Mirosław Galicki

The Planning of Robotic Optimal Motions in the Presence of Obstacles

An approach to the planning of optimal robotic motions in the pres ence of obstacles is proposed. It is based on the use of nonclassical formulation of Pontryagins maximum principle, which makes it possible to handle efficiently the state constraints resulting from the robotic tasks to be performed. The convergence properties of the algorithm are examined. A computer example involving a pla nar redundant manipulator of three revolute kinematic pairs, which performs two tasks in a two-dimensional work space including ob stacles, is given. A comparison of the proposed approach with the well-known method of penalty function is made.

Designing and optimization of parameters of delta-4 parallel manipulator for a given workspace

In the paper, the algorithm of designing some geometrical parameters of a Delta parallel manipulator has been described. The manipulator is to work in a specified workspace, which is given as a set of points. The first step of the algorithm seeks the possible solutions, and because there are an infinite number of them, the objective of the second step is to limit the number by an optimization. Owing to this, it is possible to find parameters of the manipulator, whose workspace contains the specified points.

Finite-time control of robotic manipulators

This work offers the solution at the control feed-back level of the accurate trajectory tracking subject to finite-time convergence. Dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory. Based on the suitably defined non-singular terminal sliding vector variable and the Lyapunov stability theory, we propose a class of absolutely continuous robust controllers which seem to be effective in counteracting both uncertain dynamics and unbounded disturbances. The numerical simulation results carried out for a robotic manipulator consisting of two revolute kinematic pairs operating in a two-dimensional joint space illustrate performance of the proposed controllers.

Inverse Kinematics Solution to Mobile Manipulators

This paper presents the solution at the control feedback level to the inverse kinematics problem for mobile manipulators operating in both obstacle-free task spaces and task spaces including obstacles. Using the Frechet differential of a certain criterion function, the fully specified system of algebraic and differential equations of the minimal amount has been obtained to solve the inverse kinematics problem. Based on the Lyapunov stability theory, a full differential form generating the mobile manipulator trajectory, whose attractor attained in a finite time fulfills the above system of algebraic and differential equations, has been derived. The problem of both singularity and collision avoidance is solved here based on a concept of (local) velocity perturbation which results in continuous mobile manipulator velocities near singularities and obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic wheel and a holonomic manipulator of two revolute kinematic pairs, operating in both an obstacle-free task space and task space including obstacles, illustrate the trajectory performance of the proposed solution scheme.

Task space control of mobile manipulators

This study offers the solution of the end-effector trajectory tracking problem subject to state constraints, suitably transformed into control-dependent ones, for mobile manipulators. Based on the Lyapunov stability theory, a class of controllers fulfilling the above constraints and generating the mobile manipulator trajectory with (instantaneous) minimal energy, is proposed. The problem of manipulability enforcement is solved here based on an exterior penalty function approach which results in continuous mobile manipulator controls even near boundaries of state constraints. The numerical simulation results carried out for a mobile manipulator consisting of a non-holonomic unicycle and a holonomic manipulator of two revolute kinematic pairs, operating in a two-dimensional task space, illustrate the performance of the proposed controllers.

Motion control of robotic manipulators in task space

This paper addresses the problem of position control of robotic manipulators in the task space. A computationally simple class of task space regulators consisting of a transpose Jacobian controller plus an integral term including a function of task space position error, is proposed. These regulators require very little information regarding the robot dynamic equations or the payload and ensure (based on the Lyapunov stability theory) that the task space position error is asymptotically convergent. The performance of the proposed control strategy is illustrated through computer simulation for a direct-drive arm of a SCARA type manipulator.

Real-Time Trajectory Generation for Redundant Manipulators with Path Constraints

This paper addresses the problem of tracking a prescribed geometric path by the end effector of a kinematically redundant manipulator at the control loop level. The constraints imposed on the robot actuator controls are taken into account. The Lyapunov stability theory and/or the calculus of variations is used to derive the control scheme. Through the use of an exterior penalty function approach, an additional objective to be fulfilled by the robot, thatis, collisionavoidance of the manipulator links with obstacles, is ensured. The extensive computer simulation results illustrate the trajectory performance of the proposed control scheme for a geometric end effector path given in both an obstacle-free work space and a work space including obstacles.

Finite-time trajectory tracking control in a task space of robotic manipulators

This work addresses the problem of the accurate task space control subject to finite-time convergence. Dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end-effector. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of absolutely continuous Jacobian transpose robust controllers, which seem to be effective in counteracting uncertain dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the end-effector trajectory. The numerical simulations carried out for a robotic manipulator of a SCARA type consisting of two revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers.

Design of parameters of parallel manipulators for a specified workspace

In this paper an algorithm for designing spatial parallel manipulator parameters for a given workspace has been presented. At the beginning, architecture has been chosen that describes a general parallel manipulator. The manipulator may possess any number of limbs, consisting of links connected by spherical, revolute or linear joints as well as actuators. The parameters, which will be determined, are the lengths of the links of kinematic chains, the coordinates of the fixing points of the chains to the platform and the base, and orientations of the revolute engines axes situated at the base. The workspace may be specified in the form of any shape in the space containing a set of points of known coordinates and the limits in which the geometrical parameters may vary. The algorithm does not determine the exact values of the parameters, but only their functions. It leads to the necessity for further research in order to optimise the solutions.

Time-optimal motions of robotic manipulators

An approach to planning time-optimal collision-free motions of robotic manipulators is presented. It is based on using a negative formulation of the Pontryagin Maximum Principle which handles efficiently various control and/or state constraints imposed on the manipulator motions, which arise naturally out of manipulator joint limits and obstacle avoidance. This approach becomes similar to that described by Weinreb and Bryson, as well as by Bryson and Ho if no state inequality constraints are imposed. In contrast to the penalty function method, the proposed algorithm does not require an initial admissible solution (i.e. an initial admissible trajectory) and finds manipulator trajectories with a smaller cost value than the penalty function approach. A computer example involving a planar redundant manipulator of three revolute kinematic pairs is included. The numerical results are compared with those obtained using an exterior penalty function method.