An Analytical Method for Sensitivity Analysis of Rigid Multibody System Dynamics Using Projective Geometric Algebra

Motion planning of robots based on the Markov decision process (MDP) is now one of the most important topics of robotics research. In motion planning of robots by the MDP, an efficient way to divide robot motion is essential because discrete expressions of states and transitions are used in the calculation. In preparing the discrete expressions of robot motion, it is important that the motion follows the MDP, second, that the time and the amount of memory for the planning calculation are reduced, and that the maneuverability and smoothness of the robot motion are not lost. This paper proposes a new discrete expression of robot motion that can meet these requirements considering the effect of robot dynamics to robot kinematics. The method uses a continuous-time continuous-variable neuron model, which has the stimulation and adaptation properties. The performance of the proposed method was examined by simulation of the motion planning of an under actuated underwater robot and under actuated manipulator with a free joint. The results show the high reliability and flexibility of the method.

Dynamics and motion planning of a wheel-legged robot with two manipulator arms is discussed in this paper. This robot can move on flat surfaces fast, while it has the capability of moving over rough terrains. The two locomotion subsystems, i.e. wheeled mechanism and legged mechanism, will be discussed separately. Wheeled locomotion mechanism includes three wheels, two of them are in the back as active wheels with a differential driver. Legged locomotion mechanism includes two legs each with 4 revolute joints, i.e. 4 degrees of freedom (DOF). Two manipulators are installed on the main body to perform variant tasks, each of them is a PRR 3 DOF arm. Using direct path method (DPM) the robot kinematics is developed, and using Lagrangian approach the equations of motion are derived. A new method, called return path method (RPM), is proposed to add the constraints of the system to the kinetics equations without introducing additional variables. To eliminate the terms corresponding to the constraints, natural orthogonal complement method is used. Finally, motion planning of the robot is investigated to develop a stable gait planning procedure.

Whole-body motion and footstep planning for humanoid robots with multi-heuristic search

This paper deals with motion planning and control for mobile robots. The various components of an integrated architecture for the mobile robot Hilare pulling a trailer are presented. The nonholonomic path planner is based on an original steering method accounting for the small-time controllability of the system. Then the path is transformed into a trajectory by including the dynamical constraints of the system (bounded velocity and bounded acceleration). Finally, the motion control is addressed. Due to the geometric transformation for a virtual robot, we show how to reduce the problem to a classical approach of trajectory tracking for a mobile robot moving forward only. The experimental results presented include two types of robot-trailer connection systems.

This chapter contains sections titled: Introduction Motion Planning Implicit Methods Explicit Methods Optimal Control and Variational Approaches Modeling Errors and Uncertainty Concluding Remarks References

This paper presents a fuzzy-flatness technique for the efficient manipulation of mobile robots with nonholonomic constraints. A decoupled “path trajectory” planning approach is firstly defined to ensure the generation of reference trajectories that respect the nonholonomic constraints. An auto-tuned endogenous feedback control law is then designed to ensure good tracking of the desired tasks despite uncertainties. The controller gains are adjusted online by using a suitable fuzzy controller. Based on the developed algorithm and the laboratory test prototype Pioneer-3dx, numerical tests were carried out to evaluate the performances of the proposed approach.

This paper presents a hybrid approach that integrates trajectory optimization (TO) and reinforcement learning (RL) for motion planning and control of free-flying multi-arm robots in on-orbit servicing scenarios. The proposed system integrates TO for generating feasible, efficient paths while accounting for dynamic and kinematic constraints, and RL for adaptive trajectory tracking under uncertainties. The multi-arm robot design, equipped with thrusters for precise body control, enables redundancy and stability in complex space operations. TO optimizes arm motions and thruster forces, reducing reliance on the arms for stabilization and enhancing maneuverability. RL further refines this by leveraging model-free control to adapt to dynamic interactions and disturbances. The experimental results validated through comprehensive simulations demonstrate the effectiveness and robustness of the proposed hybrid approach. Two case studies are explored: surface motion with initial contact and a free-floating scenario requiring surface approximation. In both cases, the hybrid method outperforms traditional strategies. In particular, the thrusters notably enhance motion smoothness, safety, and operational efficiency. The RL policy effectively tracks TO-generated trajectories, handling high-dimensional action spaces and dynamic mismatches. This integration of TO and RL combines the strengths of precise, task-specific planning with robust adaptability, ensuring high performance in the uncertain and dynamic conditions characteristic of space environments. By addressing challenges such as motion coupling, environmental disturbances, and dynamic control requirements, this framework establishes a strong foundation for advancing the autonomy and effectiveness of space robotic systems.

A novel vector-field-based motion planning algorithm for 3D nonholonomic robots

Motion planning and control issue of quadruped robots is a challenging topic because it requires a lot of professional knowledge and tedious manual design based on traditional control methods. This paper proposes a novel method of training quadruped robots to generate locomotion gaits by combining the deep reinforcement learning. The control problem of quadruped robots is modeled as a Markov Decision Process, and a universal quadruped robot motion control reward mechanism is developed. A variety of gaits for the quadruped robot is generated by adding a gait reference frame. Two deep reinforcement learning algorithms are used for training and comparison. The desired gait locomotion control strategy is generated through training so that the robot can realize stable walking with the desired gait. Finally, the proposed method is tested and evaluated in a simulation environment using the A1 quadruped robot model.

As robotic systems evolve and get more sophisticated, expectations of them to accomplish high-level tasks increase gradually and their motion planning becomes more complex and difficult. The motion planning problem has been studied for more than four decades from different aspects such that presently has a vast literature. This paper investigates different components of the robot motion planning (RMP) problem and presents a new comprehensive taxonomy for a wide range of RMP problems. The taxonomy is based on a survey of the literature on RMP problems and applications in robotics and computer science.

