法。该方法通过使用特定的染色体表示方法和进化算子,能有效的搜索到飞行器编队重组轨道规划问题的时间-能量前沿,并引入等值分享法保证优秀个体具有较大的选中概率和前沿的多样性。该方法能同时提供多种变轨方案,编队飞行的任务制定者从而可以根据实际应用情况选择最合适的方案。仿真结果表明了该方法的正确性。

一种基于进化计算的空间飞行器编队重构轨道规划方法

基于进化算法提出了一种两层结构的空间飞行器编队重构的轨道规划算法,高层算法通过优化构型映射来优化编队的总燃耗,实现全局规划并确保飞行器之间保持一定的安全距离以避免相互碰撞;低层规划算法采用Chebyshev多项式逼近控制变量空间,为每颗飞行器规划满足约束条件的最优轨道。该方法充分利用了编队的分布式结构,由各飞行器并行实现各自的轨道规划,能有效解决大型编队的轨道规划问题。仿真结果表明了该方法的有效性。

带燃料均衡的空间多飞行器编队重构的轨道规划方法

航天任务需求的多样化对空间多飞行器编队重构的轨道规划问题不仅提出了燃料或时间最优的要求,还提出了燃料和时间最优以及燃料均衡的要求。将带燃料均衡的多飞行器编队重构的轨道规划建模为一个多目标优化问题,通过将进化计算与问题领域的知识相结合,提出了一种基于小生境进化算法的最优轨道规划方法。该方法能从变轨时间、燃料消耗和燃料消耗方差三方面分别评价一个变轨方案的最优性,并且一次规划能够提供多个Pareto最优变轨方案。仿真结果证明了该方法的正确性和有效性,还揭示了编队重构轨道规划问题的三个优化目标之间的关系,对于制定任务计划具有重要的参考价值.