Trajectory Optimization of Continuum arm robots

This study proposes an innovative algorithm integrating kinematic modeling and intelligent optimization to address the motion planning of multi-segment cable-driven continuum manipulator. Under the piecewise constant curvature (PCC) hypothesis, a forward kinematic framework is formulated to define a structured mapping between joint-space parameters and task-space coordinates. Leveraging the established model, a refined APF strategy is implemented to synthesize collisionavoidance paths for the manipulator, while the Jacobian pseudo-inverse method is applied to obtain corresponding general joint angle solutions. Moreover, to enhance optimization efficiency, the initial population is generated by leveraging the least-squares solution as a baseline, with search boundaries dynamically defined through the null-space properties of the Jacobian pseudoinverse. Then the trajectory optimization is executed under dual constraints of end-effector pose and arm shape via the cheetah optimizer (CO). Numerical simulations validate the algorithm's capability to maintain trajectory tracking accuracy while accounting for end-effector pose, providing an effective solution for motion planning of multi-segment continuum manipulators.

The polyhedron model is a powerful model to identify and apply systematically loop transformations that improve data locality (e.g., via tiling) and enable parallelization. In the polyhedron model, a loop transformation is, essentially, represented as an affine function. Well-established algorithms for the discovery of promising transformations are based on performance models. These algorithms have the drawback of not being easily adaptable to the characteristics of a specific program or target hardware. An iterative search for promising loop transformations is more easily adaptable and can help to learn better models. We present an iterative optimization method in the polyhedron model that targets tiling and parallelization. The method enables either a sampling of the search space of legal loop transformations at random or a more directed search via a genetic algorithm. For the latter, we propose a set of novel, tailored reproduction operators. We evaluate our approach against existing iterative and model-driven optimization strategies. We compare the convergence rate of our genetic algorithm to that of random exploration. Our approach of iterative optimization outperforms existing optimization techniques in that it finds loop transformations that yield significantly higher performance. If well configured, then random exploration turns out to be very effective and reduces the need for a genetic algorithm.

This paper considers the problem of multi robot localization. The analysis is focused on the problem of determining which are the optimal robot trajectories in order to minimize the localization error at the final robot configurations. Furthermore, the analysis takes into account several constraints expressing the maximum robot energy consumption. The problem is formulated as an optimal control problem. For the special case of holonomic vehicles, an analytical solution is derived. In particular, this solution satisfies second order differential equations. The trajectories corresponding to this optimal control are plotted for different initial and final robot configurations and for several values of the system parameters (characterizing the precision of the robot sensors and the values of the constraints). Extensive simulations validate the derived analytical results.

Unmanned Aerial Vehicles (UAVs), in multi-UAV collaborative search systems, need to realize adaptive autonomous trajectory planning based on their own state and surrounding environmental conditions. To allow for a fast trajectory planning of multiple UAVs from the current state to the target state, this paper proposes a trajectory planning method for multi-UAV collaborative search tasks based on genetic algorithm (GA). And using genetic algorithm, the UAV's trajectory can be optimized online based on the current mission. Through the analysis of the tasks of the multi-UAV collaborative decision-making part and the autonomous trajectory planning part, the genetic algorithm is used to model and optimize the trajectory planning problem to obtain a feasible and efficient optimal search trajectory from the current state to the decision-making target state. Finally, through specific simulation experiments, the optimal trajectory from the current state to the target state of the UAV i in the multi-UAV system is obtained, which verifies the effectiveness of the algorithm.

We investigate energy-optimal control of robots with ultracapacitor based regenerative drive systems. Based on a previously introduced framework, a fairly generic model is considered for the robot and the drive system. An optimal control problem is formulated to find point-to point trajectories maximizing the amount of energy regenerated and stored in the capacitor. The optimization problem, its numerical solution and an experimental evaluation are demonstrated using a PUMA 560 manipulator. A comprehensive experimental setup was prepared to evaluate power flows and energy regeneration. Tracking of optimal trajectories was enforced on the robot using a standard robust passivity based control approach. Experimental results show that when following optimal trajectories, a reduction of about 13\% in energy consumption can be achieved for the conditions of the study.

The design of reinforced concrete (RC) structures involves several kinds of uncertainties, which are usually considered through the partial safety factors prescribed in the codes of practice. The traditional design optimization of RC structures uses deterministic information of the problem. The partial safety factors are used to consider loading fluctuation and the variability of material properties. The use of these safety factors in deterministic optimization usually leads to over-designing structures, as these safety factors are calibrated for a large class of structures. In the deterministic optimization procedure the reliability cannot be controlled. For this reason, the Reliability-Based Design Optimization (RBDO) is devoted to design economical and reliable structures. However, the RBDO problem involves the evaluation of probabilistic constraints performed by the reliability analysis. The most common RBDO formulations are based on a nested optimization problem, with an outer loop for the design optimization and an inner loop for the reliability analysis. Therefore, an expensive computation effort is required to solve the RBDO problem. In this paper, a new RBDO method of RC structures is proposed. The RBDO problem is decomposed to several cycles of deterministic design optimization (DDO) based on new safety factors called Optimal System Safety Factors (OSSF). At each cycle of the DDO, the system reliability analysis is performed to verify the reliability of the optimal design, the OSSF are computed by a probabilistic method on the basis of the previous system reliability analysis, then the updated OSSF are provided for the next cycle of the DDO. The application to the design of an RC structure shows the interest and the efficiency of the proposed method.

