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Showing papers on "Robot published in 1990"


Book
01 Jul 1990
TL;DR: This paper reformulated the manipulator control problem as direct control of manipulator motion in operational space-the space in which the task is originally described-rather than as control of the task's corresponding joint space motion obtained only after geometric and kinematic transformation.
Abstract: This paper presents a unique real-time obstacle avoidance approach for manipulators and mobile robots based on the artificial potential field concept. Collision avoidance, tradi tionally considered a high level planning problem, can be effectively distributed between different levels of control, al lowing real-time robot operations in a complex environment. This method has been extended to moving obstacles by using a time-varying artificial patential field. We have applied this obstacle avoidance scheme to robot arm mechanisms and have used a new approach to the general problem of real-time manipulator control. We reformulated the manipulator con trol problem as direct control of manipulator motion in oper ational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and kine matic transformation. Outside the obstacles' regions of influ ence, we caused the end effector to move in a straight line with an...

3,063 citations


Proceedings ArticleDOI
23 May 1990
TL;DR: In this article, a preliminary study of what role recent results in adaptive robot control and the understanding of time-delays may play in the development of effective telerobotics systems, which would best exploit the presence of the human operator while making full use of available robot control technology and computing power.
Abstract: Telerobotics, the body of science and technology which bridges human control and purely autonomous machines, is expected to be a merging point of modern developments in robotics, control theory, cognitive science, machine design, and computer science. Besides traditional applications in space, subsea, and handling of hazardous material, many new potential uses of advanced telerobotic systems have recently been suggested or explored, such as safety applications or microsurgery. This paper is a preliminary study of what role recent results in adaptive robot control and the understanding of time-delays may play in the development of effective telerobotics systems, which would best exploit the presence of the human operator while making full use of available robot control technology and computing power. The key paradigm it explores is that of simplifying, transforming, or enhancing the remote dynamics perceived by the operator by proper use of adaptive robot control techniques and tools from passivity theory.

936 citations


Book
01 Jul 1990
TL;DR: A sonar-based mapping and navigation system developed for an autonomous mobile robot operating in unknown and unstructured environments is described, which uses sonar range data to build a multileveled description of the robot's surroundings.
Abstract: A sonar-based mapping and navigation system developed for an autonomous mobile robot operating in unknown and unstructured environments is described. The system uses sonar range data to build a multileveled description of the robot's surroundings. Sonar readings are interpreted using probability profiles to determine empty and occupied areas. Range measurements from multiple points of view are integrated into a sensor-level sonar map, using a robust method that combines the sensor information in such a way as to cope with uncertainties and errors in the data. The resulting two-dimensional maps are used for path planning and navigation. From these sonar maps, multiple representations are developed for various kinds of problem-solving activities. Several dimensions of representation are defined: the abstraction axis, the geographical axis, and the resolution axis. The sonar mapping procedures have been implemented as part of an autonomous mobile robot navigation system called Dolphin. The major modules of this system are described and related to the various mapping representations used. Results from actual runs are presented, and further research is mentioned. The system is also situated within the wider context of developing an advanced software architecture for autonomous mobile robots.

690 citations


Journal ArticleDOI
TL;DR: The Autonomous Robot Architecture is the framework within which experiments in the application of knowledge to reactive control are conducted and actual robot experiments and simulation studies demonstrate the flexibility and feasibility of this approach over a wide range of navigational domains.

463 citations


Proceedings ArticleDOI
Lance Williams1
01 Sep 1990
TL;DR: A means of acquiring the expressions of real faces, and applying them to computer-generated faces is described as an "electronic mask" that offers a means for the traditional talents of actors to be flexibly incorporated in digital animations.
Abstract: As computer graphics technique rises to the challenge of rendering lifelike performers, more lifelike performance is required. The techniques used to animate robots, arthropods, and suits of armor, have been extended to flexible surfaces of fur and flesh. Physical models of muscle and skin have been devised. But more complex databases and sophisticated physical modeling do not directly address the performance problem. The gestures and expressions of a human actor are not the solution to a dynamic system. This paper describes a means of acquiring the expressions of real faces, and applying them to computer-generated faces. Such an "electronic mask" offers a means for the traditional talents of actors to be flexibly incorporated in digital animations. Efforts in a similar spirit have resulted in servo-controlled "animatrons," high-technology puppets, and CG puppetry [1]. The manner in which the skills of actors and puppetteers as well as animators are accommodated in such systems may point the way for a more general incorporation of human nuance into our emerging computer media.The ensuing description is divided into two major subjects: the construction of a highly-resoved human head model with photographic texture mapping, and the concept demonstration of a system to animate this model by tracking and applying the expressions of a human performer.

