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

Dynamic whole-body motion generation under rigid contacts and other unilateral constraints

The most widely used technique for generating wholebody motions on a humanoid robot accounting for various tasks and constraints is inverse kinematics. Based on the task-function approach, this class of methods enables the coordination of robot movements to execute several tasks in parallel and account for the sensor feedback in real time, thanks to the low computation cost. To some extent, it also enables us to deal with some of the robot constraints (e.g., joint limits or visibility) and manage the quasi-static balance of the robot. In order to fully use the whole range of possible motions, this paper proposes extending the task-function approach to handle the full dynamics of the robot multibody along with any constraint written as equality or inequality of the state and control variables. The definition of multiple objectives is made possible by ordering them inside a strict hierarchy. Several models of contact with the environment can be implemented in the framework. We propose a reduced formulation of the multiple rigid planar contact that keeps a low computation cost. The efficiency of this approach is illustrated by presenting several multicontact dynamic motions in simulation and on the real HRP-2 robot

Contact aware robust semi-autonomous teleoperation of mobile manipulators

In the context of human-robot collaboration, cooperation and teaming, the use of mobile manipulators is widespread on applications involving unpredictable or hazardous environments for humans operators, like space operations, waste management and search and rescue on disaster scenarios. Applications where the manipulator's motion is controlled remotely by specialized operators. Teleoperation of manipulators is not a straightforward task, and in many practical cases represent a common source of failures. Common issues during the remote control of manipulators are: increasing control complexity with respect the mechanical degrees of freedom; inadequate or incomplete feedback to the user (i.e. limited visualization or knowledge of the environment); predefined motion directives may be incompatible with constraints or obstacles imposed by the environment. In the latter case, part of the manipulator may get trapped or blocked by some obstacle in the environment, failure that cannot be easily detected, isolated nor counteracted remotely. While control complexity can be reduced by the introduction of motion directives or by abstraction of the robot motion, the real-time constraint of the teleoperation task requires the transfer of the least possible amount of data over the system's network, thus limiting the number of physical sensors that can be used to model the environment. Therefore, it is of fundamental to define alternative perceptive strategies to accurately characterize different interaction with the environment without relying on specific sensory technologies. In this work, we present a novel approach for safe teleoperation, that takes advantage of model based proprioceptive measurement of the robot dynamics to robustly identify unexpected collisions or contact events with the environment. Each identified collision is translated on-the-fly into a set of local motion constraints, allowing the exploitation of the system redundancies for the computation of intelligent control laws for automatic reaction, without requiring human intervention and minimizing the disturbance of the task execution (or, equivalently, the operator efforts). More precisely, the described system consist in two different building blocks. The first, for detecting unexpected interactions with the environment (perceptive block). The second, for intelligent and autonomous reaction after the stimulus (control block). The perceptive block is responsible of the contact event identification. In short, the approach is based on the claim that a sensorless collision detection method for robot manipulators can be extended to the field of mobile manipulators, by embedding it within a statistical learning framework. The control deals with the intelligent and autonomous reaction after the contact or impact with the environment occurs, and consist on an motion abstraction controller with a prioritized set of constrains, where the highest priority correspond to the robot reconfiguration after a collision is detected; when all related dynamical effects have been compensated, the controller switch again to the basic control mode

Learning Utility Surfaces for Movement Selection

Humanoid robots are highly redundant systems with respect to the tasks they are asked to perform. This redundancy manifests itself in the number of degrees of freedom of the robot exceeding the dimensionality of the task. Traditionally this redundancy has been utilised through optimal control in the null-space. Some cost function is defined that encodes secondary movement goals and movements are optimised with respect to this functio

Probabilistic prioritization of movement primitives

Movement prioritization is a common approach to combine controllers of different tasks for redundant robots, where each task is assigned a priority. The priorities of the tasks are often hand-tuned or the result of an optimization, but seldomly learned from data. This paper combines Bayesian task prioritization with probabilistic movement primitives to prioritize full motion sequences that are learned from demonstrations. Probabilistic movement primitives (ProMPs) can encode distributions of movements over full motion sequences and provide control laws to exactly follow these distributions. The probabilistic formulation allows for a natural application of Bayesian task prioritization. We extend the ProMP controllers with an additional feedback component that accounts inaccuracies in following the distribution and allows for a more robust prioritization of primitives. We demonstrate how the task priorities can be obtained from imitation learning and how different primitives can be combined to solve even unseen task-combinations. Due to the prioritization, our approach can efficiently learn a combination of tasks without requiring individual models per task combination. Further, our approach can adapt an existing primitive library by prioritizing additional controllers, for example, for implementing obstacle avoidance. Hence, the need of retraining the whole library is avoided in many cases. We evaluate our approach on reaching movements under constraints with redundant simulated planar robots and two physical robot platforms, the humanoid robot “iCub” and a KUKA LWR robot arm

DETC2005-85166 A NEW METHODOLOGY FOR ROBOT CONTROLLER DESIGN

ABSTRACT Gauss' principle of least constraint and its generalizations have provided a useful insights for the development of trackin

Efficient resolution of potentially conflicting linear constraints in robotics

Submitted to IEEE TRO (05/August/2015)—A classical approach to handling potentially conflicting linear equality and inequality constraints in robotics is to impose a strict prioritization between them. Ensuring that the satisfaction of constraints with lower priority does not impact the satisfaction of constraints with higher priority is routinely done by solving a hierarchical least-squares problem. Such a task prioritization is often considered to be computationally demanding and, as a result, it is often approximated using a standard weighted least-squares problem. The main contribution of this article is to address this misconception and demonstrate, both in theory and in practice, that the hierarchical problem can in fact be solved faster than its weighted counterpart. The proposed approach to efficiently solving hierarchical least-squares problems is based on a novel matrix factorization, to be referred to as " lexicographic QR " , or ℓ-QR in short. We present numerical results based on three representative examples adopted from recent robotics literature which demonstrate that complex hierarchical problems can be tackled in real-time even with limited computational resources