An analogy between the dynamics of a cart-pole system and vehicle rollover dynamics is used to derive a controller for tipping up and stabilizing a planar model of a passenger vehicle near rollover by controlling lateral tire friction forces. The controller is based on a previously published controller for stabilizing a cart-pole using partial feedback linearization and energy shaping. A necessary condition for tip-up is given based on the surface friction coefficient and the location of the vehicle center of gravity (c.g.). A multi-body vehicle model with suspension is presented in the form of the robotic manipulator equations. Simulation results are presented demonstrating the effect of friction and suspension properties on the tip-up problem.

This paper describes a robotic-arm exoskeleton that uses a parallel mechanism inspired by the human forearm to allow naturalistic shoulder movements. The mechanism can produce large forces through a substantial portion of the range of motion (RoM) of the human arm while remaining lightweight. This paper describes the optimization of the exoskeleton's torque capabilities by the modification of the key geometric design parameters.

This paper describes Newton and quasi-Newton optimization algorithms for dynamics-based robot movement generation. The robots that we consider are modeled as rigid multibody systems containing multiple closed loops, active and passive joints, and redundant actuators and sensors. While one can, in principle, always derive in analytic form the equations of motion for such systems, the ensuing complexity, both numeric and symbolic, of the equations makes classical optimization-based movement-generation schemes impractical for all but the simplest of systems. In particular, numerically approximating the gradient and Hessian often leads to ill-conditioning and poor convergence behavior. We show in this paper that, by extending (to the general class of systems described above) a Lie theoretic formulation of the equations of motion originally developed for serial chains, it is possible to recursively evaluate the dynamic equations, the analytic gradient, and even the Hessian for a number of physically plausible objective functions. We show through several case studies that, with exact gradient and Hessian information, descent-based optimization methods can be forged into an effective and reliable tool for generating physically natural robot movements.

The goal of this research was to develop a general approach for the generation of motions for robots that make and break contact with the ground, such as hopping, walking, or tumbling robots. We first develop a general contact model and show how to smooth the forces arising from this contact to make them C/sup 1/ functions of the state. This is essential for our motion generation algorithm, which relies on the solution of an optimal control problem for different phases of the motion. We apply our approach to the generation of motion primitives to a simple experimental robot that is capable of producing hand-stands and tumbling.

We investigate approaches to balance control of an under-actuated robot. The robot is similar in structure to the Acrobot, but it is actuated with a pneumatic cylinder rather than an electric motor, and it is capable of hopping. Regions of attraction of the control system are studied, and two methods are presented that increase the size of this region. One is a different mechanical design, and the other is a more robust control approach based on H/sub /spl infin// methods. The result is a much improved balance controller for a hopping robot.

We present a practical method for finding obstacle free minimum-time motions for manipulators subject to the bounds of velocity-dependent actuator forces. The optimal motion planning problem is converted into a finite dimensional nonlinear programming by means of parameter optimizations with quintic B-splines. We introduce the concept of the minimum-overload trajectories in which the motion time is specified to be faster than the motors can handle, and the actuator overloads are minimized during the motion. By successive searches for the minimum-overload trajectories, the minimum-time motions are determined for a spatial 6-link manipulator without simplifying any of the kinematic, dynamic or geometric properties of the manipulator or the obstacles. In the resultant minimum-time motions, almost all of the joint actuators are close to saturation during the motions.

We describe a technique to generate motion segments, for a Luxo hopping robot by solving an optimal control problem using exact analytic gradients of the cost function. Analytic gradients are required to solve the optimal control problem reliably; obtaining them is made possible by a hybrid recursive algorithm that calculates the system dynamics and its exact derivatives. Each motion segment, or primitive, is determined by a unique cost function, so that a complete movement is created from the robot model, the customized optimal control problem, and the objective function, without need for detailed path planning by a person. Once the primitives are generated, they are used to control an experimental robot as it performs the motion in the primitive. The problem formulation takes into account limitations such as torque and velocity limits of the motors on the experimental robot.

We examine a method to control the stepping motion of a paralyzed person suspended on a treadmill using a robot attached to the torso and hips. A leg swing motion is created by moving the hips without contact with the legs. The problem is formulated as an optimal control problem for an underactuated articulated chain. The optimal control problem is converted into a discrete parameter optimization and an efficient gradient-based algorithm is used to solve it. Motion capture data from a human subject is compared to the results from the dynamic motion optimization. Our results indicate that it is possible for the robot to create a gait for the paralyzed person that is close to that of an unimpaired subject.

Although the dynamic equations of motion of open-chained robot systems are well known, they are seldom taken into account during the planning of motions. In this work, we show that the dynamics of a robot can be used to produce motions that extend the payload capability beyond the limit set by traditional methods. In particular, we develop a point-to-point weightlifting motion planner for open-chained robots. The governing optimal control problem is converted into a direct, SQP parameter optimization in which the gradient is determined analytically. The joint trajectories are defined by B-spline polynomials along with a time-scale factor. The algorithm is applied to a Puma 762 robot, with its physical limitations incorporated into the formulation. The torque limits are formulated as soft constraints added into the objective function while the position and velocity limits are formulated as hard, linear inequality constraints, on the parameters. The solutions obtained with our algorithm extend the robot's payload capability while reducing the joint torques. Interestingly, nearly all the trajectories found pass through singular configurations, where large internal forces from the robot are applied to the payload and little torque is needed from the motors.

