This paper presents a new sensor-based online method for generating collision-free near-optimal p... more This paper presents a new sensor-based online method for generating collision-free near-optimal paths for mobile robots pursuing a moving target amidst dynamic and static obstacles. At each iteration, first the set of all collision-free directions are calculated using velocity vectors of the robot relative to each obstacle and target, forming the Directive Circle (DC), which is a novel concept. Then, a direction close to the shortest path to the target is selected from feasible directions in DC. The DC prevents the robot from being trapped in deadlocks or local minima. It is assumed that the target's velocity is known, while the speeds of dynamic obstacles, as well as the locations of static obstacles, are to be calculated online. Extensive simulations and experimental results demonstrated the efficiency of the proposed method and its success in coping with complex environments and obstacles.
The International Journal of Robotics Research, Jul 1, 1998
This paper addresses a method for robot motion planning in dynamic environments, avoiding the mov... more This paper addresses a method for robot motion planning in dynamic environments, avoiding the moving and static obstacles while the robot drives towards the goal. The method maps the dynamic environment into a velocity space, using the concept of estimated arriving time to compute the times to potential collision and potential escape. The problem of finding the best motion command is directly treated in the velocity space, providing the trajectory which satisfies an optimization criterium (tipically the minimum time or the shortest path). In this work the method is applied to robots which are subject to both kinematic constraints (i.e. involving the configuration parameters of the robot and their derivatives), and dynamic constraints, (i.e. the constraints imposed by the dynamics of the robot and the limits of its actuators). Some experimental results are discussed.
This paper presents an on-line planner for sub-optimal obstacle avoidance. It generates near-shor... more This paper presents an on-line planner for sub-optimal obstacle avoidance. It generates near-shortest paths incrementally by avoiding obstacles optimally one at a time. In known environments, obstacles are avoided in an order determined by a global criterion. In unknown environments, obstacles are avoided as they are detected by on-board sensors. This avoidance strategy is guaranteed to reach the goal regardless of the order in which the obstacles are avoided. The method is demonstrated in several examples for an omnidirectional point robot moving amongst planar polygonal obstacles.
We present two different optimal control problem formulations that can be used to solve various t... more We present two different optimal control problem formulations that can be used to solve various trajectory planning scenarios of an Unmanned Ground Vehicle (UGV). It is less a study of trajectory planning than it is an analysis of the optimal control planning method itself. Numerous issues regarding vehicle modeling, obstacle modeling and computational complexity are discussed. The results and recommendations presented in this work are quite simple concepts, but have not been covered in the literature of trajectory planning to the knowledge of the co-authors. Simulation results illustrate successful implementation in various scenarios.
IEEE Transactions on Robotics and Automation, Apr 1, 1997
... Although these methods are more efficient than the traditional search over the entire visibil... more ... Although these methods are more efficient than the traditional search over the entire visibility graph ... This paper presents a novel approach to the on-line shortest path problem. ... Bellman (HJB) theory, which establishes a sufficient condition of optimality for optimal control problems ...
Journal of Dynamic Systems Measurement and Control-transactions of The Asme, Dec 1, 1995
This paper addresses the problem of motion planning of tracked vehicles. It is shown that the for... more This paper addresses the problem of motion planning of tracked vehicles. It is shown that the force equilibrium perpendicular to the tracks introduces a non-integrable state dependent equality constraint, making the path planning problem nonholonomic. A method is then presented for computing the nominal driving track forces for motions along a specified path at desired speeds. It consists of selecting the angular speeds along the path that satisfy vehicle dynamics and the non-integrable constraint. The computation of the angular speeds is formulated as a parameter optimization, minimizing the violation of the equality constraint. The method is demonstrated for motions along a circular path.
Autonomous navigation has recently gained great interest in the field of reinforcement learning. ... more Autonomous navigation has recently gained great interest in the field of reinforcement learning. However, little attention was given to the time optimal velocity control problem, i.e. controlling a vehicle such that it travels at the maximal speed without becoming dynamically unstable (roll-over or sliding). Time optimal velocity control can be solved numerically using existing methods that are based on optimal control and vehicle dynamics. In this paper, we use deep reinforcement learning to generate the time optimal velocity control. Furthermore, we use the numerical solution to further improve the performance of the reinforcement learner. It is shown that the reinforcement learner outperforms the numerically derived solution, and that the hybrid approach (combining learning with the numerical solution) speeds up the training process.
