Whole-body motion planning with centroidal dynamics and full kinematics

Abstract

Abstract-To plan dynamic, whole-body motions for robots, one conventionally faces the choice between a complex, fullbody dynamic model containing every link and actuator of the robot, or a highly simplified model of the robot as a point mass. In this paper we explore a powerful middle ground between these extremes. We exploit the fact that while the full dynamics of humanoid robots are complicated, their centroidal dynamics (the evolution of the angular momentum and the center of mass (COM) position) are much simpler. By treating the dynamics of the robot in centroidal form and directly optimizing the joint trajectories for the actuated degrees of freedom, we arrive at a method that enjoys simpler dynamics, while still having the expressiveness required to handle kinematic constraints such as collision avoidance or reaching to a target. We further require that the robot's COM and angular momentum as computed from the joint trajectories match those given by the centroidal dynamics. This ensures that the dynamics considered by our optimization are equivalent to the full dynamics of the robot, provided that the robot's actuators can supply sufficient torque. We demonstrate that this algorithm is capable of generating highly-dynamic motion plans with examples of a humanoid robot negotiating obstacle course elements and gait optimization for a quadrupedal robot. Additionally, we show that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance.

Trajectory and foothold optimization using low-dimensional models for rough terrain locomotion

“…Note that when the cart-table is falling down, the CoM trajectory increases exponentially in (2). This effect arises from the fact that we decouple the horizontal and vertical dynamics, hence adding this soft-constraint guarantees the validity of the model.…”

Hybrid direct collocation and control in the constraint-consistent subspace for dynamic legged robot locomotion

“…Posa et al [7] apply direct transcription and an implicit hard contact model to a locomotion problem using the contact forces as decision variables. Similarly, Dai et al [9] used direct transcription over a reduced model of the dynamics together with kinematic constraints. Xi and Remy [20] applied direct collocation in a planar model using soft contact models.…”

“…With this motivation, many approaches based on Trajectory Optimization (TO) have been proposed [6], [7], [8], [9], [10], [11], [12] demonstrating that optimization is a valid framework to derive motion plans that are not driven by quasi-static stability criteria. However, legged robots are floating-base, high dimensional systems, underactuated and permanently influenced by contact forces.…”

An Adaptive Feedforward Control Method for Under-Actuated Bipedal Walking on the Compliant Ground

“…During a SSP, the desired trajectories of actuated joints are expressed as (6) and generated online at the beginning of this phase. In the first cycle, the initial and final state for the desired trajectories generation is assigned with [q i ,q i ] and [q f ,q f ] , respectively.…”

“…Because of the high manoeuvrability and low cost of system resource, underactuated bipedal walking robot has been studied prevalently [2], [3]. Some famous bipedal robots, such as RABBIT [4], ATRIAS [5], ATLAS [6], MA-BEL [7], and AMBER [8] hand, in virtue of high adaptability and acceptability in human society, the potential application of humanoid robot is universal, ranging from housework to disaster relief [9]. As the result, the rigid robot-ground contact model would be not applicable for all road surface materials, especially when the robot is carrying heavy equipment and marching at a quick pace [10], [11].…”