2 min read•july 25, 2024
Robots need to plan their movements carefully. Path planning maps out the route, while adds timing to create a smooth, feasible motion. This process involves interpolating between waypoints, smoothing the path, and considering the robot's physical limitations.
Various techniques help create optimal trajectories. These include , , and optimization methods. The goal is to balance smoothness, speed, energy efficiency, and safety while accounting for the robot's capabilities and the specific application requirements.
Path planning determines geometric route while trajectory generation creates time-parameterized path
Steps in trajectory generation:
Feasibility considerations account for robot's physical limitations (velocity and ) and
ensure continuity in position, velocity, and acceleration while minimizing jerk
adjusts trajectory based on constraints and optimizes for desired properties
Polynomial interpolation uses cubic polynomials for smooth transitions and quintic polynomials for continuous acceleration
Spline fitting employs for local control and smoothness and for complex curves
utilize control points for shaping trajectories and for evaluation
matches position and velocity at waypoints
assigns time values to waypoints ensuring consistent velocity profiles
Constraint satisfaction incorporates kinematic limits into interpolation and adjusts coefficients to meet dynamic constraints
minimize total time, reduce energy consumption, or maximize smoothness
Optimization techniques include for local optimization, for global search, and for real-time optimization
formulates trajectory generation as a convex problem using tools (, )
breaks down trajectory into subproblems using for optimal substructure
minimizes quadratic cost functions subject to linear constraints
incorporates obstacle avoidance and respects and
: smoother trajectories may take longer to execute while time-optimal trajectories may have abrupt changes
: optimal trajectories may push robot limits while feasible trajectories ensure safe execution
: slower movements often consume less energy while rapid movements may require more power
: real-time constraints may limit optimization while offline planning allows for more refined trajectories
: smoother trajectories often more robust to disturbances while optimal trajectories may be sensitive to model inaccuracies
: manufacturing balances precision vs throughput, mobile robots consider battery life vs task completion time, manipulation weighs force control vs speed of operation
Safety and human interaction: use slower, smoother trajectories while isolated industrial settings allow rapid movements