Unicycle Kinematics Research Articles

On convergence results for nonlinear cyclic pursuit strategies

The paper focuses on the generation of a circular formation centred at a target point using a homogeneous group of autonomous agents in a cyclic pursuit framework. The agents are assumed to have a severely under-actuated form of the unicycle kinematics, with the linear speeds being constant and the angular speeds being their only control inputs. The target is assumed to be stationary and can represent a landmark, beacon, etc. In order to achieve the desired formation, the controller design is carried out in two stages. In the first stage, a bearing based attractive control law is proposed for every agent. Under the proposed law, the analysis of the relative motions reveals interesting behaviours like gathering and scattering of the agents. Building upon the attractive control law, in the second stage, the appropriate values of the controller parameters are determined which lead to a target centric circular formation. These parameters can also be suitably adjusted to achieve a pre-specified value of the radius of the circle and a desired distribution of the agents along the circle. The highlight of the work is that the convergence to the desired formation is guaranteed from almost all initial conditions of the agents by controlling only their angular speeds. Simulation results are also presented to illustrate the proposed theoretical results.

Robot Navigation in Complex Workspaces Employing Harmonic Maps and Adaptive Artificial Potential Fields.

In this work, we address the single robot navigation problem within a planar and arbitrarily connected workspace. In particular, we present an algorithm that transforms any static, compact, planar workspace of arbitrary connectedness and shape to a disk, where the navigation problem can be easily solved. Our solution benefits from the fact that it only requires a fine representation of the workspace boundary (i.e., a set of points), which is easily obtained in practice via SLAM. The proposed transformation, combined with a workspace decomposition strategy that reduces the computational complexity, has been exhaustively tested and has shown excellent performance in complex workspaces. A motion control scheme is also provided for the class of non-holonomic robots with unicycle kinematics, which are commonly used in most industrial applications. Moreover, the tuning of the underlying control parameters is rather straightforward as it affects only the shape of the resulted trajectories and not the critical specifications of collision avoidance and convergence to the goal position. Finally, we validate the efficacy of the proposed navigation strategy via extensive simulations and experimental studies.

Decentralized Multi-Agent Pursuit Using Deep Reinforcement Learning

Pursuit-evasion is the problem of capturing mobile targets with one or more pursuers. We use deep reinforcement learning for pursuing an omni-directional target with multiple, homogeneous agents that are subject to unicycle kinematic constraints. We use shared experience to train a policy for a given number of pursuers that is executed independently by each agent at run-time. The training benefits from curriculum learning, a sweeping-angle ordering to locally represent neighboring agents and encouraging good formations with reward structure that combines individual and group rewards. Simulated experiments with a reactive evader and up to eight pursuers show that our learning-based approach, with non-holonomic agents, performs on par with classical algorithms with omni-directional agents, and outperforms their non-holonomic adaptations. The learned policy is successfully transferred to the real world in a proof-of-concept demonstration with three motion-constrained pursuer drones.

Nonlinear MPC for collision-free and deadlock-free navigation of multiple nonholonomic mobile robots

In this paper, we present an online nonlinear Model Predictive Control (MPC) method for collision-free, deadlock-free navigation by multiple autonomous nonholonomic Wheeled Mobile Robots (WMRs). Our proposed method solves a nonlinear constrained optimization problem at each time step over a specified horizon to compute a sequence of optimal control inputs that drive the robots to target poses along collision-free trajectories, where the robots’ future states are predicted according to a unicycle kinematic model. To reduce the computational complexity of the optimization problem, we formulate it without stabilizing terminal constraints or terminal costs. We describe a computationally efficient approach to programming and solving the optimization problem, using open-source software tools for fast nonlinear optimization and applying the multiple-shooting method. We also provide rigorous proofs of the feasibility of the optimization problem and the stability of the proposed method. To validate the performance of our MPC method, we implement it in both 3D robot simulations and experiments with real nonholonomic WMRs for different multi-robot navigation scenarios with up to six robots. In all scenarios, the robots successfully navigate to their goal poses without colliding with one another or becoming trapped in a deadlock.

Output-Lifted Learning Model Predictive Control

Abstract We propose a computationally efficient Learning Model Predictive Control (LMPC) scheme for constrained optimal control of a class of nonlinear systems where the state and input can be reconstructed using lifted outputs. For the considered class of systems, we show how to use historical trajectory data collected during iterative tasks to construct a convex value function approximation along with a convex safe set in a lifted space of virtual outputs. These constructions are iteratively updated with historical data and used to synthesize predictive control policies. We show that the proposed strategy guarantees recursive constraint satisfaction, asymptotic stability, and non-decreasing closed-loop performance at each policy update. Finally, simulation results demonstrate the effectiveness of the proposed strategy on the kinematic unicycle.

