arXiv subjects

Alexandr Klimchik

Publications and source records attributed to Alexandr Klimchik.

At least 19 recordsLinked to original sources

arXiv2025

MSA - Technique for Stiffness Modeling of Manipulators with Complex and Hybrid Structures

The paper presents a systematic approach for stiffness modeling of manipulators with complex and hybrid structures using matrix structural analysis. In contrast to previous results, it is suitable for mixed architectures containing closed-loops, flexible links, rigid connections, passive and elastic joints with external loadings and preloadings. The proposed approach produces the Cartesian stiffness matrices in a semi-analytical manner. It presents the manipulator stiffness model as a set of conventional equations describing the link elasticities that are supplemented by a set of constraints describing connections between links. Its allows user straightforward aggregation of stiffness model equations avoiding traditional column/row merging procedures in the extended stiffness matrix. Advantages of this approach are illustrated by stiffness analysis of NaVaRo manipulator.

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arXiv2025

A Real-Time Framework for Intermediate Map Construction and Kinematically Feasible Off-Road Planning Without OSM

Off-road environments present unique challenges for autonomous navigation due to their complex and unstructured nature. Traditional global path-planning methods, which typically aim to minimize path length and travel time, perform poorly on large-scale maps and fail to account for critical factors such as real-time performance, kinematic feasibility, and memory efficiency. This paper introduces a novel global path-planning method specifically designed for off-road environments, addressing these essential factors. The method begins by constructing an intermediate map within the pixel coordinate system, incorporating geographical features like off-road trails, waterways, restricted and passable areas, and trees. The planning problem is then divided into three sub-problems: graph-based path planning, kinematic feasibility checking, and path smoothing. This approach effectively meets real-time performance requirements while ensuring kinematic feasibility and efficient memory use. The method was tested in various off-road environments with large-scale maps up to several square kilometers in size, successfully identifying feasible paths in an average of 1.5 seconds and utilizing approximately 1.5GB of memory under extreme conditions. The proposed framework is versatile and applicable to a wide range of off-road autonomous navigation tasks, including search and rescue missions and agricultural operations.

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arXiv2025

On Kinodynamic Global Planning in a Simplicial Complex Environment: A Mixed Integer Approach

This work casts the kinodynamic planning problem for car-like vehicles as an optimization task to compute a minimum-time trajectory and its associated velocity profile, subject to boundary conditions on velocity, acceleration, and steering. The approach simultaneously optimizes both the spatial path and the sequence of acceleration and steering controls, ensuring continuous motion from a specified initial position and velocity to a target end position and velocity.The method analyzes the admissible control space and terrain to avoid local minima. The proposed method operates efficiently in simplicial complex environments, a preferred terrain representation for capturing intricate 3D landscapes. The problem is initially posed as a mixed-integer fractional program with quadratic constraints, which is then reformulated into a mixed-integer bilinear objective through a variable transformation and subsequently relaxed to a mixed-integer linear program using McCormick envelopes. Comparative simulations against planners such as MPPI and log-MPPI demonstrate that the proposed approach generates solutions 104 times faster while strictly adhering to the specified constraints

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arXiv2025

A Genetic Approach to Gradient-Free Kinodynamic Planning in Uneven Terrains

This paper proposes a genetic algorithm-based kinodynamic planning algorithm (GAKD) for car-like vehicles navigating uneven terrains modeled as triangular meshes. The algorithm's distinct feature is trajectory optimization over a fixed-length receding horizon using a genetic algorithm with heuristic-based mutation, ensuring the vehicle's controls remain within its valid operational range. By addressing challenges posed by uneven terrain meshes, such as changing face normals, GAKD offers a practical solution for path planning in complex environments. Comparative evaluations against Model Predictive Path Integral (MPPI) and log-MPPI methods show that GAKD achieves up to 20 percent improvement in traversability cost while maintaining comparable path length. These results demonstrate GAKD's potential in improving vehicle navigation on challenging terrains.