448 citations


Proceedings Article
29 Jul 1990
TL;DR: An algorithm which allows a behavior-based robot to learn on the basis of positive and negative feedback when to activate its behaviors has been described and tested successfully on an autonomous 6-legged robot.
Abstract: We describe an algorithm which allows a behavior-based robot to learn on the basis of positive and negative feedback when to activate its behaviors. In accordance with the philosophy of behavior-based robots, the algorithm is completely distributed: each of the behaviors independently tries to sensors find out (i) whether it is relevant (i.e. whether it is at all correlated to positive feedback) and (ii) what the conditions are under which it becomes reliable (i.e. the conditions under which it maximises the probability of receiving positive feedback and minimises the probability of receiving negative feedback). The algorithm has been tested successfully on an autonomous 6-legged robot which had to learn how to coordinate its legs so as to walk forward.

431 citations


Proceedings ArticleDOI
13 May 1990
TL;DR: Predictive display enhanced the human operator's telemanipulation task performance significantly during free motion when there is a long time delay, it appears, however, that either two-view or stereoscopic predictive displays are necessary for general three-dimensional tasks.
Abstract: An enhanced teleoperation technique for time-delayed bilateral teleoperator control is discussed. The control technique selected for time delay is based on the use of a high-fidelity graphics phantom robot that is being controlled in real time (without time delay) against the static task image. Thus, the motion of the phantom robot image on the monitor predicts the motion of the real robot. The real robot's motion will follow the phantom robot's motion on the monitor with the communication time delay implied in the task. Real-time high-fidelity graphics simulation of a PUMA arm is generated and overlaid on the actual camera view of the arm. A simple camera calibration technique is used for calibrated graphics overlay. A preliminary experiment is performed with the predictive display by using a very simple tapping task. The results with this simple task indicate that predictive display enhanced the human operator's telemanipulation task performance significantly during free motion when there is a long time delay. It appears, however, that either two-view or stereoscopic predictive displays are necessary for general three-dimensional tasks. >

387 citations


Proceedings Article
29 Jul 1990
TL;DR: The hypothesis is that the appropriateness of a particular meta-level reasoning strategy will depend in large part upon the characteristics of the environment in which the agent incorporating that strategy is situated.
Abstract: We describe a system called Tileworld, which consists of a simulated robot agent and a simulated environment which is both dynamic and unpredictable. Both the agent and the environment are highly parameterized, enabling one to control certain characteristics of each. We can thus experimentally investigate the behavior of various meta-level reasoning strategies by tuning the parameters of the agent, and can assess the success of alternative strategies in different environments by tuning the environmental parameters. Our hypothesis is that the appropriateness of a particular meta-level reasoning strategy will depend in large part upon the characteristics of the environment in which the agent incorporating that strategy is situated. We describe our initial experiments using Tileworld, in which we have been evaluating a version of the meta-level reasoning strategy proposed in earlier work by one of the authors [Bratman et al., 1988].

369 citations


Proceedings ArticleDOI
13 May 1990
TL;DR: A path-planning method of nonholonomic motion is developed using a Lyapunov function that can be controlled in addition to the joint variables of the manipulator by actuating only the Joint variables, if the trajectory is carefully planned.
Abstract: The path planning of nonholonomic motion of space robot systems is discussed. A space vehicle with a 6-DOF (degrees of freedom) manipulator is described as a nine-variable system with six inputs. It is shown that, by carefully utilizing the nonholonomic mechanical structure, the vehicle orientation in addition to the joint variables of the manipulator can be controlled by actuating only the joint variables. The nonholonomic mechanical structure of space robot systems is shown. A rigorous mathematical proof of the nonholonomic nature of the free-flying space robot systems is provided using Frobenius's theorem. A method for nonholonomic motion planning for space robot systems is established by using a Lyapunov function. >