This paper presents a design method of multi-degree-of-freedom mechanisms for near-time optimal m... more This paper presents a design method of multi-degree-of-freedom mechanisms for near-time optimal motions. The design objective is to select system parameters, such as link lengths and actuator sizes, so as to minimize the optimal motion time of the mechanism along a given path. The exact time optimization problem is approximated by a simpler procedure that maximizes the acceleration near the end points. Representing the directions of maximum acceleration with the acceleration lines, and the reachability constraints as explicit functions of the design parameters, we transform the constrained optimization to a simpler curve fitting problem that can be formulated analytically. This allows the use of efficient gradient type optimizations, instead of the pattern search optimization that is otherwise required. Examples for optimizing the dimensions of a five-bar planar mechanism demonstrate close correlation of the approximate with the exact solutions, and an order of magnitude better computational efficiency than the previously developed unconstrained optimization methods.
A method is presented which finds the minirnum time motions for a manipulator between given end s... more A method is presented which finds the minirnum time motions for a manipulator between given end states. Tne method considers the full nonlinear manipulator dynamics, actuator saturation characteristics , and accounts for both the presence of oostacles in the work spaca and restrictions on the motions of the manipulator's joints. The method is computationally practical and has been irnplemanted
This paper describes an interactive software system , developed at the Robotics and Automation La... more This paper describes an interactive software system , developed at the Robotics and Automation Laboratory at UCLA to demonstrate innovative approaches to of f-line robot programming and work-cell layout design . The software computes the time-optimal motions along specified paths , local optimal paths around an initial guess , and the global optimal path between given end-points . It considers the full robot dynamics , actuator constraints , on the payload acceleration or the gripping force , and any number of polygonal obstacles of any shape . The graphic displays provide a useful tool for interactive motion planning and workcell design .
This paper addresses the issue of autonomous competitive yet safe driving in the context of the I... more This paper addresses the issue of autonomous competitive yet safe driving in the context of the Indy Autonomous Challenge (IAC) simulation race. The IAC is the first multi-vehicle autonomous head-tohead competition, reaching speeds of 300 km/h along an oval track modeled after the Indianapolis Motor Speedway (IMS). We present a racing controller that attempts to maximize progress along the track while avoiding collisions with opponent vehicles and obeying the race rules. To this end, the racing controller first computes a race line offline. During the race, it repeatedly computes a small set of dynamically feasible maneuver candidates, each tested for collision with the opponent vehicles. It then selects a collision-free maneuver that maximizes the progress along the track and obeys the race rules. Our controller was tested in a 6-vehicle simulation, managing to run competitively with no collision over 30 laps. In addition, it managed to drive within a close range of the leading vehicle during most of the IAC final simulation race.
ABSTRACT Motion planning in dynamic environments is made possible using the concept of velocity o... more ABSTRACT Motion planning in dynamic environments is made possible using the concept of velocity obstacles. It maps the colliding velocities of the robot with any moving or static obstacle to the robot’s velocity space. Collision avoidance is achieved by selecting the robot velocity outside the velocity obstacles. This concept was first proposed in [3] for the linear case of obstacles moving on straight line trajectories, and is extended here to obstacles moving along arbitrary trajectories. The non-linear velocity obstacle (NLVO) takes into account the shape, velocity and path curvature of the moving obstacle. It allows to select a single avoidance maneuver (if one exists) that avoids any number of obstacles that move on any known trajectories. The nonlinear v-obstacle can be generated as a time integral of the colliding velocities, or by computing its boundaries using analytic expressions.