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arXiv2024

Resilient Timed Elastic Band Planner for Collision-Free Navigation in Unknown Environments

In autonomous navigation, trajectory replanning, refinement, and control command generation are essential for effective motion planning. This paper presents a resilient approach to trajectory replanning addressing scenarios where the initial planner's solution becomes infeasible. The proposed method incorporates a hybrid A* algorithm to generate feasible trajectories when the primary planner fails and applies a soft constraints-based smoothing technique to refine these trajectories, ensuring continuity, obstacle avoidance, and kinematic feasibility. Obstacle constraints are modelled using a dynamic Voronoi map to improve navigation through narrow passages. This approach enhances the consistency of trajectory planning, speeds up convergence, and meets real-time computational requirements. In environments with around 30\% or higher obstacle density, the ratio of free space before and after placing new obstacles, the Resilient Timed Elastic Band (RTEB) planner achieves approximately 20\% reduction in traverse distance, traverse time, and control effort compared to the Timed Elastic Band (TEB) planner and Nonlinear Model Predictive Control (NMPC) planner. These improvements demonstrate the RTEB planner's potential for application in field robotics, particularly in agricultural and industrial environments, where navigating unstructured terrain is crucial for ensuring efficiency and operational resilience.

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arXiv2023

Robust explicit model predictive control for hybrid linear systems with parameter uncertainties

Explicit model-predictive control (MPC) is a widely used control design method that employs optimization tools to find control policies offline; commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP in the case of hybrid systems. However, mixed-integer SDPs are computationally expensive, motivating alternative formulations, such as zonotope-based MPC (zonotopes are a special type of symmetric polytopes). In this paper, we propose a robust explicit MPC method applicable to hybrid systems. More precisely, we extend existing zonotope-based MPC methods to account for multiplicative parametric uncertainty. Additionally, we propose a convex zonotope order reduction method that takes advantage of the iterative structure of the zonotope propagation problem to promote diagonal blocks in the zonotope generators and lower the number of decision variables. Finally, we developed a quasi-time-free policy choice algorithm, allowing the system to start from any point on the trajectory and avoid chattering associated with discrete switching of linear control policies based on the current state's membership in state-space regions. Last but not least, we verify the validity of the proposed methods on two experimental setups, varying physical parameters between experiments.

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arXiv2023

Residual Dynamics Learning for Trajectory Tracking for Multi-rotor Aerial Vehicles

This paper presents a technique to cope with the gap between high-level planning, e.g., reference trajectory tracking, and low-level controlling using a learning-based method in the plan-based control paradigm. The technique improves the smoothness of maneuvering through cluttered environments, especially targeting low-speed velocity profiles. In such a profile, external aerodynamic effects that are applied on the quadrotor can be neglected. Hence, we used a simplified motion model to represent the motion of the quadrotor when formulating the Nonlinear Model Predictive Control (NMPC)-based local planner. However, the simplified motion model causes residual dynamics between the high-level planner and the low-level controller. The Sparse Gaussian Process Regression-based technique is proposed to reduce these residual dynamics. The proposed technique is compared with Data-Driven MPC. The comparison results yield that an augmented residual dynamics model-based planner helps to reduce the nominal model error by a factor of 2 on average. Further, we compared the proposed complete framework with four other approaches. The proposed approach outperformed the others in terms of tracking the reference trajectory without colliding with obstacles with less flight time without losing computational efficiency.

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arXiv2022

Motion Planning for Multirotor Aerial Vehicles in Plan-based Control Paradigm: a Review

In general, optimal motion planning can be performed both locally and globally. In such a planning, the choice in favour of either local or global planning technique mainly depends on whether the environmental conditions are dynamic or static. Hence, the most adequate choice is to use local planning or local planning alongside global planning. When designing optimal motion planning both local and global, the key metrics to bear in mind are execution time, asymptotic optimality, and quick reaction to dynamic obstacles. Such planning approaches can address the aforesaid target metrics more efficiently compared to other approaches such as path planning followed by smoothing. Thus, the foremost objective of this study is to analyse related literature in order to understand how the motion planning, especially trajectory planning, problem is formulated, when being applied for generating optimal trajectories in real-time for Multirotor Aerial Vehicles (MAVs), impacts the listed metrics. As a result of the research, the trajectory planning problem was broken down into a set of subproblems, and the lists of methods for addressing each of the problems were identified and described in detail. Subsequently, the most prominent results from 2010 to 2022 were summarized and presented in the form of a timeline.