323 citations


Proceedings ArticleDOI
01 Sep 1990
TL;DR: In this paper, the authors present a real-time robot motion planner that can handle any polyhedral geometry of robot and obstacles, including disjoint and highly concave unions of polyhedra.
Abstract: We present a real-time robot motion planner that is fast and complete to a resolution. The technique is guaranteed to find a path if one exists at the resolution, and all paths returned are safe. The planner can handle any polyhedral geometry of robot and obstacles, including disjoint and highly concave unions of polyhedra.The planner uses standard graphics hardware to rasterize configuration space obstacles into a series of bitmap slices, and then uses dynamic programming to create a navigation function (a discrete vector-valued function) and to calculate paths in this rasterized space. The motion paths which the planner produces are minimal with respect to an L1 (Manhattan) distance metric that includes rotation as well as translation.Several examples are shown illustrating the competence of the planner at generating planar rotational and translational plans for complex two and three dimensional robots. Dynamic motion sequences, including complicated and non-obvious backtracking solutions, can be executed in real time.

287 citations


Journal ArticleDOI
TL;DR: An extension of T. Kohonen's (1982) self-organizing mapping algorithm together with an error-correction scheme based on the Widrow-Hoff learning rule is applied to develop a learning algorithm for the visuomotor coordination of a simulated robot arm.
Abstract: An extension of T. Kohonen's (1982) self-organizing mapping algorithm together with an error-correction scheme based on the Widrow-Hoff learning rule is applied to develop a learning algorithm for the visuomotor coordination of a simulated robot arm. Learning occurs by a sequence of trial movements without the need for an external teacher. Using input signals from a pair of cameras, the closed robot arm system is able to reduce its positioning error to about 0.3% of the linear dimensions of its work space. This is achieved by choosing the connectivity of a three-dimensional lattice consisting of the units of the neural net. >

Journal ArticleDOI
01 Sep 1990
TL;DR: It turns out that extensive modifications of simpler tactile algorithms are needed to take full advantage of additional sensing capabilities, and two algorithms that guarantee convergence and exhibit different styles of behavior are described, and their performance is demonstrated in simulated examples.
Abstract: A model of mobile robot navigation is considered in which the robot is a point automaton operating in an environment with unknown obstacles of arbitrary shapes. The robot's input information includes its own and the target-points coordinates as well as local sensing information such as that from stereo vision or a range finder. These algorithmic issues are addressed: (1) Is it possible to combine sensing and planning functions to produce 'active sensing' guided by the needs of planning? (The answer is yes). (2) Can richer sensing (e.g., stereo vision versus tactile) guarantee better performance, that is, resulting in shorter paths? (The general answer is no). A paradigm for combining range data with motion planning is presented. It turns out that extensive modifications of simpler tactile algorithms are needed to take full advantage of additional sensing capabilities. Two algorithms that guarantee convergence and exhibit different styles of behavior are described, and their performance is demonstrated in simulated examples. >

Proceedings ArticleDOI
13 May 1990
TL;DR: It is shown that robot manipulator control can be accomplished using simple decentralized linear time invariant time-delayed joint controllers instead of the complicated computed torque control scheme, which means that all the online computational problems associated with computing robot inverse dynamics can be avoided.
Abstract: It is shown that robot manipulator control can be accomplished using simple decentralized linear time invariant time-delayed joint controllers instead of the complicated computed torque control scheme. This means that all the online computational problems associated with computing robot inverse dynamics can be avoided, and the robot control problem is essentially reduced to that of computing n linear proportional-derivation controls for n joint subsystems. The proposed control technique employs a time-delayed control with a specially designed constant diagonal gain matrix to decouple and linearize the robot joint dynamics so that linear centralized joint control can be achieved. It is shown that the proposed controller is stable, and the value of the special gain matrix can be selected based on a sufficient condition of stability presently developed. However, the establishment of this sufficient condition requires knowledge of the inertial matrix of the robot. It is also shown that the controller is robust in the presence of payload uncertainty. A two-link planar robot is presented to illustrate the controller design procedures and the performance of the controller. >

Journal ArticleDOI
TL;DR: Design of a practical mobile robot is attempted, with an inspection task in a nuclear reactor as a concrete objective for development, and basic control problems such as signal process ing for tactile sensors and control of statically indeterminant forces are investigated.
Abstract: Mobile robots having good terrain adaptability, sufficient payload capability, and high mobility are now urgently in de mand In this paper, design of a practical mobile robot is attempted, with an

