Kinodynamic Planning and Control
of Closed-chain Robotic Systems

The kinodynamic planning problem remains as one of the most challenging open problems in robotics. The problem entails finding feasible trajectories connecting two given states of a robot, each defined by a configuration and a velocity of the underlying mechanical structure. To ensure feasibility, the trajectory should fulfill all kinematic constraints of the system (like loop-closure constraints or velocity limits), be compliant with the robot’s equation of motion, avoid the collisions with obstacles, and be controllable with the limited force of the actuators.

Existing approaches to solve the planning problem, however, are hard to apply to systems with closed-kinematic chains, like parallel robots, collaborative arms manipulating an object, or legged robots keeping their feet in contact with the environment. The state space of such systems is an implicitly- defined manifold, which complicates the design of a motion planner able to explore the manifold efficiently. Moreover, if the dynamic model of the robot is not properly handled, the obtained trajectories may deviate substantially from the manifold, leading to unrealistic trajectories, or to a failure to reach the goal. Even if a trajectory is kept on the manifold, the design of a robust controller able track the trajectory is also problematic. Closed kinematic chains exhibit so-called forward singularities, which make traditional computed-torque controllers fail in their vicinity, producing large control efforts that can even harm the robot’s structure. It is probably for the previous reasons that, to date, mature algorithms for kinodynamic planning and control have not been developed for closed kinematic chains. Our purpose in this work is to help filling this gap to the largest possible extent.

Supplementary Material

Thesis document: [pdf]

Chapter 2: Closed-chain Systems

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Chapter 3: Trajectory Planning

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Chapter 4: Trajectory Optimization

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Chapter 5: Trajectory Tracking

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