Organizations: Department of Biomedical Engineering, National University of Singapore, Singapore 117583 · Peng Cheng Laboratory, Shenzhen 518057, China · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
This paper proposes a task-oriented model predictive control (ToMPC) framework for safe and efficient robotic manipulation in open workspaces. The framework unifies collision-free motion and robot-environment interaction to address diverse scenarios. Additionally, it introduces task-oriented obstacle avoidance that leverages kinematic redundancy to enhance manipulation efficiency in obstructed environments. This complex optimization problem is solved by the alternating direction method of multipliers (ADMM), which decomposes the problem into two subproblems tackled by differential dynamic programming (DDP) and quadratic programming (QP), respectively. The effectiveness of this approach is validated in simulation and hardware experiments on a Franka Panda robotic manipulator. Results demonstrate that the framework can plan motion and/or force trajectories in real time, maximize the manipulation range while avoiding obstacles, and strictly adhere to safety-related hard constraints.
Figures & tables
Fig. 1: A schematic diagram depicting the the proposed ToMPC planner, where the ADMM solves the optimization problem in a distributed fashion.
Fig. 2: Illustration of interaction model (left) and task-oriented avoidance (right).
Fig. 3: Scenario # 1: Simulation of the robot performing obstacle avoidance with various shapes and quantities of surrounding objects.
Fig. 4: Simulation results for Scenario #1. Top: Minimum distances to the obstacle (Fig. 3 Left ). The FDDP and ADMM methods are compared under different parameter settings. Bottom: Cartesian trajectories for all six test cases.
Method
σ or ρ
T
Min Dist (m)
Max Time (s)
Avg Time (s)
FDDP [ 6 ]
2
10
0.0014
0.0275
0.0091
3
10
0.0060
0.0246
0.0093
10
10
0.0151
0.0288
0.0108
ADMM (ours)
2
10
0.0229
0.0013
0.0009
2
30
0.0205
0.0037
0.0025
2
50
0.0205
0.0059
0.0043
TABLE I: Minimum Distance and Computation Time in Scenario #1
Fig. 5: Scenario #2: The robot manipulates a red block while avoiding a ball obstacle. The two diagrams are experimental snapshots of conventional avoidance (oaMPC) and task-oriented avoidance (ToMPC), respectively.
Fig. 6: Experimental results for Scenario #2. Top: Cartesian trajectory in the X-Y plane. Middle: Norm of Cartesian trajectory errors. Bottom: Minimum distance to the ball obstacle.
Fig. 7: Joint torque of the ToMPC in Scenario #2. Top: MPC torque τmpc , final desired torque τdes , and measured torque τ for the second joint. Bottom: Percentage of the feedforward torque in the total command.
Fig. 8: Scenario #3: Evaluation of environment interaction. Left: Experimental setup. Right: Sensor frame and contact frame relationship. Notably, the F/T sensor is solely used for evaluation, without being involved in feedback control.
Fig. 9: Force measurement results for Scenario #3. The diagrams from top to bottom correspond to the frequencies w=0.4,0.8,1.5 , respectively. The left grey-shaded area is magnified in the right diagram.
Fig. 10: Scenario #4: The robot wipes a whiteboard with a contact force of 8 N. Top: Experimental snapshots of the oaMPC and the ToMPC methods. Bottom: Rainbow plots illustrating the Cartesian trajectory and measured contact force.
Method
Position Error Norm
Force Error Norm
Mean (m)
RMS (m)
Mean (N)
RMS (N)
oaMPC
0.0303
0.0355
1.0505
1.2425
ToMPC
0.0201
0.0236
2.0335
2.3020
TABLE II: Comparison of Position and Force Errors in Scenario #4