Proceedings., IEEE International Conference on Robotics and Automation
A method is presented for optimally planning the motions of autonomous vehicles, considering vehi... more A method is presented for optimally planning the motions of autonomous vehicles, considering vehicle dynamics, terrain topography, obstacles, and surface mobility. The terrain is represented by a smooth cubic B patch, and the geometric path consists of a two dimensional B spline curve mapped to the three-dimensional surface. The path is optimized with a parameter optimization procedure, using motion time
American Journal of Engineering Education (AJEE), 2016
This article presents a case study that illustrates the paradigmatic shift in higher education fr... more This article presents a case study that illustrates the paradigmatic shift in higher education from content-centered teaching to learning-centered academic programs. This pragmatic change, triggered by the STEM movement, calls for the introduction of success measures in the course development process. The course described in this paper illustrates such a goal-driven approach to the development of an entire multidisciplinary curriculum in mechanical engineering and mechatronics. The effectiveness of this new curriculum was confirmed by findings of a survey of graduates of the first six graduating classes who studied on the basis of this curriculum.
"The Traction Trebuchet: A Triumph of Four Civilizations." This study of the traction t... more "The Traction Trebuchet: A Triumph of Four Civilizations." This study of the traction trebuchet offers new perspectives on the development and employment of the piece of ordnance that dominated warfare far longer than any other form of artillery. The inquiry is both interdisciplinary and intercultural, combining an historical investigation with an engineering analysis of manually-powered artillery used for a millennium across Eurasia and North Africa. It reviews the accomplishments of China, Islam, Byzantium, and the Latin West to the development of the traction trebuchet and describes how Islamic, Byzantine, and European trebuchets were able to surpass their Chinese counterparts, despite the fact that China was the first to devise this class of artillery. Contrary to prevailing opinion, the traction trebuchet reached an advanced stage of development, comparable to the performance of the stone-projectors of the gravity-powered age of artillery; and it remained in use long after the invention of counterwei...
This paper presents a method for computing themotions of a robot in dynamic environments, subject... more This paper presents a method for computing themotions of a robot in dynamic environments, subjectto the robot dynamics and its actuator constraints.This method is based on the concept ofVelocity Obstacle, which defines the set of feasiblerobot velocities that would result in a collisionbetween the robot and an obstacle moving at agiven velocity. The avoidance maneuver at a specifictime is thus computed by selecting robot'svelocities out of that set. A trajectory consistingof a...
This paper presents a new sensor-based online method for generating collision-free near-optimal p... more This paper presents a new sensor-based online method for generating collision-free near-optimal paths for mobile robots pursuing a moving target amidst dynamic and static obstacles. At each iteration, first the set of all collision-free directions are calculated using velocity vectors of the robot relative to each obstacle and target, forming the Directive Circle (DC), which is a novel concept. Then, a direction close to the shortest path to the target is selected from feasible directions in DC. The DC prevents the robot from being trapped in deadlocks or local minima. It is assumed that the target's velocity is known, while the speeds of dynamic obstacles, as well as the locations of static obstacles, are to be calculated online. Extensive simulations and experimental results demonstrated the efficiency of the proposed method and its success in coping with complex environments and obstacles.
The International Journal of Robotics Research, Jul 1, 1998
This paper addresses a method for robot motion planning in dynamic environments, avoiding the mov... more This paper addresses a method for robot motion planning in dynamic environments, avoiding the moving and static obstacles while the robot drives towards the goal. The method maps the dynamic environment into a velocity space, using the concept of estimated arriving time to compute the times to potential collision and potential escape. The problem of finding the best motion command is directly treated in the velocity space, providing the trajectory which satisfies an optimization criterium (tipically the minimum time or the shortest path). In this work the method is applied to robots which are subject to both kinematic constraints (i.e. involving the configuration parameters of the robot and their derivatives), and dynamic constraints, (i.e. the constraints imposed by the dynamics of the robot and the limits of its actuators). Some experimental results are discussed.
This paper presents an on-line planner for sub-optimal obstacle avoidance. It generates near-shor... more This paper presents an on-line planner for sub-optimal obstacle avoidance. It generates near-shortest paths incrementally by avoiding obstacles optimally one at a time. In known environments, obstacles are avoided in an order determined by a global criterion. In unknown environments, obstacles are avoided as they are detected by on-board sensors. This avoidance strategy is guaranteed to reach the goal regardless of the order in which the obstacles are avoided. The method is demonstrated in several examples for an omnidirectional point robot moving amongst planar polygonal obstacles.