A simple and reliable technique to design kinematic-based sideslip estimators

This paper proposes two novel vehicle sideslip estimators, that aim at achieving ease of implementation and tuning, low computational cost and robustness, using only the most common automotive measurements, like vehicle position, acceleration and rotational velocity. The two estimators are only based on the unicycle kinematic model, thus they do not require any knowledge of uncertain or time-varying parameters, like vehicle parameters, or of road conditions, as it usually happens when dynamic models are adopted, and they have been derived by recasting an estimation problem into a linear control problem. Different experiments, ranging from standard driving manoeuvres to drifting driving and autonomous driving, have been performed to demonstrate the effectiveness of the proposal even in particularly critical scenarios, like driving at the limits of vehicle’s handling. A comparison with a state-of-the-art sideslip estimator, using simulation and experimental data, is presented, as well.

A Hierarchical Collision Avoidance Architecture for Multiple Fixed-Wing UAVs in an Integrated Airspace

This paper studies the collision avoidance problem for autonomous multiple fixed-wing UAVs in the complex integrated airspace. By studying and combining the online path planning method, the distributed model predictive control algorithm, and the geometric reactive control approach, a three-layered collision avoidance system integrating conflict detection and resolution procedures is developed for multiple fixed-wing UAVs modeled by unicycle kinematics subject to input constraints. The effectiveness of the proposed methodology is evaluated and validated via test results of comparative simulations under both deterministic and probabilistic sensing conditions.

Approximate Optimal Motion Planning to Avoid Unknown Moving Avoidance Regions

In this article, an infinite-horizon optimal regulation problem is considered for a control-affine nonlinear autonomous agent subject to input constraints in the presence of dynamic avoidance regions. A local model-based approximate dynamic programming method is implemented to approximate the value function in a local neighborhood of the agent. By performing local approximations, prior knowledge of the locations of avoidance regions is not required. To alleviate the a priori knowledge of the number of avoidance regions in the operating domain, an extension is provided that modifies the value function approximation. The developed feedback-based motion planning strategy guarantees uniformly ultimately bounded convergence of the approximated control policy to the optimal policy while also ensuring the agent remains outside avoidance regions. Simulations are included to demonstrate the preliminary development for a kinematic unicycle and generic nonlinear system. Results from three experiments are also presented to illustrate the performance of the developed method, where a quadcopter achieves approximate optimal regulation while avoiding three mobile obstacles. To demonstrate the developed method, known avoidance regions are used in the first experiment, unknown avoidance regions are used in the second experiment, and an unknown time-varying obstacle directed by a remote pilot is included in the third experiment.

Shape-centric modeling for control of traveling wave rectilinear locomotion on snake-like robots

A traveling wave rectilinear gait for elongated, continuous bodies is modeled as a cyclically-varying backbone curve. The gait shapes are represented as planar deviations relative to an average body curve and an associated, rigidly-attached body frame. Body-ground contact patterns and other geometric properties integral to computation of external forcing are conveniently defined with respect to this average body curve. Introducing a body-ground rolling friction model permits the controlled equations of motion to be derived in closed form. Incorporating a constant curvature into the average body realizes turning movements, and hence turning control. Repeated numerical integration of the system dynamics facilitates construction of a control-to-action mapping, characterizing steady system behavior with respect to the gait’s parameter space. The control-to-action map reduces this complex dynamical system to a kinematic unicycle model for which feedback tracking strategies are well understood. To illustrate its utility, it is applied in a trajectory planning and tracking framework for locomotion around obstacles. Using the framework, a robotic snake exercising the traveling wave rectilinear gait successfully plans feasible trajectories and traverses non-trivial obstacle arrangements to reach specified goal positions.

A Smooth Distributed Feedback for Formation Control of Unicycles

This paper investigates a formation control problem in which a group of kinematic unicycles is made to converge to a desired formation with parallel heading angles and come to a stop. A control law is presented, which solves this problem for almost all initial conditions in any given compact set. The proposed control law is local and distributed, meaning that each unicycle is only required to sense its relative displacement measured in its own body frame, and the relative heading angle with respect to each of its neighbors. No communication between the unicycles is required. The sensing graph is assumed to be connected, undirected, and time invariant. The idea used to solve the above-mentioned formation control problem is to rigidly attach to the body frame of each unicycle an appropriate fixed offset vector. Stabilizing the desired formation amounts to achieving consensus of the endpoints of the offset vectors, and simultaneously synchronizing the unicycles’ heading angles. A control law achieving this goal is constructed by combining a bounded translational consensus controller with an attitude synchronizer. As a special case, the proposed solution solves the full unicycle synchronization problem, in which the unicycle positions are made to converge to each other, while the unicycle headings are made to align.

