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An original method called the three-cubic method is proposed to generate online robot joint trajectories interpolating given position points with associated velocities. The method is based on an acceleration profile composed of three cubic polynomial segments, which ensure a zero acceleration at each intermediate point. Velocity and acceleration continuity is obtained, and this three-cubics combination allows the analytical solution to the minimum time trajectory problem under maximum velocity and acceleration constraints. Possible wandering is detected and can be overcome. Furthermore, the analytical solution to the minimum time trajectory problem leads to an online trajectory computation. [ABSTRACT FROM AUTHOR]

Studies the use of semi-infinite optimization techniques to control real-time collision-free trajectory. Reduction of an optimal control problem to be reduced to a finite-dimensional parameter-optimization problem; How the reduced problem can be solved; Reference to the case of a time-varying robot environment.

This article presents a method for real-time control of vehicle trajectory on a highway based on an on-board vision system using a single camera. The system has been designed to avoid damage (e.g., due to a sleepy driver). The method is based on the real-time extraction of the lateral vehicle location, which is used to determine the vehicle trajectory. Furthermore, the system is able to correct possible bad road tracking in order to have a complete autonomy. The whole system has been implemented on a single TMS320C50 DSP-based card. Reliable results have been obtained on the highway over several hundreds of kilometers at low and high speeds reaching more than 130 km/hr. [ABSTRACT FROM AUTHOR]

This article discusses the problem of tracking manipulator end-link trajectories passing through ordinary singularities. It is based on a method developed recently by Kieffer (1992), who suggested parameterizing the end-link trajectory with a parameter that is not time, and considering this parameter as a dependent variable. We show that this is equivalent to a kinematically redundant mechanism comprising the original nonredundant kinematic chain augmented by one more virtual link. The trajectory is actually mapped onto the joint space augmented by the parameter variable. Although the new mechanism performs only a "self-motion" tracking of the projected trajectory through regular points and ordinary singularities, the end-link of the real mechanism tracks the desired trajectory. Our solution is based on effective null space methods that have been widely applied to kinematically redundant manipulators. Asymptotic convergence of the tracking error to zero and stability is guaranteed through a closed-loop approach. [ABSTRACT FROM AUTHOR]

A new class of robust control algorithms is proposed for the trajectory following problem of a robot manipulator. It is shown that every proposed control can guarantee three kinds of global stability results based on the designer's choice: uniformly and ultimately bounded stability, asymptotic stability, and exponential stability. Exact knowledge of robot dynamics is not required except that unknown dynamics must be bounded in Euclidean norm by a second-order polynomial function with known coefficients. [ABSTRACT FROM AUTHOR]

We present a fast algorithm for solving the problem of the verification of a trajectory for a 6-DOF parallel manipulator with respect to its workspace: i.e., given two different postures for the end effector, is the straight line joining these two postures in the parameters space fully inside the workspace? This algorithm is based on the analysis of the algebraic inequalities describing the constraints on the workspace and provides a technique for computing those parts of the trajectory that lie outside the workspace. This method is exact if the orientation of the end effector is kept constant along the trajectory and approximate if the orientation is allowed to vary. [ABSTRACT FROM AUTHOR]

This article addresses the problem of time-optimal motions for a mobile platform in a planar environment. The platform has two nonsteerable, independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories between these configurations, assuming an unobstructed environment. Using Pontryagin's maximum principle (PMP), we formally demonstrate that all time-optimal motions of the platform for this problem occur for bang-bang controls on the wheels (at each instant, the acceleration on each wheel is at either its upper or its lower limit). The PMP, however, provides only the conditions necessary for time optimality. To find the time-optimal robot trajectories, we first parameterize the bang-bang trajectories using the switch times on the wheels (the times at which the wheel accelerations change sign). With this parameterization, we can fully search the robot trajectory space and find the switch times that will produce particular paths to a desired final configuration of the platform. We show numerically that robot trajectories with three switch times (two on one wheel and one on the other) can reach any position, while trajectories with four switch times can reach any configuration. By numerical comparison with other trajectories involving similar or greater numbers of switch times, we then identify the sets of time-optimal trajectories. These are uniquely defined using ranges of the parameters and consist of subsets of trajectories with three switch times (for the problem when the final orientation of the robot is not specified) or four switch times (when a full final configuration is specified). We conclude with a description of the use of the method for trajectory planning for one of our robots and discuss some comparisons of sample time-optimal paths with minimum length paths. [ABSTRACT FROM AUTHOR]