We present two different optimal control problem formulations that can be used to solve various t... more We present two different optimal control problem formulations that can be used to solve various trajectory planning scenarios of an Unmanned Ground Vehicle (UGV). It is less a study of trajectory planning than it is an analysis of the optimal control planning method itself. Numerous issues regarding vehicle modeling, obstacle modeling and computational complexity are discussed. The results and recommendations presented in this work are quite simple concepts, but have not been covered in the literature of trajectory planning to the knowledge of the co-authors. Simulation results illustrate successful implementation in various scenarios.
IEEE Transactions on Robotics and Automation, Apr 1, 1997
... Although these methods are more efficient than the traditional search over the entire visibil... more ... Although these methods are more efficient than the traditional search over the entire visibility graph ... This paper presents a novel approach to the on-line shortest path problem. ... Bellman (HJB) theory, which establishes a sufficient condition of optimality for optimal control problems ...
Journal of Dynamic Systems Measurement and Control-transactions of The Asme, Dec 1, 1995
This paper addresses the problem of motion planning of tracked vehicles. It is shown that the for... more This paper addresses the problem of motion planning of tracked vehicles. It is shown that the force equilibrium perpendicular to the tracks introduces a non-integrable state dependent equality constraint, making the path planning problem nonholonomic. A method is then presented for computing the nominal driving track forces for motions along a specified path at desired speeds. It consists of selecting the angular speeds along the path that satisfy vehicle dynamics and the non-integrable constraint. The computation of the angular speeds is formulated as a parameter optimization, minimizing the violation of the equality constraint. The method is demonstrated for motions along a circular path.
Autonomous navigation has recently gained great interest in the field of reinforcement learning. ... more Autonomous navigation has recently gained great interest in the field of reinforcement learning. However, little attention was given to the time optimal velocity control problem, i.e. controlling a vehicle such that it travels at the maximal speed without becoming dynamically unstable (roll-over or sliding). Time optimal velocity control can be solved numerically using existing methods that are based on optimal control and vehicle dynamics. In this paper, we use deep reinforcement learning to generate the time optimal velocity control. Furthermore, we use the numerical solution to further improve the performance of the reinforcement learner. It is shown that the reinforcement learner outperforms the numerically derived solution, and that the hybrid approach (combining learning with the numerical solution) speeds up the training process.
This paper presents a design method of multi-degree-of-freedom mechanisms for near-time optimal m... more This paper presents a design method of multi-degree-of-freedom mechanisms for near-time optimal motions. The design objective is to select system parameters, such as link lengths and actuator sizes, so as to minimize the optimal motion time of the mechanism along a given path. The exact time optimization problem is approximated by a simpler procedure that maximizes the acceleration near the end points. Representing the directions of maximum acceleration with the acceleration lines, and the reachability constraints as explicit functions of the design parameters, we transform the constrained optimization to a simpler curve fitting problem that can be formulated analytically. This allows the use of efficient gradient type optimizations, instead of the pattern search optimization that is otherwise required. Examples for optimizing the dimensions of a five-bar planar mechanism demonstrate close correlation of the approximate with the exact solutions, and an order of magnitude better computational efficiency than the previously developed unconstrained optimization methods.
A method is presented which finds the minirnum time motions for a manipulator between given end s... more A method is presented which finds the minirnum time motions for a manipulator between given end states. Tne method considers the full nonlinear manipulator dynamics, actuator saturation characteristics , and accounts for both the presence of oostacles in the work spaca and restrictions on the motions of the manipulator's joints. The method is computationally practical and has been irnplemanted
This paper describes an interactive software system , developed at the Robotics and Automation La... more This paper describes an interactive software system , developed at the Robotics and Automation Laboratory at UCLA to demonstrate innovative approaches to of f-line robot programming and work-cell layout design . The software computes the time-optimal motions along specified paths , local optimal paths around an initial guess , and the global optimal path between given end-points . It considers the full robot dynamics , actuator constraints , on the payload acceleration or the gripping force , and any number of polygonal obstacles of any shape . The graphic displays provide a useful tool for interactive motion planning and workcell design .