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arXiv2022

Non-linear stiffness behavior of planar serial robotic manipulators

The paper focuses on the stiffness analysis of multi-link serial planar manipulators, which may demonstrate nonlinear stiffness behavior under the compressive loading. Two important cases are considered, where the manipulator has either a straight or non-straight initial configuration. It was proved that in the first case the loading may cause the buckling if it exceeds some critical value, and the manipulator suddenly changes its straight shape and stiffness properties. For computing this critical force, a general eigenvalue-based technique was proposed that can be applied to any multi-link serial manipulator. For the second case dealing with non-straight initial configurations, a universal energy-based technique was applied that allowed to detect quasi-buckling phenomenon when it is observed very fast but not instant change of the manipulator shape and its stiffness coefficient under the loading. These results are illustrated by numerous examples of non-linear stiffness behavior of three-and four-link manipulators that are subjected to compressive force.

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arXiv2022

Optimization-based Trajectory Tracking Approach for Multi-rotor Aerial Vehicles in Unknown Environments

The goal of this paper is to develop a continuous optimization-based refinement of the reference trajectory to 'push it out' of the obstacle-occupied space in the global phase for Multi-rotor Aerial Vehicles in unknown environments. Our proposed approach comprises two planners: a global planner and a local planner. The global planner refines the initial reference trajectory when the trajectory goes either through an obstacle or near an obstacle and lets the local planner calculate a near-optimal control policy. The global planner comprises two convex programming approaches: the first one helps to refine the reference trajectory, and the second one helps to recover the reference trajectory if the first approach fails to refine. The global planner mainly focuses on real-time performance and obstacles avoidance, whereas the proposed formulation of the constrained nonlinear model predictive control-based local planner ensures safety, dynamic feasibility, and the reference trajectory tracking accuracy for low-speed maneuvers, provided that local and global planners have mean computation times 0.06s (15Hz) and 0.05s (20Hz), respectively, on an NVIDIA Jetson Xavier NX computer. The results of our experiment confirmed that, in cluttered environments, the proposed approach outperformed three other approaches: sampling-based pathfinding followed by trajectory generation, a local planner, and graph-based pathfinding followed by trajectory generation.

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arXiv2021

Kinematic Control of compliant serial manipulators composed of dual-triangles

The paper focuses on the kinematics control of a compliant serial manipulator composed of a new type of dualtriangle elastic segments. Some useful optimization techniques were applied to solve the geometric redundancy problem, ensure the stability of the manipulator configurations with respect to the external forces/torques applied to the endeffector. The efficiency of the developed control algorisms is confirmed by simulation.

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arXiv2020

Mechanics of compliant serial manipulator composed of dual-triangle segments

The paper focuses on the mechanics of a compliant serial manipulator composed of new type of dual-triangle elastic segments. Both the analytical and numerical methods were used to find the manipulator stable and unstable equilibrium configurations, as well as to predict corresponding manipulator shapes. The stiffness analysis was carried on for both loaded and unloaded modes, the stiffness matrices were computed using the Virtual Joint Method (VJM). The results demonstrate that either buckling or quasi-buckling phenomenon may occur under the loading, if the manipulator corresponding initial configuration is straight or non-straight one. Relevant simulation results are presented that confirm the theoretical study.

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arXiv2020

Path Planning Followed by Kinodynamic Smoothing for Multirotor Aerial Vehicles (MAVs)

We explore path planning followed by kinodynamic smoothing while ensuring the vehicle dynamics feasibility for MAVs. We have chosen a geometrically based motion planning technique \textquotedblleft RRT*\textquotedblright\; for this purpose. In the proposed technique, we modified original RRT* introducing an adaptive search space and a steering function which help to increase the consistency of the planner. Moreover, we propose multiple RRT* which generates a set of desired paths, provided that the optimal path is selected among them. Then, apply kinodynamic smoothing, which will result in dynamically feasible as well as obstacle-free path. Thereafter, a b spline-based trajectory is generated to maneuver vehicle autonomously in unknown environments. Finally, we have tested the proposed technique in various simulated environments.

