Task and Motion Planning (Tamp)

Task and Motion Planning (TAMP) is a robotics planning approach that integrates high-level task planning with low-level motion planning — combining discrete symbolic reasoning about tasks with continuous geometric reasoning about robot motions, enabling robots to plan complex manipulation and navigation tasks in realistic environments.

What Is TAMP?

• Task Planning: High-level reasoning about what to do — which objects to manipulate, in what order.
• Motion Planning: Low-level reasoning about how to move — finding collision-free paths for robot.
• Integration: TAMP combines both — ensuring task plans are geometrically feasible.

Why TAMP?

• Task Planning Alone: Doesn't consider geometry — may generate infeasible plans.
• Example: "Pick up cup" — but cup is unreachable from current position.

• Motion Planning Alone: Doesn't reason about tasks — can't decide what to do.
• Example: Can plan path to cup, but doesn't know whether to pick it up or move around it.

• TAMP: Combines both — generates task plans that are geometrically feasible.

TAMP Components

• Symbolic State: Discrete facts about the world.
• on(block_A, table), holding(robot, cup), at(robot, location_1)

• Geometric State: Continuous configuration of objects and robot.
• Robot joint angles, object poses, obstacle positions.

• Symbolic Actions: High-level operations.
• pick(object), place(object, location), navigate(location)

• Motion Primitives: Low-level motions.
• Collision-free paths, grasping motions, placement motions.

TAMP Example: Table Setting

Task: Set table with plates and cups

High-Level Plan (Task Planning):
1. pick(plate1)
2. place(plate1, table_position1)
3. pick(cup1)
4. place(cup1, table_position2)
5. pick(plate2)
6. place(plate2, table_position3)
...

For each action, Motion Planning:
- pick(plate1):
  - Navigate to plate1 location
  - Compute grasp pose
  - Plan arm motion to grasp
  - Execute grasp

- place(plate1, table_position1):
  - Plan arm motion to placement pose
  - Ensure no collisions with table, other objects
  - Execute placement
  - Open gripper

Geometric Feasibility Checks:
- Is plate1 reachable from current robot position?
- Is table_position1 collision-free?
- Can robot navigate between locations?

TAMP Approaches

• Hierarchical: Plan tasks first, then plan motions.
• Fast but may generate infeasible task plans.
• Requires backtracking if motion planning fails.

• Integrated: Interleave task and motion planning.
• More robust but computationally expensive.
• Considers geometric constraints during task planning.

• Sampling-Based: Sample geometric configurations, build task plan around them.
• Probabilistically complete.

• Optimization-Based: Formulate TAMP as optimization problem.
• Find plan minimizing cost (time, energy, etc.).

TAMP Algorithms

• FFRob: Fast-Forward planner extended with geometric reasoning.
• aSyMov: Asymptotically optimal TAMP.
• PDDLStream: Extends PDDL with streams for continuous sampling.
• TMKit: Task-Motion Kit for TAMP.

Example: Block Stacking with TAMP

Goal: Stack blocks A, B, C (A on B on C)

Task Plan:
1. pick(A)
2. place(A, B)
3. pick(C)
4. place(C, table)
5. pick(B)
6. place(B, C)
7. pick(A)
8. place(A, B)

Motion Planning for each action:
- pick(A):
  - Check: Is A graspable from current robot pose?
  - If not: Navigate to better position
  - Compute grasp pose for A
  - Plan collision-free arm motion to grasp
  - Verify grasp stability

- place(A, B):
  - Compute placement pose on top of B
  - Check: Is placement stable?
  - Check: Does placement collide with other objects?
  - Plan collision-free arm motion to placement
  - Verify placement success

If any motion planning fails:
  - Backtrack in task plan
  - Try alternative task sequence

Geometric Feasibility Constraints

• Reachability: Can robot reach object from current position?
• Collision-Free: Are motions collision-free?
• Stability: Are object placements stable?
• Grasp Quality: Can robot grasp object securely?
• Kinematic Constraints: Does robot have sufficient degrees of freedom?

Applications

• Manipulation: Pick-and-place, assembly, packing.
• Mobile Manipulation: Robots that navigate and manipulate.
• Warehouse Automation: Picking items, organizing shelves.
• Household Robots: Cleaning, cooking, organizing.
• Manufacturing: Assembly lines, flexible manufacturing.

Challenges

• Computational Complexity: Combining discrete and continuous reasoning is hard.
• Scalability: Large state spaces (both symbolic and geometric).
• Uncertainty: Real-world geometry is uncertain — sensor noise, object pose errors.
• Dynamic Environments: Objects and obstacles may move during execution.

TAMP with Learning

• Learning Motion Primitives: Learn common motion patterns from data.
• Learning Heuristics: Learn which task plans are likely to be feasible.
• Learning from Failures: Improve planning from execution failures.
• LLM Integration: Use LLMs for high-level task understanding and decomposition.

Example: LLM + TAMP

User: "Organize the kitchen"

LLM generates high-level plan:
1. Put dishes in dishwasher
2. Put food in refrigerator
3. Wipe counters
4. Arrange utensils in drawer

TAMP system:
- For each high-level task, generates detailed task-motion plan
- "Put dishes in dishwasher":
  - Identify dishes on counter
  - For each dish:
    - Navigate to dish
    - Pick up dish
    - Navigate to dishwasher
    - Open dishwasher door
    - Place dish in rack
  - Close dishwasher door
- Ensures all motions are geometrically feasible

Benefits

• Feasibility: Ensures task plans are geometrically executable.
• Completeness: Finds solutions that pure task or motion planning alone would miss.
• Realism: Handles real-world geometric constraints.
• Versatility: Applicable to diverse manipulation and navigation tasks.

Limitations

• Computational Cost: Expensive to compute — combines two hard problems.
• Scalability: Difficult for long-horizon tasks or complex environments.
• Uncertainty: Assumes accurate geometric models — real world is messier.

TAMP is essential for practical robot planning — it bridges the gap between high-level task reasoning and low-level motion execution, enabling robots to perform complex manipulation tasks in realistic environments where geometric constraints matter.