A swarm-based approach to dynamic coverage control of multi-agent systems

In this paper, we propose a swarm-based dynamic coverage scheme where we consider groups of coverage agents that behave as swarms for completing the coverage task. Agents are deployed to uncovered regions via swarming control where a leader agent selects a target position that is in an uncovered region while all other agents are commanded to swarm around the leader agent’s target position. Coverage and swarming control inputs are decoupled, meaning that only one of them is active at a given time. Through the decoupling of these control inputs, we attain simpler control problems that we analyze separately for different behavior modes and provide stability results for the overall control schemes through Lyapunov-like analysis for two different cases: swarms of kinematic unicycle agents and multiple swarms of single-integrator agents. In addition to the coverage objective, we design control inputs for collision and static obstacle avoidance and proximity maintenance.

Real-time Conflict Resolution Algorithm for Multi-UAV Based on Model Predict Control

A real-time conflict resolution algorithm based on model predictive control (MPC) is introduced to address the flight conflict resolution problem in multi-UAV scenarios. Using a low-level controller, the UAV dynamic equations are abstracted into simpler unicycle kinematic equations. The neighboring UAVs exchange their predicted trajectories at each sample time to predict the conflicts. Then, under the predesignated resolution rule and strategy, decentralized coordination and cooperation are performed to resolve the predicted conflicts. The controller structure of the distributed nonlinear model predictive control (DNMPC) is designed to predict potential conflicts and calculate control variables for each UAV. Numerical simulations of multi-UAV coordination are performed to verify the performance of the proposed algorithm. Results demonstrate that the proposed algorithm can resolve the conflicts sufficiently in real time, while causing no further conflicts.

Multi-rate unscented Kalman filtering for pose and curvature estimation in 3D ultrasound-guided needle steering

This paper presents a new method for estimating the needle pose and curvature in the context of robotically steered needles. The needle tip trajectory is represented by a modified unicycle kinematic model. A multi-rate unscented Kalman filter is proposed for the first time in needle steering to fuse asynchronous data coming from 3D B-mode ultrasound images, robot sensors and pre-operative elastography measurements. To demonstrate it, 51 unconstrained 3D insertions have been made in various media. The instantaneous localisation error is smaller than 0.6 mm and the prediction of the final tip position is smaller than 2 mm based on the observation of the first 2 cm of 8 cm deep insertions.

A Smooth Distributed Feedback for Global Rendezvous of Unicycles

This paper presents a solution to the rendezvous control problem for a network of kinematic unicycles in the plane, each equipped with an onboard camera measuring its relative displacement with respect to its neighbors in body frame coordinates. A smooth, time-independent control law is presented that drives the unicycles to a common position from arbitrary initial conditions, under the assumption that the sensing digraph contains a reverse-directed spanning tree. The proposed feedback is very simple, and relies only on the onboard measurements. No global positioning system is required, nor any information about the unicycles’ orientations.

A Distributed Feedback Motion Planning Protocol for Multiple Unicycle Agents of Different Classes

This paper presents a novel feedback method for the motion planning and coordination of multiple agents that belong to two classes, namely class-A and class-B. All agents are modeled via unicycle kinematics. Agents of class-B do not share information with agents of class-A and do not participate in ensuring safety, modeling thus agents with failed sensing/communication systems, agents of higher priority, or moving obstacles with known upper bounded velocity. The method is built upon a family of 2-D analytic vector fields, which under mild assumptions are proved to be safe feedback motion plans with a unique stable singular point. The conditions which ensure collision free and almost global convergence for a single agent and the analytical form of the vector fields are then utilized in the design the proposed distributed, semi-cooperative multi-agent coordination protocol. Semi-cooperative coordination has been defined in prior work as the ad hoc prioritization and conflict resolution among agents of the same class ; more specifically, participation in conflict resolution and collision avoidance for each agent is determined on-the-fly based on whether the agent's motion results in decreasing its distance with respect to its neighbor agents; based on this condition, the agent decides to either ignore its neighbors, or adjust its velocity and avoid the neighbor agent with respect to which the rate of decrease of the pairwise inter agent distance is maximal. The proposed coordination protocol builds upon this logic and addresses the case of multiple agents of distinct classes (class-A and class-B) in conflict. Guarantees on the safety of the multi-agent system and the almost global convergence of the agents to their destinations are proved. The efficacy of the proposed methodology is demonstrated via simulation results in static and dynamic environments.

