James E. Bobrow

Time-optimal control of robotic manipulators along specified paths

The minimum-time manipulator control problem is solved for the case when the path is specified and the actuator torque limitations are known. The optimal open-loop torques are found, and a method is given for implementing these torques with a conventional linear feedback control system. The algorithm allows bounds on the torques that may be arbitrary functions of the joint angles and angular velocities. This method is valid for any path and orientation of the end- effector that is specified. The algorithm can be used for any manipulator that has rigid links, known dynamic equations of motion, and joint angles that can be determined at a given position on the path.

Optimizing Compliant, Model-Based Robotic Assistance to Promote Neurorehabilitation

Based on evidence from recent experiments in motor learning and neurorehabilitation, we hypothesize that three desirable features for a controller for robot-aided movement training following stroke are high mechanical compliance, the ability to assist patients in completing desired movements, and the ability to provide only the minimum assistance necessary. This paper presents a novel controller that successfully exhibits these characteristics. The controller uses a standard model-based, adaptive control approach in order to learn the patients abilities and assist in completing movements while remaining compliant. Assistance-as-needed is achieved by adding a novel force reducing term to the adaptive control law, which decays the force output from the robot when errors in task execution are small. Several tests are presented using the upper extremity robotic therapy device named Pneu-WREX to evaluate the performance of the adaptive, ldquoassist-as-neededrdquo controller with people who have suffered a stroke. The results of these experiments illustrate the ldquoslackingrdquo behavior of human motor control: given the opportunity, the human patient will reduce his or her output, letting the robotic device do the work for it. The experiments also demonstrate how including the ldquoassist-as-neededrdquo modification in the controller increases participation from the motor system.

Optimal robot plant planning using the minimum-time criterion

A path planning technique is presented which produces time-optimal manipulator motions in a workspace containing obstacles. The full nonlinear equations of motion are used in conjunction with the actuator limitations to produce optimal trajectories. The Cartesian path of the manipulator is represented with B-spline polynomials, and the shape of this path is varied in a manner that minimizes the traversal time. Obstacle avoidance constraints are included in the problem through the use of distance functions. In addition to computing the optimal path, the time-optimal open-loop joint forces and corresponding joint displacements are obtained as functions of time. The examples presented show a reduction in the time required for typical motions. >

A Lie group formulation of robot dynamics

In this article we present a unified geometric treatment of robot dynamics. Using standard ideas from Lie groups and Rieman nian geometry, we formulate the equations of motion for an open chain manipulator both recursively and in closed form. The recursive formulation leads to an O(n) algorithm that ex presses the dynamics entirely in terms of coordinate-free Lie algebraic operations. The Lagrangian formulation also ex presses the dynamics in terms of these Lie algebraic operations and leads to a particularly simple set of closed-form equations, in which the kinematic and inertial parameters appear explic itly and independently of each other. The geometric approach permits a high-level, coordinate-free view of robot dynamics that shows explicitly some of the connections with the larger body of work in mathematics and physics. At the same time the resulting equations are shown to be computationally ef fective and easily differentiated and factored with respect to any of the robot parameters. This latter feature makes the ge ometric formulation attractive for applications such as robot design and calibration, motion optimization, and optimal control, where analytic gradients involving the dynamics are required.

A Robot and Control Algorithm That Can Synchronously Assist in Naturalistic Motion During Body-Weight-Supported Gait Training Following Neurologic Injury

Locomotor training using body weight support on a treadmill and manual assistance is a promising rehabilitation technique following neurological injuries, such as spinal cord injury (SCI) and stroke. Previous robots that automate this technique impose constraints on naturalistic walking due to their kinematic structure, and are typically operated in a stiff mode, limiting the ability of the patient or human trainer to influence the stepping pattern. We developed a pneumatic gait training robot that allows for a full range of natural motion of the legs and pelvis during treadmill walking, and provides compliant assistance. However, we observed an unexpected consequence of the devices compliance: unimpaired and SCI individuals invariably began walking out-of-phase with the device. Thus, the robot perturbed rather than assisted stepping. To address this problem, we developed a novel algorithm that synchronizes the device in real-time to the actual motion of the individual by sensing the state error and adjusting the replay timing to reduce this error. This paper describes data from experiments with individuals with SCI that demonstrate the effectiveness of the synchronization algorithm, and the potential of the device for relieving the trainers of strenuous work while maintaining naturalistic stepping.

