minPAs

MinPAs, short for Minimum Path Activations, is a framework used in robotics and motion planning to minimize the number of actuator activations required to complete a task. In this context, PAs stands for actuator activations or propulsion activation events, treated as discrete decisions within a plan. The central idea is to produce a feasible trajectory from a starting state to a goal while reducing the count or total cost of activations, which can correlate with energy use, wear, and noise.

The core problem can be described as a combinatorial optimization: given a robot model, a set of states, possible activations with associated costs, and environmental constraints, find a sequence of activations that achieves the desired objective while obeying dynamics and obstacle constraints. Typical formulations cast the problem as minimizing the sum of activation costs subject to kinematic or dynamic equations and collision avoidance. Variants may allow continuous control in combination with discrete activation decisions or use relaxations to enable tractable solution methods.

Algorithms for minPAs range from exact to heuristic. Exact approaches include mixed-integer linear programming (MILP) formulations and dynamic programming, which can guarantee optimality but may be computationally expensive for large systems. Heuristic and approximate methods employ greedy activation selection, graph-search techniques with activation-aware cost functions, or sparse optimization to encourage few activations while maintaining feasibility.

Applications span mobile robotics, aerial or legged robotics, and any domain where reducing actuator usage aligns with energy efficiency or long-term reliability. Related concepts include energy-aware planning, sparse optimization, and traditional motion planning. The field continues to explore trade-offs between activation minimization, task performance, and real-time planning requirements.