Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Effluent limits, ambient quality, and monitoring

Effluent limits are frequently based on a uniform emission standard, which applies to all polluting facilities within in a single industry. However, the implementation of many environmental protection laws does not lead to uniform effluent limits due to considerations of local environmental conditions. In this paper, we theoretically examine the relationships among the stringency of effluent limits imposed on individual polluting facilities, environmental protection agencies’ monitoring decisions, and the ambient quality of the local environment. We then extend the theoretical analysis by exploring the establishment of effluent limits when (1) the national emission standard represents only an upper bound on the local issuance of limits and (2) negotiation efforts expended by both regulated polluting facilities and environmentally concerned citizens play a role. We find that the negotiated discharge limit depends on the political weight enjoyed and the negotiation effort costs faced by both citizens and the regulated facility, along with the stringency of the national standard and local ambient quality condition

COCrIP: Compliant OmniCrawler In-pipeline Robot

This paper presents a modular in-pipeline climbing robot with a novel compliant foldable OmniCrawler mechanism. The circular cross-section of the OmniCrawler module enables a holonomic motion to facilitate the alignment of the robot in the direction of bends. Additionally, the crawler mechanism provides a fair amount of traction, even on slippery surfaces. These advantages of crawler modules have been further supplemented by incorporating active compliance in the module itself which helps to negotiate sharp bends in small diameter pipes. The robot has a series of 3 such compliant foldable modules interconnected by the links via passive joints. For the desirable pipe diameter and curvature of the bends, the spring stiffness value for each passive joint is determined by formulating a constrained optimization problem using the quasi-static model of the robot. Moreover, a minimum friction coefficient value between the module-pipe surface which can be vertically climbed by the robot without slipping is estimated. The numerical simulation results have further been validated by experiments on real robot prototype

Robotic control of the seven-degree-of-freedom NASA laboratory telerobotic manipulator

A computationally efficient robotic control scheme for the NASA Laboratory Telerobotic Manipulator (LTM) is presented. This scheme utilizes the redundancy of the seven-degree-of-freedom LTM to avoid joint limits and singularities. An analysis to determine singular configurations is presented. Performance criteria are determined based on the joint limits and singularity analysis. The control scheme is developed in the framework of resolved rate control using the gradient projection method, and it does not require the generalized inverse of the Jacobian. An efficient formulation for determining the joint velocities of the LTM is obtained. This control scheme is well suited for real-time implementation, which is essential if the end-effector trajectory is continuously modified based on sensory feedback. Implementation of this scheme on a Motorola 68020 VME bus-based controller of the LTM is in progress. Simulation results demonstrating the redundancy utilization in the robotic mode are presented

Multidisciplinary systems optimization by linear decomposition

In a typical design process major decisions are made sequentially. An illustrated example is given for an aircraft design in which the aerodynamic shape is usually decided first, then the airframe is sized for strength and so forth. An analogous sequence could be laid out for any other major industrial product, for instance, a ship. The loops in the discipline boxes symbolize iterative design improvements carried out within the confines of a single engineering discipline, or subsystem. The loops spanning several boxes depict multidisciplinary design improvement iterations. Omitted for graphical simplicity is parallelism of the disciplinary subtasks. The parallelism is important in order to develop a broad workfront necessary to shorten the design time. If all the intradisciplinary and interdisciplinary iterations were carried out to convergence, the process could yield a numerically optimal design. However, it usually stops short of that because of time and money limitations. This is especially true for the interdisciplinary iterations