The need for combined task and motion planning (CTAMP) in robotics is well known as robotic technologies become more mature. The goal of CTAMP is to determine a proper sequence of a robot’s actions based on symbolic and geometric reasoning. Because of the fundamental difference in symbolic and geometric reasoning, a CTAMP system often requires an interface module between the two reasoning modules. We propose a CTAMP system in which a symbolic action sequence is generated in task planning, and each action is verified geometrically in motion planning using the off-the-shelf planners and reasoners. The approach is that a set of action models is defined with PDDL in the interface module (action library) and the required information to each planner is automatically provided by the interface module. The proposed method was successfully implemented in three simulated experiments that involve manipulation tasks. According to our findings, the proposed method is effective in responding to changes in the environment and uncertainty with errors in recognition of the environment and the robot motion control.

In this paper, different research trends that use symbolic techniques for robot motion planning and control are illustrated. As it often happens in new research areas, contributions to this topic started at about the same time by different groups with different emphasis, approaches, and notation. This article tries to describe a framework in which many of the current methods and ideas can be placed and to provide a coherent picture of what the authors want to do, what have they got so far, and what the main missing pieces are. Generally speaking, the aim of symbolic control as is envisioned in this article is to enable the usage of methods of formal logic, languages, and automata theory for solving effectively complex planning problems for robots and teams of robots. The results presented in this article can be divided in two groups: top-down approaches, whereby formal logic tools are employed on rather abstract models of robots; and bottom up approaches, whose aim is to provide means by which such abstractions are possible and effective. The two ends do not quite tie as yet, and much work remains to be done in both directions to obtain generally applicable methods. However, the prospects of symbolic control of robots are definitely promising, and the challenging nature of problems to be solved warrants for the interest of a wide community of researchers

This study is devoted to the challenges of motion planning for mobile robots with smart machine vision systems. Motion planning for mobile robots in the environment with obstacles is a problem to deal with when creating robots suitable for operation in real-world conditions. The solutions found today are predominantly private, and are highly specialized, which prevents judging of how successful they are in solving the problem of effective motion planning. The purpose of this study: develop and investigate a motion planning algorithm for a mobile robot with a smart machine vision system. The research subject for this article is a motion planning algorithm for a mobile robot with a smart machine vision system. This study provides a review of domestic and foreign mobile robots that solve the motion planning problem in a known environment with unknown obstacles. The following navigation methods are considered for mobile robots: local, global, individual. In the course of work and research, a mobile robot prototype has been built, capable of recognizing obstacles of regular geometric shapes, as well as plan and correct the movement path. Environment objects are identified and classified as obstacles by means of digital image processing methods and algorithms. Distance to the obstacle and relative angle are calculated by photogrammetry methods, image quality is improved by linear contrast enhancement and optimal linear filtering using the Wiener-Hopf equation. Virtual tools, related to mobile robot motion algorithm testing, have been reviewed, which led us to selecting Webots software package for prototype testing. Conclusions have been drawn regarding the concluded research.

This study is devoted to the challenges of motion planning for mobile robots with smart machine vision systems. Motion planning for mobile robots in the environment with obstacles is a problem to deal with when creating robots suitable for operation in real-world conditions. The solutions found today are predominantly private, and are highly specialized, which prevents judging of how successful they are in solving the problem of effective motion planning. Solutions with a narrow application field already exist and are being already developed for a long time, however, no major breakthrough has been observed yet. Only a systematic improvement in the characteristics of such systems can be noted. The purpose of this study: develop and investigate a motion planning algorithm for a mobile robot with a smart machine vision system. The research subject for this article is a motion planning algorithm for a mobile robot with a smart machine vision system. This study provides a review of domestic and foreign mobile robots that solve the motion planning problem in a known environment with unknown obstacles. The following navigation methods are considered for mobile robots: local, global, individual. In the course of work and research, a mobile robot prototype has been built, capable of recognizing obstacles of regular geometric shapes, as well as plan and correct the movement path. Environment objects are identified and classified as obstacles by means of digital image processing methods and algorithms. Distance to the obstacle and relative angle are calculated by photogrammetry methods, image quality is improved by linear contrast enhancement and optimal linear filtering using the Wiener-Hopf equation. Virtual tools, related to mobile robot motion algorithm testing, have been reviewed, which led us to selecting Webots software package for prototype testing. Testing results allowed us to make the following conclusions. The mobile robot has successfully identified the obstacle, planned a path in accordance with the obstacle avoidance algorithm, and continued moving to the destination. Conclusions have been drawn regarding the concluded research.

This work presents a novel architecture that unifies footstep planning, motion planning, and online feedback control for legged robots moving through complex environments. Our approach contrasts related prior works that treat planning and control as separate components in a hierarchical framework (first plan, then control). Though prior works have demonstrated success, existing state-of-the-art planning and control architectures for legged robots quickly become brittle in highly uncertain environments due to an inherent inability to dynamically and decisively react to unplanned events. To address this, this work presents a novel framework that uses modeling and analysis tools from the hybrid systems and nonlinear control communities to reformulate planning footsteps and dynamic trajectories as well as deriving closed-loop controllers as a single trajectory optimization problem. By combining these previously disparate steps we empirically show that we can remove much of complexity that underlies the hierarchical decision posed by conventional approaches, making it possible to dynamically and safely react to large external disturbances in sub-real-time. We present results that highlight the reactive and robust nature of the unified framework developed.