Due to the space constraints and obstacles, the traditional industrial manipulator is too difficult to achieve some tasks, such as the gluing for the wing bulkhead of the aircraft and the maintenance for cooling pipes of the nuclear power plant, etc. Continuum manipulator, inspired by the trunk and the tentacle, proves to be very effective for above-mentioned tasks. A novel octopus-like biomimetic robots, is proposed in this paper, which is consisting of continuum joints and discrete joints, and provide a host of benefits, such as the large space of movement, the high flexibility and the heavy load. A novel analytical approach for solving kinematics of the octopus-like arm manipulator with mixed joints is presented in this paper. Based on the bionic mechanism of the continuum manipulator constructed from mixed joints, the robot configuration is established. In this paper, we present a detailed formulation and explanation of a novel kinematic model for the continuum robots with mixed joints. The modeling method based on the Denavit–Hartenberg parameters(also called DH parameters) is used to depict the motion of robot. The robot is comprised of the continuum joint and the rotated joint, so the kinematic model of continuum joint is crucial for constructing that of the whole robot. The continuum joint is equivalent to a section of elastic body, whose D-H parametors can be obtain from the constant-curvature method. Then the forward kinematics of the whole robot can be builded in a D-H frame. Research results will create a new modeling method for the octopus-like continuum manipulators with mixed joints, which can give a new approach for the design on the biomimetic manipulators operating in the unstructured envirement.

The traditional method of designing the initial configuration of off-axis reflective optical system is to first obtain the initial configuration of coaxial reflective optical system, and then achieve the unobscured design with an offset aperture stop or a biased input field, or both. Because the aberration distribution of coaxial reflective optical system is not applicable to the off-axis reflective optical system, the obtained unobscured off-axis reflective optical system has large aberration, and the unobscured design process is complicated. In this paper we present a method of designing an initial configuration of off-axis reflective optical system based on vector aberration theory. With this design method, a good unobscured initial configuration of off-axis reflective optical system can be directly obtained by using an offset aperture stop or a biased input field, or both. Based on the vector aberration theory and gaussian brackets, the third-order aberration coefficient is derived for off-axis reflective optical system. Initial configuration performance is important for optical design, especially for the complicated optical system design. The selection of initial configuration highly affects the final system imaging performance, fabrication difficulty and alignment difficulty. An error function is established to evaluate the performance of off-axis reflective optical system, and it consists of aberration coefficients and other constraints. The genetic algorithm is a highly parallel, random and adaptive global optimization algorithm. To obtain a good initial configuration for the off-axis reflective optical system, the genetic algorithm is used to search for the initial configuration with minimum residual aberration. This method can obtain a good initial configuration of off-axis reflective optical system for further optimization. The benefit of this design method is demonstrated by designing an off-axis three-mirror optical system. For the focal plane array, a long-wave infrared off-axis three-mirror optical system is designed. A good initial configuration is obtained with the proposed method, which achieves the unobscured design by using an offset aperture stop and a biased input field. To improve the performance of initial configuration, the obtained initial configuration is optimized with the optical design software. The designed optical system has good imaging quality. As the mirrors are free from the tilts and decenters, the designed optical system is aligned easily.

This paper addresses the challenge of simultaneously satisfying collision-free trajectory, path quality optimization, and execution time optimization in trajectory planning for industrial robots in confined spaces. A multi-objective integrated trajectory optimization algorithm is proposed based on the TD3 reinforcement learning framework. Firstly, the motion generation mechanism is improved using a Butterworth filter and a dynamic noise attenuation strategy to enhance trajectory smoothness. Secondly, a genetic algorithm is employed to automatically optimize the hyperparameters of the TD3 algorithm, and a prioritized experience replay mechanism is introduced to improve the utilization efficiency of critical experiences, thereby enhancing the algorithm's convergence speed and stability. Finally, a composite reward function based on time-distance information is designed to effectively guide the industrial robot in optimizing trajectory execution time under collision-free conditions. This paper uses the Fairino Robot5 robotic arm model as the training object and conducts simulation experiments in a PyBullet environment, as well as real physical experiments. Compared to the RRT method, manual teaching method, traditional TD3 method, and SAC method, the actual trajectory execution time was reduced by 57.03% , 22.94% , 26.05%, and 20.5%, respectively.

