Path Coordination Planning and Control in Robotic Material Handling and Processing

This chapter presents a unified approach to coordination planning and control for robotic position and orientation trajectories in Cartesian space and its applications in robotic material handling and processing. The unified treatment of the end-effector positions and orientations is based on the robot pose ruled surface concept and used in trajectory interpolations. The focus of this chapter is on the determination and control of the instantaneous change laws of position and orientation, i.e., the generation and control of trajectories with good kinematics and dynamics performances along such trajectories. The coordination planning and control is implemented through controlling the motion laws of two end points of the orientation vector and calculating the coordinates of instantaneous corresponding points. The simulation and experiment in robotic surface profiling/finishing processes are presented to verify the feasibility of the proposed approach and demonstrate the capabilities of planning and control models. Keywords: Robot pose ruled surface, Unified approach, Trajectory planning and control, Off-line programming, Robotics polishin

Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots

In this dissertation, we develop an efficient method of generating minimal jerk trajectories for redundant robots in trajectory following problems. We show that high jerk is a local phenomenon, and therefore focus on optimizing regions of high jerk that occur when using traditional trajectory generation methods. The optimal trajectory is shown to be located on the foliation of self-motion manifolds, and this property is exploited to express the problem as a minimal dimension Bolza optimal control problem. A numerical algorithm based on ideas from pseudo-spectral optimization methods is proposed and applied to two example planar robot structures with two redundant degrees of freedom. When compared with existing trajectory generation methods, the proposed algorithm reduces the integral jerk of the examples by 75% and 13%. Peak jerk is reduced by 98% and 33%. Finally a real time controller is proposed to accurately track the planned trajectory given real-time measurements of the tool-tip\u27s following error

Time-Optimal Trajectory Generation for 5-Axis On-the-Fly Laser Drilling

On-the-fly laser drilling provides a highly productive method for producing hole clusters (pre-defined groups of holes to be laser drilled) on freeform surfaced parts, such as gas turbine combustion chambers. Although the process is capable of achieving high throughputs, current machine tool controllers are not equipped with appropriate trajectory functions that can take full advantage of the achievable laser drilling speeds. While the problem of contour following has received previous attention in time-optimal trajectory generation literature, on-the-fly laser drilling presents different technological requirements, needing a different kind of trajectory optimization solution, which has not been studied prior to this thesis. The duration between consecutive hole locations, which corresponds to the laser pulsing period, has to be kept constant, ideally throughout the part program. However, the toolpath between the holes is not fixed and can be optimized to enable the shortest possible segment duration. To preserve the dynamic beam positioning accuracy and avoid inducing excessive vibrations on the laser optics, the axis velocity, acceleration, and jerk profiles need to be limited. Furthermore, to ensure that hole elongation does not violate the given part tolerances, the orthogonal component of part velocity relative to the laser beam needs to be capped. All of these requirements have been fulfilled in the trajectory optimization algorithm developed in this thesis. The hole locations are provided as pre-programmed sequences by the Computer Aided Design/Manufacturing software (CAD/CAM). A time-optimized trajectory for each sequence is planned through a series of time-scaling and unconstrained optimization operations, which guarantees a feasible solution. The initial guess for this algorithm is obtained by minimizing the integral square of the fourth time derivative (i.e. ‘snap’). The optimized trajectories for each cluster are then joined together or looped onto themselves (for repeated laser shots) using a time-optimized looping/stitching (optimized/smooth toolpath to repeat/loop a cluster or connect/stitch between consecutive clusters) algorithm. This algorithm also minimizes the integral square of jerk in the faster axes. The effectiveness of the overall solution has been demonstrated in simulations and preliminary experimental results for on-the-fly laser drilling of a hole pattern for a gas turbine combustion chamber panel. It is shown that the developed algorithm improves the cycle time for a single pass by at least 6% (from kinematic analysis of the motion duration), and more importantly reduces the integral square of jerk by 56%, which would enable the process speed to be pushed up further

Time-Optimal Trajectory Generation and Way-Point Sequencing for 5-Axis Laser Drilling