Modeling, identification, and control of a pneumatically actuated, force controllable robot

Focuses on modeling and control of a light-weight and inexpensive pneumatic robot that can be used for position tracking and for end-effector force control. Unlike many previous controllers, our approach more fully accounts for the nonlinear dynamic properties of pneumatic systems such as servovalve flow characteristics and the thermodynamic properties of air compressed in a cylinder. We show with theory and experiments that pneumatic actuators can rival the performance of more common electric actuators. Our pneumatic robot is controlled by extending existing manipulator control algorithms to handle the nonlinear flow and compressibility of air. The control approach uses the triangular form of the coupled rigid body and air flow dynamics to establish path tracking. In addition to the trajectory tracking control law, a hybrid position/force control algorithm is developed. The experimental results indicate that the tip forces on the robot can be controlled without the need for an expensive force/torque sensor usually required by electric motors driven systems.

NC machine tool path generation from CSG part representations

Abstract Recent improvements in geometric modelling systems have led to the need for more reliable and highly automated software for machine tool path generation. Current machining algorithms require that any part geometric information which cannot be determined from the modelling system be supplied by the user. Much geometric information is needed if the model used to represent the part is incomplete. This is the case with many conventional boundary representation systems. However, this information can easily be determined automatically if a solid modelling system is used. This paper presents a method for generating numerically-controlled milling machine tool paths directly from constructive solid geometry part representations. The algorithm requires less user interaction than APT boundary representation methods. A wide variety of parts may be machined using standard torus (bull) ended milling cutters. The algorithm is computationally efficient, and requires iteration only on portions of the part where gouging may occur.

Tools for understanding and optimizing robotic gait training

This article reviews several tools we have developed to improve the understanding of locomotor training following spinal cord injury (SCI), with a view toward implementing locomotor training with robotic devices. We have developed (1) a small-scale robotic device that allows testing of locomotor training techniques in rodent models, (2) an instrumentation system that measures the forces and motions used by experienced human therapists as they manually assist leg movement during locomotor training, (3) a powerful, lightweight leg robot that allows investigation of motor adaptation during stepping in response to force-field perturbations, and (4) computational models for locomotor training. Results from the initial use of these tools suggest that an optimal gait-training robot will minimize disruptive sensory input, facilitate appropriate sensory input and gait mechanics, and intelligently grade and time its assistance. Currently, we are developing a pneumatic robot designed to meet these specifications as it assists leg and pelvic motion of people with SCI.

Accurate Sliding-Mode Control of Pneumatic Systems Using Low-Cost Solenoid Valves

A control law is developed for an inexpensive pneumatic motion control system using four solenoid on/off valves and a position feedback sensor. A sliding-mode approach is used, which is well known for its tolerance for system uncertainties. In contrast to previous control laws, our approach does not use pulsewidth modulation. The control law has an energy-saving mode that saves electrical power, reduces chattering, and prolongs the valves life. Our simulation and experimental results show that the proposed tracking control law performs very well with good tracking and relatively low steady-state position errors

A direct minimization approach for obtaining the distance between convex polyhedra

Computational methods used for the automatic generation of robot paths must be fully developed if truly automated manu facturing systems are to become a reality. An important requirement for determining feasible robot paths is the ability to compute the distance between the various elements of the robot and the workspace fixtures, jigs, and machinery. In this research, it is assumed that the robot and workspace solid geometry are represented as a collection of convex polyhe drons, and an efficient numerical algorithm for determining the minimum distance between two such polyhedrons is presented. In addition to determining the minimum distance between solids, the algorithm can also be used to efficiently ascertain whether a collision has occurred. The numerical technique presented uses a sequence of constrained minimizations to obtain the closest three-dimen sional points on any two solid objects. Computational effi ciency is achieved with the algorithm presented because only the collection of planes (points and normals) which define the solids are used for the analysis. The bounding lines and vertices do not need to be explicitly calculated during the minimization procedure. The algorithm uses a direct ap proach for minimizing the nonlinear distance function which generates a sequence of search directions along the surfaces of the objects to obtain the global minimum. An extensive set of numerical tests are used to demonstrate the performance of the algorithm.