Proceedings ArticleDOI
13 May 1990
TL;DR: In the method used to perform path planning, a trial path through the c-span-time is chosen and then modified under the influence of the potential fields until an appropriate path is found.
Abstract: A technique for coordinating the paths of multiple robots in the presence of obstacles is presented. To accomplish this, the robots are prioritized. A path that avoids only the stationary obstacles is planned for the highest-priority robot. A trajectory for the next-lowest priority robot is planned so that it avoids both the stationary obstacles and the higher-priority robot, which is treated as a moving obstacle. This process is continued until trajectories for all of the robots have been planned. The planning is accomplished by first mapping the real space of the robots into configuration-space-time. Potential fields are applied around the c-space-time obstacles and are used to modify the path of the robot. The advantage of using artificial potential fields is that they offer a relatively fast and efficient way to solve for safe trajectories around both stationary and moving obstacles. In the method used to perform path planning, a trial path through the c-span-time is chosen and then modified under the influence of the potential fields until an appropriate path is found. >

Journal ArticleDOI
01 Apr 1990-Robotica
TL;DR: This paper presents solutions for a complete modeling of the DELTA parallel robot (direct and inverse kinematics, inverse statics, inverse dynamics), with few arithmetic and trigonometric operations.
Abstract: The DELTA parallel robot, designed by an EPFL (Ecole Polytechnique Federale de Lausanne) research team, is a mechanical structure which has the advantage of parallel robots and ease of serial robots modeling. This paper presents solutions for a complete modeling of the DELTA parallel robot (direct and inverse kinematics, inverse statics, inverse dynamics), with few arithmetic and trigonometric operations. Our method is based on a satisfactory choice of kinematic parameters and on a few restricting hypotheses for the static and dynamic models. We give some details of each model, we present some computation results and we put the emphasis on some particular points, showing the capabilities of this mechanical structure.

01 May 1990
TL;DR: A distributed method for mobile robot navigation, spatial learning, and path planning is presented and the main issues addressed are: distributed, procedural, and qualitative representation and computation, emergent behaviors, dynamic landmarks, minimized communication.
Abstract: A distributed method for mobile robot navigation, spatial learning, and path planning is presented. It is implemented on a sonar-based physical robot, Toto, consisting of three competence layers: 1) Low-level navigation: a collection of reflex-like rules resulting in emergent boundary-tracing. 2) Landmark detection: dynamically extracts landmarks from the robot''s motion. 3) Map learning: constructs a distributed map of landmarks. The parallel implementation allows for localization in constant time. {\it Spreading of activation} computes both topological and physical shortest paths in linear time. The main issues addressed are: distributed, procedural, and qualitative representation and computation, emergent behaviors, dynamic landmarks, minimized communication.

Journal ArticleDOI
01 Feb 1990
TL;DR: Experiments show that the overall scheme, while simple to implement, is powerful and reliable enough to permit walking from level to slope or vice versa, and it is argued that the proposed mechanism can be extended to quasi-dynamic and dynamic gaits.
Abstract: A scheme to enable the SD-2 biped robot to climb sloping surfaces is proposed. By means of sensing devices, namely position sensors on the joints and force sensors underneath the heel and toe, the robot is able to detect the transition of the supporting terrain from a flat floor to a sloping surface. An algorithm is developed for the biped robot control system to evaluate the inclination of the supporting foot and the unknown gradient, and a compliant motion scheme is then used to enable the robot to transfer from level walking to climbing the slope. While the robot walks on the slope, the gait synthesis is a simple modification to the one used for level walking. Experiments with the SD-2 biped robot show that the overall scheme, while simple to implement, is powerful and reliable enough to permit walking from level to slope or vice versa. Finally, it is argued that the proposed mechanism can be extended to quasi-dynamic and dynamic gaits. >

Book
01 Jul 1990
TL;DR: The actuated inverse and sensed forward solutions are applied to the kinematic control of Uranus by calculating in real-time the robot position from shaft encoder readings; formulating an algorithm to detect wheel slippage; and developing an algorithm for feedback control.
Abstract: We have introduced a methodology for the kinematic modeling of wheeled mobile robots. In this paper, we apply our methodology to Uranus, an omnidirectional wheeled mobile robot which is being developed in the Robotics Institute of Carnegie Mellon University. We assign coordinate systems to specify the transformation matrices and write the kinematic equations-of-motion. We illustrate the actuated inverse and sensed forward solutions; i.e., the calculation of actuator velocities from robot velocities and robot velocities from sensed wheel velocities. We apply the actuated inverse and sensed forward solutions to the kinematic control of Uranus by: calculating in real-time the robot position from shaft encoder readings (i.e., dead reckoning); formulating an algorithm to detect wheel slippage; and developing an algorithm for feedback control.