VFO Path following Control with Guarantees of Positionally Constrained Transients for Unicycle-Like Robots with Constrained Control Input

The Vector-Field-Orientation (VFO) method is a control design concept which was originally introduced for the unicycle kinematics to solve two classical control tasks corresponding to the trajectory tracking and set-point control problems. A unified solution to both the tasks was possible by appropriate definitions of the so-called convergence vector field. So far, there has not been a version of the VFO control law for the third classical control task concerning the path following problem, which is particularly meaningful in the context of practical applications. The paper fills this gap by presenting a novel VFO path following controller devised for robots of unicycle-like kinematics with the amplitude-limited control input. Opposite to most path following controllers proposed in the literature, the new control law utilizes the recently introduced level curve approach which does not employ any parametrization of a reference path. In this way, the proposed solution is free of main limitations resulting from the need of unique determination of the shortest distance from a robot to the path. In contrast to other solutions, a formal analysis of the closed-loop dynamics presented in this paper provides sufficient conditions which guarantee constrained transients of robot motion with the position confined to a prescribed subset around a reference path. Theoretical results have been validated by numerical examples and experimentally verified with utilization of a laboratory-scale differentially driven robot.

Fail-safe encircling of multiple unmanned aerial vehicles with bearing only measurements

This paper presents a cooperative strategy to achieve evenly spaced circular formation of a group of unmanned aerial vehicles. The strategy is claimed to be fail-safe because the circular formation remains unaltered even if one or more unmanned aerial vehicles fail. We can also add more unmanned aerial vehicles without altering the formation. The control law uses only bearing angle information. We can pre-specify the centre of the circular formation of the unmanned aerial vehicles. The unmanned aerial vehicles will maintain the desired distance from the centre with bearing angle measurement only. We assume that the unmanned aerial vehicles are identical and can measure the bearing angle of all the other unmanned aerial vehicles. The strategy is analysed using unicycle kinematic and verified using six-degree-of-freedom model of the unmanned aerial vehicles. Extensive simulations are carried out for noisy measurement, presence of wind and moving target.

Sliding-Based Switching Control for Image-Guided Needle Steering in Soft Tissue

This letter represents a sliding-based controller for steering beveled-tip needles to stationary locations in soft tissue in a 2-D environment by performing appropriate switches of bevel orientation by 180° axial rotations while the needle is being inserted. Assuming the rotation velocity to be large enough with respect to insertion velocity, the out of plane motions of the needle can be neglected. The proposed controller has a nonmodel-based structure, which is fed by the needle tip deflection error and its derivative obtained from ultrasound images and outputs the switching pattern as the control law. To analyze the stability and convergence of the error, the kinematic unicycle model for beveled-tip needle motion in soft tissue is employed and the constraints on switching parameters are derived. The performance of the controller in the sense of targeting error and number of switches is verified using an experimental setup to insert the needle into gelatin phantom tissue and ex-vivo biological tissue.

A Velocity-Based Dynamic Model and Its Properties for Differential Drive Mobile Robots

An important issue in the field of motion control of wheeled mobile robots is that the design of most controllers is based only on the robot's kinematics. However, when high-speed movements and/or heavy load transportation are required, it becomes essential to consider the robot dynamics as well. The control signals generated by most dynamic controllers reported in the literature are torques or voltages for the robot motors, while commercial robots usually accept velocity commands. In this context, we present a velocity-based dynamic model for differential drive mobile robots that also includes the dynamics of the robot actuators. Such model has linear and angular velocities as inputs and has been included in Peter Corke's Robotics Toolbox for MATLAB, therefore it can be easily integrated into simulation systems that have been built for the unicycle kinematics. We demonstrate that the proposed dynamic model has useful mathematical properties. We also present an application of such model on the design of an adaptive dynamic controller and the stability analysis of the complete system, while applying the proposed model properties. Finally, we show some simulation and experimental results and discuss the advantages and limitations of the proposed model.

Stability, Trajectory Following and Formation Control of Wheel Mobile Robot

This paper comprises of two parts, the first one is concerned with controlling a wheeled mobile robot, where the robot is trained to follow a trajectory and the second part is an extension of controlling of the robots by following a trajectory while maintaining their formation intact. Unicycle kinematics is considered for the control design of each robot, and the leader-follower structure for the formation. It is assumed that every robot except the one located at the end of each team, can potentially be a leader to the one behind it. It is also assumed that each follower is capable of sensing its relative distance and relative velocity with respect to its preceding robot. The stability of the control law is also proposed, that is investigated in the case of perfect sensing and in the presence of input saturation. The impact of measurement noise on the followers is then studied assuming that a known upper bound exists on the measurement error, and a linear matrix ine- quality (LMI) methodology is proposed to design a control law which minimizes the upper bound on the steady-state er- ror. Matlab Simulations are presented to demonstrate the efficacy of the results obtained in this paper.