In this paper we describe a technique to generate realistic human movement, specifically platform dives, by solving an optimal control problem requiring little a priori information. Solving the optimal control problem reliably requires computing exact analytic gradients of the objective function, which is made possible by a hybrid recursive algorithm that calculates the dynamics of the system. This algorithm is formulated with Lie algebra techniques and matrix exponentials, resulting in equations that are easily differentiable. This quality is essential when solving ill-conditioned systems such as the diver. Also, the importance of initial conditions in light of the constant angular momentum constraint is discussed.

In this paper we develop a point-to-point weight lifting motion planner for open-chained robots. The joint trajectories are defined by B-spline polynomials along with a time-scale factor. Physical limitations of a Puma 762 robot are incorporated into the formulation. The torque limits are formulated as a penalty function (soft constraints) added into the objective function while the position and velocity limits are formulated as linear inequalities (hard constraints). The problem is solved by a gradient-based optimization method in which the gradient is determined analytically. Not only does the optimal path extend the payload capability, but also reduces the joint torques by passing through singular configurations.

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.

In this article we examine the solution of minimum effort optimal control problems for open-chain manipulators. A local solution to the optimal control problem is determined by a constrained parameter optimization over a set of B-spline basis functions. We demonstrate that the parameter optimization formulation of the problem is numerically ill-conditioned and that it is therefore essential to include analytic, or exact, gradients of the objective function and the constraints in order to guarantee a solution. A main contribution of our approach is an explicit expression for these gradients for general serial chains. Our formulation relies on the use of matrix exponentials for the manipulator kinematics, dynamics, and task constraints. Several examples are presented that demonstrate the power and flexibility of our approach.

This research 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.

In this article we develop a geometric formulation of operational space dynamics and control based on standard results from the theory of Lie groups and Lie algebras. Beginning with the coordinate invariant formulation of robot dynamics presented in Park et al. (1995), we extend these results to develop the equations of motion in operational space coordinates. The resulting equations can be expressed in a recursive fashion for applications requiring computationally efficient algorithms, or can be expressed in terms of simple matrix factors in which the robot parameters appear transparently for applications involving high-level manipulation of the equations of motion. Further, our formulation of operational space dynamics and control is not bound to any specific choice of local reference frames to carry out the dynamic analysis.

In this paper we compute approximate minimum effort motions for open chains by solving a finite dimensional minimization problem using B-splines for the path representation. We begin by deriving the gradient of the recursive Newton-Euler dynamics formulation with respect to the parameters of a curve defining the motion, where the kinematics are expressed via the product of matrix exponentials. We then use this gradient to solve joint torque minimization problems for spatial open chains. The advantage of our approach is that the gradients are computed for each local frame recursively, therefore sharing the same efficiency advantages as the original recursive algorithm, and also can be computed for any spatial open chain. The optimization approach is applied to several open chains where minimum effort paths are found.

This article addresses the problem of designing a robotic mechanism such that it end-effector frame comes closest to reaching a set of desired goal frames. We formulate this as an optimization problem, in which the kinematic parameters are selected to minimize the total distance between the end-effector frame and each goal frame. The objective function is defined in terms of a class of distance metrics on the rigid body motions that are invariant with respect to choice of fixed reference frame. A main contribution of this article is an explicit expression for the gradient of this objective function with respect to the kinematic parameters. With this analytic gradient, efficient optimization algorithms can now be developed for the design of general spatial mechanisms. Our design methodology is illustrated with an example involving the base positioning of two cooperating robots.

We present, using standard ideas from Lie groups and Riemannian geometry, a computationally efficient recursive algorithm for the inverse dynamics of an open-chain manipulator. Our algorithm bears close resemblance to Featherstone's (1991) approach, but is derived entirely from Lie theoretic concepts and definitions. Our geometric approach permits a high-level view of robot dynamics that emphasizes the coordinate-free aspects of the equations of motion while preserving the computational efficiency of recursive algorithms.>

The authors formulate the time-optimal control problem for general robotic systems and show that the required maximum (or minimum) value of the path acceleration is the solution of a linear programming problem. The fact that such a solution is an extreme point of the set of feasible solutions makes it possible to determine the minimum number of actuators and internal forces that must be saturated during the time-optimal movement. Specifically, it is proved that, if the dynamics of a general robot system are defined by n coordinates, m differential constraint equations, and p actuators, then some combination of at least L=m+p+1-n of the actuators and internal constraint forces is saturated during a time-optimal movement of the system along a prescribed path. The result applies to general class of dynamic systems with both holonomic and non-holonomic constraints.>

It is proved that if the dynamics of a general robot system are defined by n coordinates, m differential constraint equations, and p actuators, then some combination of at least L=m+p+1-n of the actuators and internal constraint forces are saturated during a time-optimal movement of the system along a prescribed path. The result applies to a general class of dynamic systems with both holonomic and nonholonomic constraints.>

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.>