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arXiv2020

Real-Time Long Range Trajectory Replanning for MAVs in the Presence of Dynamic Obstacles

Real-time long-range local planning is a challenging task, especially in the presence of dynamics obstacles. We propose a complete system which is capable of performing the local replanning in real-time. Desired trajectory is needed in the system initialization phase; system starts initializing sub-components of the system including point cloud processor, trajectory estimator and planner. Afterwards, the multi-rotary aerial vehicle starts moving on the given trajectory. When it detects obstacles, it replans the trajectory from the current pose to pre-defined distance incorporating the desired trajectory. Point cloud processor is employed to identify the closest obstacles around the vehicle. For replanning, Rapidly-exploring Random Trees (RRT*) is used with two modifications which allow planning the trajectory in milliseconds scales. Once we replanned the desired path, velocity components(x,y and z) and yaw rate are calculated. Those values are sent to the controller at a constant frequency to maneuver the vehicle autonomously. Finally, we have evaluated each of the components separately and tested the complete system in the simulated and real environments.

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arXiv2019

Regions of Interest Segmentation from LiDAR Point Cloud for Multirotor Aerial Vehicles

We propose a novel filter for segmenting the regions of interest from LiDAR 3D point cloud for multirotor aerial vehicles. It is specially targeted for real-time applications and works on sparse LiDAR point clouds without preliminary mapping. We use this filter as a crucial component of fast obstacle avoidance system for agriculture drone operating at low altitude. As the first step, each point cloud is transformed into a depth image and then identify places near to the vehicle (local maxima) by locating areas with high pixel densities. Afterwards, we merge the original depth image with identified locations after maximizing intensities of pixels in which local maxima were obtained. Next step is to calculate the range angle image that represents angles between two consecutive laser beams based on the improved depth image. Once the corresponding range angle image is constructed, smoothing is applied to reduce the noise. Finally, we find out connected components within the improved depth image while incorporating smoothed range angle image. This allows separating the regions of interest. The filter has been tested on various simulated environments as well as an actual drone and provides real-time performance. We make our source code, dataset available at https://github.com/GPrathap/hagen.git and real world experiment result can be found on the following link: https://www.youtube.com/watch?v=iHd_ZkhKPjc available online.

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arXiv2018

Advancement of MSA-technique for stiffness modeling of serial and parallel robotic manipulators

The paper presents advancement of the matrix structural analysis technique (MSA) for stiffness modeling of robotic manipulators. In contrast to the classical MSA, it can be applied to both parallel and serial manipulators composed of flexible and rigid links connected by rigid, passive or elastic joints with multiple external loadings. The manipulator stiffness model is presented as a set of basic equations describing the link elasticities that are supplemented by a set of constraints describing connections between links. These equations are aggregated straightforwardly in a common linear system without traditional merging of the matrix rows and columns, which allows avoiding conventional manual transformations at the expense of numerical inversion of the sparse matrix of higher dimension.

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arXiv2014

Compliance error compensation in robotic-based milling

The paper deals with the problem of compliance errors compensation in robotic-based milling. Contrary to previous works that assume that the forces/torques generated by the manufacturing process are constant, the interaction between the milling tool and the workpiece is modeled in details. It takes into account the tool geometry, the number of teeth, the feed rate, the spindle rotation speed and the properties of the material to be processed. Due to high level of the disturbing forces/torques, the developed compensation technique is based on the non-linear stiffness model that allows us to modify the target trajectory taking into account nonlinearities and to avoid the chattering effect. Illustrative example is presented that deals with robotic-based milling of aluminum alloy.

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arXiv2014

Accuracy Improvement of Robot-Based Milling Using an Enhanced Manipulator Model

The paper is devoted to the accuracy improvement of robot-based milling by using an enhanced manipulator model that takes into account both geometric and elastostatic factors. Particular attention is paid to the model parameters identification accuracy. In contrast to other works, the proposed approach takes into account impact of the gravity compensator and link weights on the manipulator elastostatic properties. In order to improve the identification accuracy, the industry oriented performance measure is used to define optimal measurement configurations and an enhanced partial pose measurement method is applied for the identification of the model parameters. The advantages of the developed approach are confirmed by experimental results that deal with the elastostatic calibration of a heavy industrial robot used for milling. The achieved accuracy improvement factor is about 2.4.

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