This paper addresses the issue of autonomous competitive yet safe driving in the context of the I... more This paper addresses the issue of autonomous competitive yet safe driving in the context of the Indy Autonomous Challenge (IAC) simulation race. The IAC is the first multi-vehicle autonomous head-tohead competition, reaching speeds of 300 km/h along an oval track modeled after the Indianapolis Motor Speedway (IMS). We present a racing controller that attempts to maximize progress along the track while avoiding collisions with opponent vehicles and obeying the race rules. To this end, the racing controller first computes a race line offline. During the race, it repeatedly computes a small set of dynamically feasible maneuver candidates, each tested for collision with the opponent vehicles. It then selects a collision-free maneuver that maximizes the progress along the track and obeys the race rules. Our controller was tested in a 6-vehicle simulation, managing to run competitively with no collision over 30 laps. In addition, it managed to drive within a close range of the leading vehicle during most of the IAC final simulation race.
ABSTRACT Motion planning in dynamic environments is made possible using the concept of velocity o... more ABSTRACT Motion planning in dynamic environments is made possible using the concept of velocity obstacles. It maps the colliding velocities of the robot with any moving or static obstacle to the robot’s velocity space. Collision avoidance is achieved by selecting the robot velocity outside the velocity obstacles. This concept was first proposed in [3] for the linear case of obstacles moving on straight line trajectories, and is extended here to obstacles moving along arbitrary trajectories. The non-linear velocity obstacle (NLVO) takes into account the shape, velocity and path curvature of the moving obstacle. It allows to select a single avoidance maneuver (if one exists) that avoids any number of obstacles that move on any known trajectories. The nonlinear v-obstacle can be generated as a time integral of the colliding velocities, or by computing its boundaries using analytic expressions.
Proceedings., IEEE International Conference on Robotics and Automation
A method is presented for optimally planning the motions of autonomous vehicles, considering vehi... more A method is presented for optimally planning the motions of autonomous vehicles, considering vehicle dynamics, terrain topography, obstacles, and surface mobility. The terrain is represented by a smooth cubic B patch, and the geometric path consists of a two dimensional B spline curve mapped to the three-dimensional surface. The path is optimized with a parameter optimization procedure, using motion time
American Journal of Engineering Education (AJEE), 2016
This article presents a case study that illustrates the paradigmatic shift in higher education fr... more This article presents a case study that illustrates the paradigmatic shift in higher education from content-centered teaching to learning-centered academic programs. This pragmatic change, triggered by the STEM movement, calls for the introduction of success measures in the course development process. The course described in this paper illustrates such a goal-driven approach to the development of an entire multidisciplinary curriculum in mechanical engineering and mechatronics. The effectiveness of this new curriculum was confirmed by findings of a survey of graduates of the first six graduating classes who studied on the basis of this curriculum.
"The Traction Trebuchet: A Triumph of Four Civilizations." This study of the traction t... more "The Traction Trebuchet: A Triumph of Four Civilizations." This study of the traction trebuchet offers new perspectives on the development and employment of the piece of ordnance that dominated warfare far longer than any other form of artillery. The inquiry is both interdisciplinary and intercultural, combining an historical investigation with an engineering analysis of manually-powered artillery used for a millennium across Eurasia and North Africa. It reviews the accomplishments of China, Islam, Byzantium, and the Latin West to the development of the traction trebuchet and describes how Islamic, Byzantine, and European trebuchets were able to surpass their Chinese counterparts, despite the fact that China was the first to devise this class of artillery. Contrary to prevailing opinion, the traction trebuchet reached an advanced stage of development, comparable to the performance of the stone-projectors of the gravity-powered age of artillery; and it remained in use long after the invention of counterwei...
This paper presents a method for computing themotions of a robot in dynamic environments, subject... more This paper presents a method for computing themotions of a robot in dynamic environments, subjectto the robot dynamics and its actuator constraints.This method is based on the concept ofVelocity Obstacle, which defines the set of feasiblerobot velocities that would result in a collisionbetween the robot and an obstacle moving at agiven velocity. The avoidance maneuver at a specifictime is thus computed by selecting robot'svelocities out of that set. A trajectory consistingof a...
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