In on-line robot trajectory generation, a connecting polynomial is normally used to remove discontinuities in velocity and acceleration between adjacent path segments. This article presents a new technique for performing such transitions in which adjacent path segments are "blended" together, with excess acceleration being removed using an estimate of the initial path velocities. Because this method requires no advance knowledge of the path segments, it can handle situations where the paths are changing with time (as when tracking sensor or control inputs). The method can also be used to adjust the spatial shape of the transition curve (such as to have it pass around or through the "via point"), which may be necessary to handle constraints imposed by different types of manipulator tasks. When the blended paths are nonlinear, it is possible to set a tight bound on the resulting transition acceleration. The blend technique works directly for vector trajectories and can be modified to handle 3-D rotational trajectories. A simple trajectory generation algorithm is presented as an illustration. [ABSTRACT FROM AUTHOR]

In this study, global planning of a collision-free trajectory (simultaneous planning of geometric path and its time parameterization) involving potential functions and direct kinematic and dynamic equations of the manipulator is presented. This planning is based on using the necessary conditions of minimum for an integral type criterion. General transversality conditions corresponding to the boundary ones (resulting from the task to be performed) are derived. Thus, closed systems of boundary dependences fully specifying differential equations, which arise from the necessary conditions of extreme for the above criterion, are obtained. As a result, this system renders it possible to reduce the collision-free trajectory planning problem to a two-point boundary value problem. A numerical example involving a manipulator of three-revolute kinematic pairs of the Vth class is considered. [ABSTRACT FROM AUTHOR]

This article discusses a generalized method to produce standard foot trajectories for a quadruped walking vehicle having arbitrary reachable ranges and walking on uneven and inclined surfaces in random posture. The standard supporting foot trajectories are one of the most basic parameters for gait control, because the legs have to follow the trajectories as long as the irregular degree of terrain and posture conditions are maintained. The introduced method goes through the processes of (1) projection of the gait scheme on a horizontal plane, (2) definition of the effective searching areas, (3) selection of a crab-walking pattern between x and y types, (4) generation of the stroke contour maps, and (5) selection of the longest stroke and its existing areas. The validity of the proposed method is verified by several computer simulations. [ABSTRACT FROM AUTHOR]

Robot motion is commonly specified as a Cartesian trajectory of its end-effector. For executing the end-effector trajectory on-line, a look-ahead of a few points on the trajectory is used to generate the joint trajectories. This paper describes the construction of on-line cubic spline joint trajectories for a limited-point look-ahead on a specified end-effector trajectory, not necessarily Cartesian. An analytical derivation for the ideal number of look-ahead points on the end-effector trajectory for cubic spline interpolation is given. Experimental and simulation results of the on-line spline interpolation schemes show improved end-effector path tracking and smooth motion for a wide range of sampling rates on the effector trajectory. [ABSTRACT FROM AUTHOR]

Presents a form of trajectory control designed to embody the advantages of the polynomial approach, resulting from the creation of a method termed the cubic-quadratic-squared (CQCS) trajectory. Description of the CQCS trajectory calculation procedure; Deviation of the equations; Determination of maximum accelerations.

Posa M, Cantu C and Tedrake R (2014) A direct method for trajectory optimization of rigid bodies through contact. The International Journal of Robotics Research 33(1): 69-81. doi: 10.1177/0278364913506757 [ABSTRACT FROM AUTHOR]