Book
S. Cameron1
01 Jul 1990
TL;DR: A method is described for solving collision detection that involves transforming the problem into an intersection-detection problem over space time and an efficient implementation described based on describing the objects and motions constructively.
Abstract: The collision-detection problem is to decide, given two objects and desired motions, whether the objects will come into collision over a given time span. The solution of this problem is useful, both in robotics and in other problem domains. A method is described for solving collision detection that involves transforming the problem into an intersection-detection problem over space time. The theoretical basis for the solution is given and an efficient implementation described based on describing the objects and motions constructively. The related problems of describing the collision region and detecting collisions when there are more than two moving objects are also described. >

Proceedings ArticleDOI
05 Sep 1990
TL;DR: A new method for controlling a group of mobile robots is presented, and it turns out that in many cases most robots execute an identical simple algorithm.
Abstract: A new method for controlling a group of mobile robots is presented. The method is fully distributed in the sense that each robot plans its motion individually on the basis of a given goal of the group and the observed positions of other robots. The method is illustrated by showing how a large number of robots can form an approximation of a circle, a simple polygon, or a line segment in the plane. It is also shown how the robots can distribute themselves nearly uniformly within a circle or a convex polygon in the plane. A method of dividing the robots into two or more groups is presented. It turns out that in many cases most robots execute an identical simple algorithm. The performance of the method is demonstrated by simulation. >

Journal ArticleDOI
TL;DR: In this paper, the inverse dynamics of robot manipulators based on flexible arm models are considered and the actuator torques required for a flexible arm to track a given trajectory are formulated and computed by using special moving coordinate systems, called virtual rigid link coordinates.
Abstract: The inverse dynamics of robot manipulators based on flexible arm models are considered Actuator torques required for a flexible arm to track a given trajectory are formulated and computed by using special moving coordinate systems, called virtual rigid link coordinates Dynamic deformations of the flexible arm can be represented in a simple and compact form with use of the virtual coordinate systems

Journal ArticleDOI
TL;DR: A new, very fast algorithm for determining minimum-time trajectories for bang-bang control systems that seeks to minimize the time required to force a manipulator to travel a specified distance.
Abstract: A class of optimization problems of interest in the field of robotics is one that seeks to minimize the time required to force a manipulator to travel a specified distance. Robots employ multiple, bounded control inputs. This work describes a new, very fast algorithm for determining minimum-time trajectories for such systems. We have modified the steepest descent method of optimal programming to find time-optimal switch times for bang-bang control systems. The Switch Time Optimization (STO) program has been applied to a two-link manipulator with two control inputs. To find the minimum time for a robot end-effector to travel between two points in its workspace, one must establish the optimal position of the robot with respect to the work station. The algorithm accomplishes this by allowing optimal initial states to be determined along with the time history of the controls. Exact control switch times and optimal initial conditions have been found for minimum-time repositioning maneuvers in which the robot was required to travel a specified distance. The STO algorithm is not limited to use with manipulators; it is applicable to any bang-bang system.

Journal ArticleDOI
TL;DR: In this article, the acceleration tracing orientation method (ATOM) is applied to both controllers and the disturbance observer cancels out the total sum of these terms and enables each joint to trace the acceleration command.
Abstract: The authors propose a novel approach to force and compliance control of multi-degree-of-freedom (DOF) robot manipulators. The acceleration tracing orientation method (ATOM) is applied to both controllers. The control law is described in the Cartesian space; however, the final command is the acceleration in the joint space. The interactive terms in each joint disturb and deteriorate the joint motion. The disturbance observer cancels out the total sum of these terms and enables each joint to trace the acceleration command. As a result, a robust control is possible in the force task. The testing of the proposed system in a three-DOF robot manipulator is discussed. >