Considering that some tasks will require the consistency of the position and attitude of the end-effector, multi-space-robot cooperative capture also needs to consider the synchronization of the two capture arms. Taking the dual-space robots as example, the trajectory planning problem before cooperative capture is focused. First, a drive-transform method based on trapezoidal velocity interpolation is proposed, which combines the advantages of these two methods to obtain the SE(3) motion trajectory, in which the attitude and position are planned synchronously. Then, the trajectory optimization model of cooperative capture is established, which takes the optimal time and the minimum attitude disturbance of the base as the optimization goals, and simultaneously satisfies that the two capture arms reach the capture point synchronously. In order to solve this multi-objective optimization problem, a dual-population multi-objective fruit fly algorithm based on non-dominated sorting was proposed. Finally, the simulation example of dual-space robots shows that the proposed algorithm is effective, and the analysis of the optimal solution set demonstrates that the optimized cooperative capture trajectory is smooth and synchronous.

Future space exploration missions will require the development of more advanced in‐space radiators. These radiators should be highly efficient and lightweight, deployable heat rejection systems. Typical radiators for in‐space heat mitigation commonly comprise a substantial portion of the total vehicle mass. A small mass savings of even 5–10% can greatly improve vehicle performance. The objective of this paper is to present the development of detailed tools for the analysis and design of in‐space radiators using evolutionary computation techniques. The optimality criterion is defined as a two‐dimensional radiator with a shape demonstrating the smallest mass for the greatest overall heat transfer, thus the end result is a set of highly functional radiator designs. This cross‐disciplinary work combines shape optimization and thermal analysis design by means of a genetic algorithm. The proposed design tool consists of the following steps; design parameterization based on the exterior boundary of the radiator, objective function definition (mass minimization and heat loss maximization), objective function evaluation via finite element analysis (thermal radiation analysis) and optimization based on evolutionary algorithms. The radiator design problem is defined as follows: the input force is a driving temperature and the output reaction is heat loss. Appropriate modeling of the space environment is added to capture its effect on the radiator. The design parameters chosen for this radiator shape optimization problem fall into two classes, variable height along the width of the radiator and a spline curve defining the material boundary of the radiator. The implementation of multiple design parameter schemes allows the user to have more confidence in the radiator optimization tool upon demonstration of convergence between the two design parameter schemes. This tool easily allows the user to manipulate the driving temperature regions thus permitting detailed design of in‐space radiators for unique situations. Preliminary results indicate an optimized shape following that of the temperature distribution regions in the “cooler” portions of the radiator. The results closely follow the expected radiator shape.

The global warming and the environmental destruction are caused from the mass consumption of energy in a factory in which robotic manipulators are used. It is necessary to take the trajectory planning into considerations in order to save the consumption energy of the manipulator controlled with Point-to-Point (PTP) motion. An optimal trajectory that minimizes the consumption energy can be obtained by solving a two-point boundary value problem. The optimal trajectory can be analyzed easily if the system is linear. However, the dynamical equation of the multi-link manipulator with Coulomb friction has a strong non-linearity. Then the Genetic Algorithm (GA) is applied to obtain the solution of two-point boundary value problem with the strong non-linearity. The GA is the method for searching discrete solution space by genes. However, the trajectory function is continuous with respect to time. In this paper, the coefficients of the approximation functions are determined as the gene’s phenotype. This method has disadvantages that are long computation time and increase the possibility of lapsing into the local optimal solution. So, a new method is proposed in order to shorten the computation time and to lessen the possibility of lapsing into the local optimal solution. It is seen from application to the minimization of the consumption energy of a manipulator with Coulomb friction that a proposed method is effective.

Flow-force relationships during energy transfer between mitochondrial proton pumps

A method for a time optimal collision free trajectory planning problem is proposed. In this paper, the dynamics of manipulator and obstacles are considered. This type of optimal trajectory planning problem is very difficult and complicated one because of the nonlinearity of manipulator dynamics and existence of obstacles. Generally, it results in a multimodal optimization problem. The proposed method is basically an iteratively improving one based on a gradient method. Firstly, two global methods (a genetic algorithm or an exact cell decomposition method) are used to search multiple initial feasible spatial paths for the gradient method. Next, the gradient method searches the time optimal solution locally with the multiple initial feasible solutions. Simulation results show that this is an effective approach to the time optimal collision free trajectory planning problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Trajectory optimization is a fundamental stochastic optimal control (SOC) problem. This article deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic models. Exact/complete solutions to these kind of control problems have been deemed analytically intractable in literature because they come under the category of partially observable Markov decision processes (MDPs). Therefore, effective solutions with reasonable approximations are widely sought for. We propose a reformulation of stochastic control in a reinforcement learning setting. This type of formulation assimilates the benefits of conventional optimal control procedure, with the advantages of maximum likelihood approaches. Finally, an iterative trajectory optimization paradigm called as SOC-expectation maximization (SOC-EM) is put forth. This trajectory optimization procedure exhibits better performance in terms of reduction in cumulative cost-to-go which is proven both theoretically and empirically. Furthermore, we also provide novel theoretical work which is related to uniqueness of control parameter estimates. Analysis of the control covariance matrix is presented, which handles stochasticity through efficiently balancing exploration and exploitation.