Laser drilling provides a highly productive method for producing arrays of holes on planar and freeform shaped components. Industrial applications include fuel injection nozzles, printed circuit boards (PCB’s), inkjet printer heads, pinholes and slits for scientific instrumentation, high-resolution circuitry, sensors, fiber-optic interconnects, medical devices, and gas turbine combustion chamber panels. This thesis deals with time-optimal trajectory planning for two mainstream laser drilling methods: on-the-fly drilling and percussion drilling, which are used in the aerospace industry. The research has been conducted in collaboration with the Canadian aero-engine producer, Pratt & Whitney Canada (P&WC). The algorithms developed have been tested in a target application involving the laser drilling of cooling hole arrays on gas turbine engine combustion chamber panels. On-the-fly drilling is an operation in which each hole receives one low powered shot at a time while the workpiece is in motion, and the beam focal point is continuously proceeding to the next hole location. The positioning sequence repeats itself until all holes are gradually opened up in small increments. Each hole location has ample time to cool down before the next shot is received. Thus, this process can yield favorable material properties in terms of preserving the desired crystal structure, and also hole quality in terms of dimensional (size) and form (shape) accuracy, due to the reduction of local thermal loading. However, there is no existing trajectory planner, in industry, or in literature, capable of generating time-optimized positioning trajectories for on-the-fly laser drilling. This thesis studies this problem and presents a new algorithm, capable of handling 5 degree-of-freedom (axis) positioning capability. The ability to generate spline-based smooth trajectories is integrated within a Traveling Salesman Problem (TSP) type sequencing algorithm. The sequencing algorithm optimizes both the order of the waypoints (i.e., hole locations) and also the timing levels in between, which affect the temporal (time-dependent) nature of the motions commanded to the laser drilling machine’s actuators. Furthermore, the duration between consecutive holes has to be an integer multiple of the laser pulsing period, considering a machine configuration in which the laser is firing at a constant frequency, and unused pulses are diverted away using a quick shutter. It is shown that the proposed algorithm is capable of generating 17-25% reduction in the beam positioning time spent during a manufacturing cycle, compared to some of the contemporary practices in industry. 17% reduction in the vibrations induced onto the laser optics is also observed, which helps prevent downtime due to the optics hardware gradually losing alignment. The second type of laser drilling operation for which optimized 5-axis trajectory planning has been developed is percussion drilling. In this process, a series of pulses are sent to each hole while the part is stationary. Once the hole is completely opened up, then positioning to the next hole proceeds. While percussion drilling is less advantageous in terms of local thermal loading and achievable part quality, it is used extensively in industry; due to its simplicity of automation compared to on-the-fly drilling. Thus, a TSP-style trajectory planning algorithm has also been developed for percussion laser drilling. The novelty, in this case, is concurrent planning of 5-axis time-optimal point-to-point movements within the sequencing algorithm, and direct minimization of the total travel time, rather than just distance (in two Cartesian axes); as is the method for which significant portion of TSP solvers and trajectory planners in literature have been developed. Compared to currently applied methods at P&WC, 32-36% reduction in the beam positioning time has been achieved. Also, 39-45% reduction in the peak magnitude of vibration has been realized. Limited benchmarking with state-of-the-art TSP solvers from combinatorial mathematics, considering only 2-axis Euclidean distance as the objective function, indicate that the proposed sequencing algorithm for percussion drilling is sub-optimal by 9-12%. Thus, it can still use further improvement in future research. Nevertheless, the two trajectory planners that have been developed in this thesis for on-the-fly drilling and percussion drilling have experimentally demonstrated very promising improvements in terms of motion time and smoothness. As more advanced Computer Numerical Control (CNC) systems and laser control electronics with deterministic execution and rapid synchronization capability become available, such algorithms are expected to facilitate significant production gains in laser drilling processes used in different industries

Smooth and Time-Optimal Trajectory Generation for High Speed Machine Tools

In machining complex dies, molds, aerospace and automotive parts, or biomedical components, it is crucial to minimize the cycle time, which reduces costs, while preserving the quality and tolerance integrity of the part being produced. To meet the demands for high quality finishes and low production costs in machining parts with complex geometry, computer numerical control (CNC) machine tools must be equipped with spline interpolation, feedrate modulation, and feedrate optimization capabilities. This thesis presents the development of novel trajectory generation algorithms for Non Uniform Rational B-Spline (NURBS) toolpaths that can be implemented on new low-cost CNC's, as well as, in conjunction with existing CNC's. In order to minimize feedrate fluctuations during the interpolation of NURBS toolpaths, the concept of the feed correction polynomial is applied. Feedrate fluctuations are reduced from around 40 % for natural interpolation to 0.1 % for interpolation with feed correction. Excessive acceleration and jerk in the axes are also avoided. To generate jerk-limited feed motion profiles for long segmented toolpaths, a generalized framework for feedrate modulation, based on the S-curve function, is presented. Kinematic compatibility conditions are derived to ensure that the position, velocity, and acceleration profiles are continuous and that the jerk is limited in all axes. This framework serves as the foundation for the proposed heuristic feedrate optimization strategy in this thesis. Using analytically derived kinematic compatibility equations and an efficient bisection search algorithm, the command feedrate for each segment is maximized. Feasible solutions must satisfy the optimization constraints on the velocity, control signal (i.e. actuation torque), and jerk in each axis throughout the trajectory. The maximized feedrates are used to generate near-optimal feed profiles that have shorter cycle times, approximately 13-26% faster than the feed profiles obtained using the worst-case curvature approach, which is widely used in industrial CNC interpolators. The effectiveness of the NURBS interpolation, feedrate modulation and feedrate optimization techniques has been verified in 3-axis machining experiments of a biomedical implant