Journal ArticleDOI
TL;DR: A mobile robot whose behavior is controlled by a structured hierarchical neural network and its learning algorithm is presented, which has four wheels and moves about freely with two motors.
Abstract: A mobile robot whose behavior is controlled by a structured hierarchical neural network and its learning algorithm is presented. The robot has four wheels and moves about freely with two motors. Twelve sensors are used to monitor internal conditions and environmental changes. These sensor signals are presented to the input layer of the network, and the output is used as motor control signals. The network model is divided into two subnetworks connected to each other by short-term memory units used to process time-dependent data. A robot can be taught behaviors by changing the patterns presented to it. For example, a group of robots were taught to play a cops-and-robbers game. Through training, the robots learned behaviors such as capture and escape. >

Proceedings ArticleDOI
C. Le Pape1
13 May 1990
TL;DR: The author advocates a mixed strategy, allowing robots to make and execute individual plans as well as to connect with a central task planner and scheduler when appropriate.
Abstract: Task planning and scheduling techniques developed as part of a project whose goal is to control the operations of many robots in the same environment are presented. Centralized approaches allow task allocation to be improved. However, they are not appropriate for coordinating the actions of multiple mobile robots in a dynamic environment where unforeseeable events occur. Consequently, the author advocates a mixed strategy, allowing robots to make and execute individual plans as well as to connect with a central task planner and scheduler when appropriate. The author first presents individual planning techniques. Then he describes a framework allowing robots to exchange information with a central system able to optimize task allocation. >

Proceedings ArticleDOI
03 Jul 1990
TL;DR: The authors suggest to divide the cooperation into two types, active and nonactive according to the setting goal of the system, and in nonactive cooperation there must be 'modest cooperation' to prevent any collision of resource access by the robots.
Abstract: The paper proposes basic concepts of cooperation of multiple autonomous mobile robots, The authors suggest to divide the cooperation into two types, active and nonactive according to the setting goal of the system. And in nonactive cooperation there must be 'modest cooperation' to prevent any collision of resource access by the robots. The way to design multiple robots system is also discussed. >

Journal ArticleDOI
TL;DR: This work investigates error detection and recovery (EDR) strategies, and describes techniques for planning multi-step EDR strat egies in the presence of uncertainty.
Abstract: Robots must plan and execute tasks in the presence of uncer tainty. Uncertainty arises from sensing errors, control errors, and the geometry of the environment. By employing a com bined strategy offorce and position control, a robot program mer can often guarantee reaching the desired final configura tion from all the likely initial configurations. Such motion strategies permit robots to carry out tasks in the presence of significant uncertainty. However, compliant motion strategies are very difficult for humans to specify. For this reason we have been working on the automatic synthesis of motion strategies for robots. In previous work (Donald 1988b; 1989), we presented a framework for computing one-step motion strategies that are guaranteed to succeed in the presence of all three kinds of uncertainty. The motion strategies comprise sensor-based gross motions, compliant motions, and simple pushing motions.However, it is not always possible to find plans that are guaranteed to succeed. For example, if tole...

Proceedings ArticleDOI
13 May 1990
TL;DR: A path planner and an execution monitoring planner that will enable the rover to navigate to its various destinations safely and correctly while detecting and avoiding hazards are described, and an overview of the complete architecture is given.
Abstract: A path planner and an execution monitoring planner that will enable the rover to navigate to its various destinations safely and correctly while detecting and avoiding hazards are described. An overview of the complete architecture is given. Implementation and testbeds are described. The robot can detect unforeseen obstacles and take appropriate action. This includes having the rover back away from the hazard and mark the area as untraversable in the rover's internal map. The experiments have consisted of paths roughly 20 m in length. The architecture works with a large variety of rover configurations with different kinematic constraints. >

Proceedings ArticleDOI
13 May 1990
TL;DR: An algorithm is presented for the computation of path-constrained time-optimal motions of robotic manipulators exploring the nature of so-called critical points and critical arcs, which makes this algorithm robust near the switching points, which are potential points of failure in the other methods.
Abstract: An algorithm is presented for the computation of path-constrained time-optimal motions of robotic manipulators exploring the nature of so-called critical points and critical arcs. At critical points the reflected inertia at one of the joints is zero, and the feasible acceleration range at the velocity limit is not unique. Time-optimal motions along critical arcs may be singular in the sense that the acceleration is neither maximum nor minimum. This is in contrast to existing motion optimization methods along specified paths which assume maximum acceleration or deceleration at all times. The consideration of critical arcs makes this algorithm robust near the switching points, which are potential points of failure in the other methods. Critical points can be anticipated along the path by mapping the locus of critical arcs to the position space. Examples are presented to demonstrate the algorithm and the existence of singular critical arcs. >